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Proceedings  of  the 
International  Symposium  on 
Seawater  Drag  Reduction 


22-23  July  1998 
Newport,  Rhode  Island 


DISTRIBUTION  STATEMENT  A 

Approved  for  Public  Release 
Distribution  Unlimited 


JJSWC 

Naval  Surface  Warfare  Center 

CARDEROCK  DIVISION 


i^qcj-ocf  odd 

X/ 


FOREWORD 


The  International  Symposium  on  Seawater  Drag  Reduction  (ISSDR),  held  in 
Newport,  RI,  on  22-23  July  1998,  focused  on  drag  reduction  methods  applicable  primar¬ 
ily  in  the  seawater  environment.  The  symposium  was  jointly  sponsored  by  the  Office  of 
Naval  Research  (including  ONR’s  European  Office),  the  Naval  Sea  Systems  Command, 
the  Defense  Advanced  Research  Projects  Agency,  the  Naval  Surface  Warfare  Center — 
Carderock  Division,  the  American  Society  of  Mechanical  Engineers  and  the  Naval  Under¬ 
sea  Warfare  Center — Newport  Division. 

The  call  for  ISSDR  papers  resulted  in  an  overwhelming  response  from  around  the 
world.  Accepted  papers  represent  authors  from  1 1  different  countries  and  include  contri¬ 
butions  from  the  government  sector,  private  industry,  and  academia.  The  resulting  pro¬ 
ceedings  volume  offers  a  comprehensive  collection  of  the  latest  thinking  on  seawater  drag 
reduction  from  leaders  of  the  international  drag  reduction  community.  Papers  are  grouped 
in  this  volume  in  the  following  categories: 

•  drag  reduction  -  historical  overview 

•  wall  turbulence  physics 

•  drag  reduction  physics 

•  seawater  physics 

•  turbulent  drag  reduction  methods — including  compliant  coating,  spanwise 
fluid  motion  and  wall  motion,  polymer,  microbubble,  electromagnetic, 
and  biology  based  methods 

One  of  the  fundamental  advances  in  the  study  of  turbulence  over  the  last  five 
decades  has  been  the  discovery  that  turbulence  production  and  self-sustainment  in  a 
boundary  layer  are  organized  phenomena  and  not  entirely  random  processes.  A  principal 
objective  of  this  symposium  and  proceedings  was  to  promote  a  closer  coupling  of  these 
wall  turbulence  physics  fundamentals  to  drag  reduction  methodologies,  while  also  seek¬ 
ing  to  increase  awareness  of  the  challenges  unique  to  seawater  drag  reduction,  and 
encouraging  wider  and  more  extensive  discussion  in  the  drag  reduction  community  of  the 
potential  applicability  to  seawater  vehicles. 


ACKNOWLEDGMENTS 

A  sincere  thank  you  goes  to  the  members  of  the  Steering,  Executive,  and  Techni¬ 
cal  Committees;  the  session  chairpersons;  the  staff  of  the  Surface  Warfare  Officers 
School;  and  the  administrative  team  at  Systems  Resource  Management,  Inc.  Their  hard 
work  and  dedication  ensured  that  both  the  symposium  and  proceedings  reflected  the  high¬ 
est  standards  of  professionalism  and  intellectual  achievement  in  the  field  of  drag  reduc¬ 
tion.  The  names  and  organizations  of  these  distinguished  professionals  follow. 


Dr.  James  C.  S.  Meng 
Symposium  Chairperson 


iii 


STEERING  COMMITTEE 


Dr.  John  Sirmalis,  Naval  Undersea  Warfare  Center 

RADM  Michael  Coyle,  Naval  Sea  Systems  Command 

Mr.  Robert  Draim,  Naval  Sea  Systems  Command 

Mr.  Timothy  Douglass,  Program  Executive  Office ,  Undersea  Warfare 

RADM  Charles  Young,  Naval  Sea  Systems  Command 

Dr.  Spyridon  Lekoudis,  Office  of  Naval  Research 

Dr.  Theo  Kooij,  Defense  Advanced  Research  Projects  Agency 

CAPT  Brian  Wegner,  Naval  Sea  Systems  Command 

Mr.  Art  Spero,  Naval  Sea  Systems  Command 

Mr.  James  Thompson,  Program  Executive  Office ,  Undersea  Warfare 

Dr.  Richard  Vogelsong,  Office  of  Naval  Research 


EXECUTIVE  COMMITTEE 

Mr.  Dennis  Bushnell,  National  Aeronautics  and  Space  Administration  -  Langley 

Mr.  James  Fein,  Office  of  Naval  Research 

Dr.  Louis  Goodman,  Office  of  Naval  Research 

Dr.  Thomas  Huang,  Naval  Surface  Warfare  Center,  Carderock  Division 

Mr.  Gary  Jones,  Defense  Advanced  Research  Projects  Agency 

Dr.  James  McMichael,  Defense  Advanced  Research  Projects  Agency 

Dr.  Richard  Nadolink,  Naval  Undersea  Warfare  Center,  Division  Newport 

CDR  Steven  Petri,  Naval  Sea  Systems  Command 

Dr.  Patrick  Purtell,  Office  of  Naval  Research 

Dr.  Edwin  Rood,  Office  of  Naval  Research 


TECHNICAL  COMMITTEE 

Dr.  Rudolph  Bannasch,  Technische  Universitat  Berlin,  Germany 

Dr.  Dietrich  Bechert,  Technische  Universitat  Berlin,  Germany 

Prof.  Herman  Branover,  Ben  Gurion  University,  Israel 

Dr.  Kwing-So  Choi,  University  of  Nottingham,  UK 

Dr.  Steven  Deutsch,  Applied  Research  Lab  /Penn  State  University,  USA 

Dr.  Robert  Mons,  Northrop  Grumman,  USA 

Dr.  Mark  Savill,  University  of  Cambridge,  UK 

Dr.  Promode  Bandyopadhyay,  Naval  Undersea  Warfare  Center,  Division  Newport,  USA 

Dr.  Peter  Hendricks,  Naval  Undersea  Warfare  Center,  Division  Newport,  USA 

Dr.  Stephen  Huyer,  Naval  Undersea  Warfare  Center,  Division  Newport,  USA 

Dr.  William  Keith,  Naval  Undersea  Warfare  Center,  Division  Newport,  USA 

Mr.  Richard  Philips,  Naval  Undersea  Warfare  Center,  Division  Newport,  USA 

Dr.  Howard  Schloemer,  Naval  Undersea  Warfare  Center,  Division  Newport,  USA 


TABLE  OF  CONTENTS 


DRAG  REDUCTION  -  HISTORICAL  OVERVIEW 

Polymer  Solution  Effects  on  Turbulent  Friction  Mechanisms  1 

J. W.  Hoyt  -  San  Diego  State  University 

Drag  Reduction  “Designer  Fluid  Mechanics”  -  Aeronautical  Status  and  7 

Associated  Hydrodynamic  Possibilities  (an  “embarrassment  of 
technical  riches”) 

D.  Bushnell  -  NASA  -  Langley  Research  Center 

European  Drag  Reduction  Research  -  Recent  Developments  and  13 

Current  Status 

K. S.  Choi  -  The  University  of  Nottingham 

Drag  Reduction  Research  in  Japan  19 

K.  Watanabe  -  Tokyo  Metropolitan  University 

WALL  TURBULENCE  PHYSICS 


Near  Wall  Turbulence:  A  Remembrance  of  Steve  Kline  29 

B.  Cantwell  -  Stanford  University 

Vortex  Packets  and  the  Structure  of  Wall  Turbulence  33 

R.  Adrian,  S.  Balachandar  -  University  of  Illinois  at  Urhana-Champaign 

Vortex  Development  and  Interactions  in  Turbulent  Boundary  Layers:  39 

Implications  for  Surface  Drag  Reduction 

C.  Smith  -  Lehigh  University 

Coherent  Structures,  Self-Sustaining  Process  and  Bifurcations  in  Shear  Flows  47 

F.  Waleffe  -  University  of  Wisconsin-Madison 

Detection  of  Transition  and  Flow  Bifurcation  Regions  on  A  Hydrofoil  53 


Using  Hot-Film  Constant  Voltage  Anemometry 

S.  Mangalam,  G.  Sarnia,  R.  Pfouts,  T.  Kwa  -  Tao  Systems,  Inc.,  J.  Casper, 

M.  Wallace,  H.  Moghadam  -  Newport  News  Shipbuilding,  R.  Nigon  - 
Naval  Surface  Warfare  Center,  Carderock  Division 

Measured  Wall  Pressure  Signatures  of  Turbulence  Producing  63 

Structures 

S.  Russell  -  Naval  Surface  Warfare  Center,  Carderock  Division 

Streamfunction  -  Vorticity  Calculations  of  Navier-Stokes  Equations  As  73 

A  Tool  For  High  Accuracy  Study  of  Pressure  -  Tension  Relation 

M.  Zakharenkov  -  Central  Aero-Hydrodynamic  Institute 

Frequency-Wavenumber  Spectral  Measurement  of  Turbulent  Boundary  83 

Layer  Wall  Pressure 

M.  Pognant  -  MS  L.A.I.A.T.  -  Universite  de  Toulon,  G.  Giovannelli, 

B.  Forestier  -  I.R.P.H.E.,  France 

High  Reynolds  Number  Turbulent  Flows  89 

A.  Smits  -  Princeton  University,  M.  Zagarola  -  Creare,  Inc. 


vii 


DRAG  REDUCTION  PHYSICS 


The  Lamb  Vector  and  Its  Divergence  in  Turbulent  Drag  Reduction 

C.  Crawford,  H.  Marmanis,  G.  Kamiadakis  -  Brown  University 

Role  of  Helicity  and  Chirality  in  Drag  Reduction  in  Turbulent  Flows 

S.  Moiseev,  0.  Chkhetiana  -  Space  Research  Institute,  Moscow, 

H.  Branover,  A.  Eidelman,  E.  Golbraikh  -  Ben-Gurion  University 

Methods  of  Influence  on  Coherent  Vortical  Structures  of  A  Boundary  Layer 

V.  Babenko  -  National  Academy  of  Sciences,  Kiev 

Drag  Reduction  with  Submerged  Ribs  and  its  Mechanism  in  A 
Turbulent  Boundary  Layer  Over  D-Type  Roughness 

S.  Mochizuki,  H.  Osaka  -  Yamaguchi  University 

A  New  Approach  to  Drag  Reduction 

A.  Cotel  -  University  of  Manitoba,  R.  Breidenthal  -  University  of 
Washington 

Direct  Numerical  Simulations  of  Drag  Modifications  Using  Randomized 
Force  Fields 

R.  Dahlburg,  W.  Sandberg,  R.  Handler  -  Naval  Research  Laboratory, 

L.  Sirovich  -  Brown  University 

Adaptive  Feed-Forward  Control  of  Turbulent  Boundary  Layers 

K.  Breuer,  R.  Rathnas ingham,  K.  Amonlirdviman  -  Massachusetts  Institute 
of  Technology 

Flow  Management  Using  Inherent  Transition  and  Receptivity  Features 

N.  Yurchenko  -  National  Academy  of  Sciences,  Kiev,  R.  Rivir  -  Wright- 
Patterson  Air  Force  Base 

SEAWATER  PHYSICS 

In-Situ  Estimation  of  the  Abundance  and  Sizes  of  Particulates  in  the  Sea 

D.  Holliday  -  Tracor  Aerospace 

Biofouling  Control:  A  Critical  Component  of  Drag  Reduction 

G.  Swain  -  Florida  Institute  of  Technology 

Environmental  Factors  For  Ocean  Bubbles 

J.Hanson  -  The  Johns  Hopkins  University/Applied  Physics  Laboratory 

A  Boat-Mounted  Foil  to  Measure  the  Drag  Properties  of  Antifouling 
Coatings  Applied  to  Static  Immersion  Panels 

B.  Kovach,  G.  Swain  -  Florida  Institute  of  Technology 

The  Effect  of  Biofilms  on  Turbulent  Boundary  Layer  Structure 

M.  Schultz,  G.  Swain  -  Florida  Institute  of  Technology 

TURBULENT  DRAG  REDUCTION  METHODS:  COMPLIANT 
COATINGS 

Recent  Advances  in  the  Use  of  Compliant  Walls  for  Drag  Reduction 

P.  Carpenter  -  University  of  Warwick,  U.K 


viii 


99 

109 

113 

121 

127 

131 


189 


Recent  Developments  in  Interference  Analysis  of  Compliant  Boundary 
Action  on  Near-Wall  Turbulence 

B.  Semenov,  A.  Semenova  -  Siberian  Branch  of  Russian  Academy  of 
Sciences 

Compliant  Coatings:  The  Simpler  Alternative  197 

M.  Gad-el-Hak  -  University  of  Notre  Dame 

Drag  Reduction  of  the  Ocean  Surface  by  the  Surface  Waves  205 

A.  Benilov  -  Stevens  Institute  of  Technology 

Blubber  and  Compliant  Coatings  for  Drag  Reduction  in  Fluids:  211 

V.  Driving  Point  Shear  Impedance  Measurements  on  Compliant 
Surfaces 

E.  Fitzgerald  -  Johns  Hopkins  University,  J.  Fitzgerald  -  Kildare 
Corporation 

Blubber  and  Compliant  Coatings  for  Drag  Reduction  in  Fluids:  215 

VI.  Rotating  Disc  Apparatus  for  Drag  Measurement  on  Compliant 
Layers 

J.  Fitzgerald,  J.  Martin,  E.  Modert  -  Kildare  Corporation 

Interface  Waves  on  A  Compliant  Coating  Bounded  by  A  Fluid  Flow  219 

and  Their  Excitation  by  Acoustic  Resonance 

H.  Uberall  -  Catholic  University  of  America,  W.  Madigosky  -  A&T,  Inc. 

Analysis  of  Evolution  of  Disturbances  in  Channel  Flow  Over  A  Wavy  225 

Wall 

D.  Riahi  -  University  of  Illinois  at  Urbana-Champaign 

TURBULENT  DRAG  REDUCTION  METHODS:  SPANWISE  FLUID 
MOTION  &  WALL  MOTION 


The  Mechanism  of  Turbulent  Drag  Reduction  with  Wall  Oscillation  229 

K. S.  Choi,  B.  Clayton  -  University  of  Nottingham,  U.K 

On  the  Physics  of  Skin  Friction  Reduction  Through  Wall  Oscillation  237 

M.  Dhanak,  C.  Si  -  Florida  Atlantic  University 

Local  Oscillating  Blowing  in  A  Turbulent  Boundary  Layer  241 

S.  Tardu  -  Laboratoire  des  Ecoulements  Geophysiques  et  Indus triels 

Drag  Reduction  Through  the  Near  Wall  Vortex  System  Management  249 

Y.  Savchenko  -  Institute  of  Hydromechanics  of  Ukrainian  National 
Academy  of  Sciences 

Boundary  Layer  Control  at  Wave-Like  Swimming  257 

L.  Koryenna  -  Institute  of  Hydromechanics  of  Ukrainian  National 
Academy  of  Sciences 

Substitution  of  Rolling  for  Slipping  as  an  Effective  Mechanism  of  263 

Decreasing  Hydrodynamic  Drag 

V.  Merkulov  -  Siberian  Branch  of  the  Russian  Academy  of  Sciences 


TURBULENT  DRAG  REDUCTION  METHODS:  POLYMER 

The  Combination  of  Polymer,  Compliant  Wall,  and  Microbubble  Drag  269 

Reduction  Schemes 

B.  Semonov  -  Siberian  Branch  of  the  Russian  Acadeny  of  Sciences 


IX 


277 


Similarities  and  Differences  in  Drag  Reduction  Behavior  of  High 
Polymer  and  Surfactant  Solutions 

J.  Zakin,  Z.  Lin  -  The  Ohio  State  University,  J.  Myska  -  Czech  Academy  of 
Sciences 

Drag  Reducing  Additive  for  Recirculating  Hydronic  Systems:  Full- 
Scale  System  Engineering  Analysis  and  Field  Test 

K.  Gasljevic,  K.  Hoyer,  E.  Matthys  -  University  of  California ,  Santa 
Barbara 

Practical  Applications  of  Dilute  Polymer  Additives  for  Water  Craft 

T.  Kowalski  -  University  of  Rhode  Island 

Experimental  Research  of  the  Influence  of  Conditions  of  Polymer 
Admission  to  the  Boundary  Layer  on  A  Drop  of  Turbulent  Friction 

V.  Pogrebnyak  -  Ecological  Center  of  Scientific  and  Applied  Researches, 
Y.  Ivanyuta  -  A.N.  Krylov  Central  Research  Institute 

Drag  Reduction  Dynamics 

V.  Kulik  -  Russian  Academy  of  Sciences 

On  the  Hydrodynamical  Smoothness  in  Polymer  Solutions 

W.  Amfilokhiev,  K.  Mazaev  -  Saint-Petersburg  State  Marine  Technical 
University 

TURBULENT  DRAG  REDUCTION  METHODS:  MICROBUBBLE 

Experimental  Evidence  for  a  Link  Between  Microbubble  Drag 
Reduction  Phenomena  and  Periodically  Excited  Wall-Bounded 
Turbulent  Flow 

M.  Guin  -  The  Johns  Hopkins  University,  H.  Kato  -  The  University  of 
Tokyo,  Y.  Takahashi  -  IHI  Ltd. 

Role  of  Bubble  Injection  Technique  Drag  Reduction 

R.  LaTorre  -  University  of  New  Orleans,  V.  Babenko  -  National  Academy 
of  Sciences,  Kiev 

Optimization  of  the  Distributed  Gas  Injection  into  A  Turbulent 
Boundary  Layer  for  the  Drag  Reduction 

V.  Bogdevich,  L.  Maltzev,  A.  Maluga  -  Siberian  Branch  of  the  Russian 
Academy  of  Sciences 

Effect  of  Microbubble  Distribution  on  Skin  Friction  Reduction 

Y.  Kodama  -  Ship  Research  Institute,  Tokyo 

Combined  Polymer  and  Microbubble  Drag  Reduction 

R.  Philips,  J  Castano,  J.  Stace  -  Naval  Undersea  Warfare  Center  Division 
Newport 

Microbubble  Formation  and  Splitting  in  a  Turbulent  Boundary  Layer 
for  Turbulence  Reduction 

J.  Meng,  J.  Uhlman  -  Naval  Undersea  Warfare  Center  Division  Newport 

TURBULENT  DRAG  REDUCTION  METHODS:  ELECTROMAGNETIC 
DRAG  REDUCTION 

Engineering  Insight  of  Near-Wall  Microturbulence  for  Drag  Reduction 
and  Derivation  of  a  Design  Map  for  Seawater  Electromagnetic 
Turbulence  Control 

J.  Meng  -  Naval  Undersea  Warfare  Center  Division  Newport 


281 

289 

295 

299 

305 

313 

319 

327 

331 

335 

341 


359 


x 


Experiments  on  Turbulent  Channel  Flow  with  Electromagnetic 

Turbulence  Control 

X.  Fan,  G.  Brown  -  Princeton  University 

369 

Drag  Reduction  Experiments  on  a  Small  Axisymmetric  Body  in 

Saltwater  Using  Electromagnetic  Microtiles 

P.  Bandyopadhyay,  J.  Castano,  D.  Thivierge,  W.  Nedderman  -  Naval 

Undersea  Warfare  Center  Division  Newport 

373 

MHD  Turbulence  Experiments,  Drag  Reduction  and  Application  to 

Non-MHD  Flow 

A.  Eidelman,  H.  Branover,  E.  Golbraikh,  -  Ben  Gurion  University , 

S.  Moiseev  -  Space  Research  Institute ,  Moscow 

379 

Drag  Reduction  by  Electro-Magnetic  Forces 

V.  Merkulov  -  Siberian  Branch  of  the  Russian  Academy  of  Sciences 

385 

Electromagnetic  Effects  on  Low  Speed  Coherent  Structures  Embedded 
in  A  Wall  Layer 

J.P.  Thibault,  V.  Botton,  L.  Rossi  -  PAMIR  Team,  LEGI,  France 

389 

Some  Results  on  Electromagnetic  Control  of  Flow  Around  Bodies 

T.  Weier,  G.  Gerbeth,  G.  Mutschke,  U.  Fey  -  MHD  Dept., 

Forschungszentrum  Rossendorf  0.  Posdziech  -  Inst.  Aerospace  Eng.,  TU 

Dresden,  0.  Lielausis,  E.  Platacis  -  Institute  of  Physics  Riga ,  Latvia 

395 

Analysis  and  Finite  Element  Simulation  of  MHD  Flows,  with  an 

Application  to  Seawater  Drag  Reduction 

A.  Meir,  P.  Schmidt  -  Auburn  University 

401 

Lorentz  Force  Modeling  in  EMHD  Turbulence  Control:  DNS  Studies 

Y.  Du,  C.  Crawford,  G.  Kamiadakis  -  Brown  University 

407 

Fundamental  Studies  on  Active  Control  of  Large  Scale  Coherent 

Structures  in  Channel  Turbulence 

P.  O’Sullivan,  S.  Biringen  -  University  of  Colorado  at  Boulder 

413 

Interactive  Electro-Magnetohydrodynamic  Control  of  Near-Wall 

Streaks 

S .  Snarski  -  Kohler,  WI 

419 

TURBULENT  DRAG  REDUCTION  METHODS:  BIOLOGY  BASED 

DRAG  REDUCTION 

Dolphin  Drag  Reduction:  Myth  or  Magic 

J.  Fein  -  Office  of  Naval  Research 

429 

Hydrodynamics  of  Wave-Like  Curvature  on  Bodies  of  Swimming 

Animals 

R.  Bannasch  -  Technische  Universitat  Berlin 

435 

Imaginative  Solutions  by  Marine  Organisms  for  Drag  Reduction 

F.  Fish  -  West  Chester  University 

443 

On  Biological  Foundations  of  Dolphin’s  Control  of  Hydrodynamic 

Resistance  Reduction 

V.  Babenko,  A.  Yaremchuk  -  National  Academy  of  Sciences,  Kiev 

451 

Hydrobionics  Principles  of  Drag  Reduction 

V.  Babenko  -  National  Academy  of  Sciences,  Kiev 


453 


457 


Phased  Vortex  Seeding  for  Thrust  Modulation  in  a  Rigid  Cylinder  with 
Flapping  Foil  Thrusters 

P.  Bandyopadhyay,  J.  Castano,  W.  Nedderman,  D.  Thivierge  -  Naval 
Undersea  Warfare  Center  Division  Newport 

Drag  Reduction  and  Turbulence  Control  in  Swimming  Fish-Like  Bodies 

M.  Wolfgang,  S.  Tolkoff,  A.  Techet,  D.  Barrett,  M.  Triantafyllou,  D.  Yue, 
F.  Hover  -  Massachusetts  Institute  of  Technology,  M.  Grosenbaugh,  W. 
McGillis  -  Woods  Hole  Oceanographic  Institution 

Flow  Separation  Control  By  Means  of  Flapping  Foils 

M.  Platzer  -  U.S.  Naval  Postgraduate  School,  J.  Lai  -  Australian  Defence 
Force  Academy,  C.  Dohring  -  German  Armed  Forces  University 

The  Vorticity  Control  Unmanned  Undersea  Vehicle  -  A  Biologically 
Inspired  Autonomous  Vehicle 

J.  Anderson  -  Charles  Stark  Draper  Laboratory 

A  Fast-Starting  and  Maneuvering  Vehicle,  the  ROBOPIKE 

J.  Kumph,  M.  Triantafyllou  -  Massachusetts  Institute  of  Technology 


463 


471 

479 

485 


INDEX  BY  AUTHOR  NAME 


491 


Drag  Reduction  -  Historical 

Overview 


POLYMER  SOLUTION  EFFECTS  ON  TURBULENT  FRICTION  MECHANISMS 


J.W.  Hoyt 

Professor  Emeritus,  Mechanical  Engineering 
San  Diego  State  University 
San  Diego,  CA  92182-1323 

Abstract  -  In  discussing  the  prospects  for  reducing  the  turbulent-friction  drag,  it  seems  important  to  first  try  to  understand  where  the 
friction  arises.  Such  a  basic  and  fundamental  knowledge  is  still  elusive.  This  paper  is  intended  as  a  basis  for  discussion,  at  least,  of 
the  known  components  of  turbulent  friction  as  they  pertain  to  flat-plate  and  external  flows.  Experimental  results  illustrating  the  various 
components  of  turbulent  drag  are  drawn  from  the  literature,  together  with  some  new  data. 


L  INTRODUCTION 

The  question  of  “where  does  the  turbulent  drag  arise?”  is  one  of  the 
most  fundamental  problems  in  fluid  mechanics,  and  one  of  the  least 
understood.  Turbulence  has  attracted  the  attention  of  some  of  the 
world’s  greatest  scientists  over  the  last  hundred  years  or  so,  and  yet  our 
understanding  is  far  from  complete.  If  substantial  progress  is  to  be  made 
in  reducing  the  friction  on  vehicles  of  various  kinds,  deeper 
understanding  of  the  fundamentals  of  turbulent  flow  seems  essential. 

Nevertheless,  a  great  amount  of  information  is  available.  With  new 
experimental  and  computational  tools,  the  last  few  years  have  given 
much  greater  insight  into  the  details  of  turbulent  flow  over  plates  and 
surfaces.  The  new  information  has  occasioned  some  friendly 
controversy,  and  authorities  can  differ  strongly  on  basic  turbulent  flow 
mechanisms.  Some  of  these  differences  will  be  discussed  here. 

If  we  restrict  our  attention  to  smooth  plates,  contributors  to  the 
overall  resistance  or  drag  include: 

•  Fluid  viscosity 

•  Reynolds  stresses 

•  Coherent  structures 

Streaks 

Vortices 

•  Pressure  fluctuations 

Each  of  these  resistance  components  will  be  examined  to  show,  if 
possible,  avenues  of  approach  which  might  lead  to  significant  drag 
reduction. 


u  =  u  +  u'  v  =  v  +  v'  and  w  =  w  +  w' 


where  the  overbar  indicates  averaged  quantities. 

When  these  values  are  introduced  into  the  Navier-Stokes  equations, 
and  time  averaged  again,  additional  terms  of  the  form: 

-p[du'2/dx  +  du'v'/dy  +  du'w'/dz] 

(3) 

appear.  Among  the  new  time-averaged  quantities,  the  term  -pu'v'  is 
believed  to  be  of  major  importance,  and  having  the  units  of  a  stress,  is 
usually  called  the  Reynolds  stress.  (The  overbar  will  be  dropped  in  all 
further  discussion,  but  the  time-averaged  concept  still  applies.) 

In  order  to  contribute  to  the  resistance,  the  fluctuating  quantities 
themselves  must  be  on  average  negative.  Modem  instrumentation  can 
detect  quantities  such  as  uV,  and  show  that  in  fact  uV  is  strongly 
negative.  Figure  1  shows  measurements  of  uV,  where  flip  fluduating 
velocity  values  have  been  weighted  by  the  frequency  of  their  occurrence 
and  plotted  as  a  function  of  their  respective  signs.  The  strongly  negative 
quadrants  2  and  4  show  that  the  overall  sign  of  the  fluctuating  quantities 
is  negative. 


II.  FLUID  VISCOSITY 

The  shear  stress  appears  in  both  laminar  and  turbulent  flow  as: 

x  =  pdu/dy  (1) 

Obviously,  reducing  the  viscosity,  p,  would  reduce  the  friction.  For  a 
vehicle  operating  in  seawater,  the  viscosity  could  be  reduced  by  heating 
the  seawater  flowing  over  the  body,  or  by  introducing  a  second  fluid  of 
lower  viscosity  around  the  hull.  Experiments  using  air  exuded  around 
the  surface  show  a  reduction  in  overall  resistance  but  this  may  be  due  to 
other  interactions  as  will  be  described  below.  In  any  event,  the 
resistance  due  to  fluid  viscosity  becomes  insignificant  compared  to  other 
components  of  the  drag  as  the  Reynolds  number  is  increased  to  values 
typical  of  vehicle  applications. 

III.  REYNOLDS  STRESSES 

To  provide  insight  into  more  significant  el em aits  of  the  turbulent 
friction,  it  is  useful  to  write  the  x-direction  term  of  the  incompressible, 
steady,  Navier-Stokes  (or  momentum)  equation: 

p[u(du/dx)  +  v(du/3y)  +  w(du/dz)]  =  -dV/dx 
+  p[d2u/dx2  +  (?  u/dy2  +  d2u/3z2] 

(2) 

But  now  we  find  that  the  viscosity  term  (with  p)  is  inadequate  for 
turbulent  motion  and  resort  to  a  strategy  proposed  by  Osborne  Reynolds 
over  100  years  ago.  We  replace  the  velocity  quantities  by  a  mean  or 
average  value,  plus  a  fluctuating  velocity  whose  mean  is  zero,  but  whose 
square  or  product  is,  of  course,  not  zero.  Thus: 


SO' 
1.5 
0.0 
- 1.5 
-3.0 


\^y 


0 


Figure  1:  Fluctuating  velocities  uV,  weighted  by  how  frequently  they 
occur.  Turbulent  boundary  layer:  Re0  =  1070;  y+  =35.  (From  Ong  [1].) 

The  maximum  values  of  uV  occur  well  away  from  the  wall,  at  y+  = 
around  30,  where  y+  =  y  u*/v,  with  u*  the  friction  velocity  and  v  the 
kinematic  viscosity.  Figure  2  shows  how,  in  a  plot  of  shear  stress  as  a 
function  of  distance  from  the  wall  in  a  channel,  the  Reynolds  stress 
forms  most  of  the  total  stress,  other  stresses  including  the  viscous  stress 
(1)  presumably  contributing  the  remainder.  The  distribution  of  stresses 
found  in  a  channel  may  be  expected  in  the  turbulent  boundary  layer. 

In  the  momentum  equation  (3),  the  y  derivative  of  u V  forms  the 
resistance  component;  hence  changing  the  slope  of  the  Reynolds  stress 
term,  as  well  as  its  value,  offers  an  opportunity  for  substantial  drag 
reduction.  This  has  been  exploited  in  drag  reduction  by  polymer 
solutions  and  fiber  suspensions. 


1 


Figure  2.  Total  shear  stress  as  function  of  distance  from  wall  to  center 
of  water  channel,  with  u'v'  data  points.  (From  Willmarth  et  al.  [2].) 


Polymer  additives  seem  to  inhibit  both  u'  and  v'  and  decreases 
their  correlation,  as  can  be  seen  from  Figures  3-5.  The  astonishing  thing 
is  that  the  Reynolds  stress  can  be  reduced  almost  to  insignificance,  but 
the  drag  reduction,  (around  60%  in  this  experiment),  seems  nowhere 
near  as  large.  This  action  of  polymer  additives  (and  also  fiber 
suspensions  and  possibly  microbubbles  [3])  appears  to  be  a  result  of 
physically  disrupting  the  interaction  between  the  vertically-moving  and 
the  axially-moving  fluctuating  velocities.  Putting  it  more  scientifically, 
the  axial  to  transverse  velocities  become  decorrelated. 


lEL  M 

Dm 


PR  2850 

HjO 

a  R©  =  15  880  j  c«  50ppm 

■  Re  =  11  920 

o  Re  =12125  ;  e  =  109  ppm 

©Re  =  17  470 

0,03 

0, 


M 


. 


/■ 

a  ° 


o* 


*  °  c 

©O 


O4!  I  5  to  2  5  lb  2  5  *100  2 


S'' 

o  a 


5  KK 

y* 


Figure  3.  Fluctuating  axial  velocities  -  polymer  solution  flow  compared 
with  water.  (  From  Gampert  &  Delgado  [4].) 

s 

Um 

0.075 

0.05 

0.025 


PR  2  850 

a  Re* 13 030 > C=  50ppm 
o  R«s  10  730;  c  =  100 ppm 

h2o 

A  Re  b  12  960 

■  Re«  15690 

o 

° 

#4  A  A 
n  ■■ 

>  o  ° 

5  10  2  5  100  2  500 


y+ 


Figure  4.  Fluctuating  vertical  velocities  -  polymer  solution  flow 
compared  with  water.  (From  Gampert  &  Delgato  [4].) 


Figure  5.  Reynolds  stress  for  water  and  polymer  solutions,  plotted 
across  the  half-width  of  the  channel.  (From  Gampert  &  Delgado  [4] 

Results  similar  to  those  obtained  by  Gampert  &  Delgado  [4]  have 
also  been  obtained  by  Willmarth  et  al.  [2]  and  Bewersdorff  [5],  among 
others.  Hence  the  large  decrease  in  u'v'  in  polymer  solution  flow  must 
be  taken  as  a  fact.  The  resistance  or  drag  reduction  is  not  as  great  as  the 
decrease  in  the  fluctuating  u'v'  component  in  channel  flow. 

One  interpretation  of  this  result  would  be  to  recognize  that  the  u'v' 
fluctuations  are  not  created  spontaneously  (i.e.  of  their  own  accord)  but 
are  the  result  of  other,  larger-scale  motions  in  the  boundary  layer.  If  the 
fluctuating  velocities  are  suppressed,  these  larger  motions  are  still  there 
requiring  energy  to  drive  them.  Thus  the  coherent  structures  could 
easily  be  the  reason  that  drag  decrease  does  not  mirror  the  decrease  in 
fluctuating  velocities.  In  pipe  flow,  where  drag  reductions  approaching 
80%  have  been  measured  with  polymers,  coherent  structures  are  limited 
in  growth  by  the  pipe  size,  and  thus  may  contribute  less  to  the  resistance. 

Nevertheless,  spectacular  drag  reductions  have  been  achieved  on 
flat  plates  immersed  in  polymer  solutions.  Figure  6  shows  results  of  a 
test  by  Levy  and  Davis  [6]  on  a  1  m  long  plate,  where  more  than  60% 
drag  reduction  was  obtained  in  a  high-speed  towing  tank. 


Figure  6.  Drag  reduction  on  a  flat  plate  towed  in  15  ppm  poly(ethylene 
oxide).  (From  Levy  &  Davis  [6].) 

IV.  COHERENT  STRUCTURES  -  STREAKS 

The  flow  region  nearest  the  wall  is  dominated  by  structures  which, 
when  made  visible  with  dye,  appear  as  low-speed  axial  streaks, 
occurring  quite  densely  but  randomly  and  then  lifting  up  and  quickly 
disappearing.  The  sketch  below  is  widely  accepted  as  a  possible 
mechanism  for  the  production  of  the  streaks,  but  how  the  vortices  are 
formed,  and  whether  they  occur  before,  together  with,  or  after  the 
streaks  appear  is  a  topic  of  current  discussion.  The  spacing  between 


Z 


End  view 


2 


streaks  is  X+  =  Zu*/v  =  100  for  Newtonian  fluids,  but  in  polymer 
solutions,  X+  becomes  substantially  larger  (Donohue  et  al,  [7]).  The 
streaks  terminate  by  lifting  away  from  the  wall,  oscillating,  then 
“bursting”  (Klein  et  al  [8]).  The  burst  rate  is  reduced  in  polymer 
solutions  [7]  by  50%  or  more.  The  bursting  is  believed  to  be  a  major 
source  of  the  u'v'  fluctuating  velocities,  occurring  as  it  does  at  y+  =  30- 
35.  Following  the  burst,  “sweeps”  [8]  of  new,  higfrer-speed  fluid  enters 
the  region.  The  action  of  polymer  solutions  to  influence  the  streak 
spacing,  burst  rate,  and  fluctuating  velocities  appears  to  be  responsible 
for  their  powerful  drag-reducing  ability. 

Riblets  are  small  V-shaped  grooves  either  machined  or  applied  as  a 
plastic  sheet  coating,  with  the  grooves  extending  in  the  axial  flow 
direction.  The  riblets  appear  to  dampen  the  lateral  motion  and  spreading 
of  the  low-speed  streaks.  As  explained  in  the  excellent  review  article 
by  Walsh  [9],  drag  reductions  of  around  8%  seem  obtainable  if  the 
groove  size  is  properly  tailored  to  the  flow.  On  an  actual  torpedo-like 
test  vehicle,  drag  reductions  of  around  8%  were  found  when  suitable 
riblets  were  applied  [10].  Drag  reductions  of  the  same  magnitude  are 
also  found  in  riblet-lined  pipes. 

There  have  been  several  studies  of  the  combination  of  riblets  and 
polymer  solutions  in  pipes.  Anderson  et  al.  [11],  Koury  &  Virk  [12], 
and  later  Mizunuma  et  al[  13]  found  a  synergistic  effect  under  certain 
conditions.  Indeed,  based  on  their  experiments,  Koury  &  Virk  suggest 
that  riblets  and  polymers  reduce  drag  by  separate  mechanisms. 

V.  COHERENT  STRUCTURES  -  VORTICES 

Horseshoe  or  hairpin  shaped  vortices  were  originally  described  by 
Theodorsen  [14]  in  1952.  Only  recently  have  reliable  experimental 
methods  of  visualizing  these  structures  become  available.  From  these 
newer  studies  it  appears  that  the  turbulent  boundary  layer  is  dominated 
by  vortex-like  motions.  In  fact,  Zhou  et  al.  [15]  believe  that  the  low- 
speed  streaks  are  also  the  result  of  vortex  action,  as  shown  in  Figure  7. 
Similar  views  have  been  expressed  by  Smith  &  Walker  [16]. 


Figure  7.  Sketch  showing  proposed  action  of  hairpin  vortices  in 
forming  low-speed  streaks.  As  the  vortex  moves  in  the  x  direction, 
quadrant  2  u'v' events  take  place.  (From  Zhou  et  al  [1 5].) 

In  contrast  to  earlier  suggestions  in  the  literature  that  horseshoe 
vortices  were  rather  rare  in  the  boundary  layer,  Zhou  et  al  [15]  using 


particle-image-velocimetry  find  the  hairpin  vortex  to  be  the  most 
frequently  recurrent  pattern  in  the  boundary  layer.  Velocity  vector  plots 
show  the  vortices  can  extend  in  height  some  30%  above  the  top  of  the 
log  layer.  The  vortices  can  appear  singly  or  in  “packets”  of  two  or  more. 
Figure  8  gives  some  of  the  results  reported  by  Zhou  et  al  [15]. 


Re9  =  930  Su *  Uc  s  0.80  U_ 


Figure  8.  PIV  velocity  plot  showing  cross-section  through  a  series  of 
hairpin  vortices.  Velocities  corresponding  to  80%  of  the  free-stream 
velocity  have  been  subtracted  from  all  vectors.  (From  Zhou  et  al  [15].) 

There  appear  to  be  no  data  on  the  effect  of  polymers  on  the  hairpin 
vortices.  However,  in  the  course  of  experimental  proposals  to  use 
“heterogeneous”  drag  reduction  involving  discharge  of  threads  of 
concentrated  polymer  solution  into  flowing  water,  a  new  method  of 
visualizing  the  coherent  structures  was  discovered  (Hoyt  &  Sellin  [17]). 
The  technique  involves  discharging  a  tracer  consisting  of  a  mixture  of 
shear-thickening  surfactant,  high  extensional  viscosity  polymer,  and 
white  emulsion  paint  into  the  lower  region  of  the  boundary  layer. 
Vortices  and  other  coherent  structures  pick  up  the  tracer  and  transport  it 
downstream,  giving  a  visual  record  of  the  boundary-layer  activity.  This 
simple  technique  is  very  effective  in  bringing  out  details  of  the  vortex 
activity,  as  can  be  seen  in  Figure  9. 


subsidiary 


Figure  9.  Horseshoe  vortices  revealed  by  the  tracer  (From  Hoyt  & 
Sellin  [18]),  compared  with  a  computer  simulation  of  a  line  vortex  in  a 
shear  layer  by  Smith  et  al  [19].  Flow  is  left  to  right. 

Extensive  computer  processing  of  a  numerically  simulated 
turbulent  boundary  layer  has  also  revealed  similar  structures,  thus 
implying  that  they  somehow  evolve  as  a  solution  of  the  Navier-Stokes 
equations.  Chacin  et  al  [20]  show  a  side  view  of  some  of  these 
structures,  which  can  be  compared  with  video  frames  of  a  side  view  of 
the  tracer  in  the  boundary  layer  of  a  flat  plate  in  FigurelO. 


3 


Figure  10.  Computational  result  (above)  from  Chacin  et  al  [20] 
compared  with  video  frames  (taken  0.24  sec  apart)  of  tracer  activity. 
Both  show  side  views  of  large  structures.  Portions  of  the  bottom  scene 
(Hoyt  &  Sellin  [18])  resemble  the  computational  result.  The  actual 
height  of  the  structure  in  the  center  video  is  ~  0.021  m  (y+  ~  270). 

Control  of  these  large  structures  should  lead  to  significant  drag 
reduction.  Large-Eddy  Breakup  Devices  (LEBU’s)  have  been 
successful  in  reducing  the  skin  friction  immediately  behind  the  devices, 
but  unfortunately  create  a  drag  themselves  which  cancels  out  most  of 
any  benefit  thus  obtained.  The  excellent  review  of  Anders  [21]  shows, 
however,  that  skin  friction  reductions  approadiing  40%  could  be 
obtained,  thus  revealing  the  large  contribution  of  the  coherent 
structures  to  turbul ait  friction 

VI.  PRESSURE  FLUCTUATIONS 

It  is  a  familiar  occurrence  that  turbulent  flow  over  a  surface  creates 
audible  noise.  The  noise  is  caused  by,  or  related  to,  surface  pressure 
fluctuations.  Early  pressure  measurements  found  that  the  smaller  the 
pressure  transducer,  the  more  intense  the  signal,  thus  indicating  that  the 
source  was  small.  Further,  the  pressure  signals  seemed  to  be  correlated 
for  short  distances  downstream,  but  not  at  all  in  the  spanwise  direction. 
Thus  the  pressure  fluctuations  seem  to  be  connected  to  some  boundary- 
layer  event. 

Smith  &  Walker  [16]  suggest  that  the  pressure  disturbances  are 
caused  by  vortices  (the  spanwise  portion  of  hairpin  structures  closest  to 
the  surface),  which  induce  the  low-speed  streaks  to  abruptly  erupt. 
Barker  [22]  in  an  elegant  experiment,  also  suggested  that  eruption  of  the 
low-speed  streaks  provided  the  pressure-fluctuation  source.  Barker  also 


investigated  the  effect  of  polymers  on  the  pressure  fluctuations,  finding, 
as  shown  in  Figure  1 1,  a  significant  reduction  with  polymers  present. 


Figure  11.  Radiated  noise  reduction  observed  with  polymer  solution  on 
a  plate.  (From  Barker  [22].) 

Similar  noise  reduction  effects  of  polymers  in  turbulent  flow  have  been 
noted  by  Brady  [23]  and  others  using  rotating  cylinders 

VII.  SUMMARY 

From  experimental  results  extending  over  the  last  30  years, 
estimates  (possibly  very  rough)  of  the  smooth -plate  turbulent-friction 
budget  can  be  made: 

•  50-60%  Reynolds  stresses,  based  on  the  puV  reduction  observed 
with  drag-reducing  polymers 

•  20-30%  coherent  structures,  based  on  LEBU  results,  and 
observation  of  their  pervasive  nature  in  the  boundary  layer 

•  6-8%  near-wall  spanwise  motions,  based  on  reductions  observed 
with  riblets 

•  Vz%  viscous  stress  (projecting  laminar-flow  equations) 

•  Vz%  noise  production  (guess) 

•  10-20%  interactions  of  the  above,  and  unknown 

Much  of  the  above  has  been  derived  from  the  many  extensive 
experiments  with  polymer  additives,  which  seem  to  affect  both  the 
fluctuating  velocities  and  the  spanwise  distribution  of  the  low-speed 
streaks.  New  observations  of  the  coherent  structures  emphasize  their 
importance  m  the  turbulent-friction  budget. 

The  scenario  for  production  of  turbulent  friction  on  a  flat  plate 
moving  through  the  water  appears  to  be: 

Viscous  stresses  — >  streaks  +  vortices  +  pufv'  — >  bursts  +  horseshoes  + 
pu'v'  +  sweeps  — >  large  eddies  — >  dissipation  via  Kolmogorov  — >  heat 

The  shear  stress  at  the  wall  must  be  the  summation  of  all  the  above. 
Intervention  at  critical  junctures  by  whatever  means  should  lead  to 
substantial  drag  reduction. 

ACKNOWLEDGEMENT 

The  development  of  the  flow  tracer  for  visualizing  coherent 
structures  in  the  flow  has  been  sponsored  by  the  National  Science 
Foundation  under  Grants  CTS-9411980,  CTS-9508409  and  CTS- 
9713857.  This  technical  and  financial  support  is  gratefully  appreciated. 

REFERENCES 

1.  L.  Ong  “Visualization  of  turbulent  flows  with  simultaneous  velocity 
and  vorticity  measurements”,  Ph..D.  dissertation,  University  of 
Maryland,  College  Park,  MD,  1992. 


4 


2.  W.W.  Willmarth,  T.  Wei  &  C.O.  Lee  “Laser  anemometer 
measurements  of  Reynolds  stress  in  a  turbulent  channel  flow  with 
drag  reducing  polymer  additives”  Physics  of  Fluids  30,  933-935,  1987. 

3.  C.L.  Merkle  &  S.  Deutsch  “Drag  reduction  in  liquid  boundary 
layers  by  gas  injection”  in  D.M.  Bushnell  &  J.N.  Hefner,  eds.  Viscous 
Drag  Reduction  in  Boundary  Layers,  Progress  in  Astronautics  and 
Aeronautics  123,  AIAA,  351-412,  1990. 

4.  B.  Gampert  &  A.  Delgado  “Laser-Doppler-anemometer 
measurements  in  turbulent  flow  of  viscoelastic  fluids”  in  International 
Symposium  on  Laser  Anemometry,  ASME,  143-150,  November,  1985. 

5.  H.-W.  Bewersdorff  “Heterogene  Wiederstandsvermin derung  bei 
turbulenten  Rohr stromun gen”  Rheologica  Acta  23,  522-543,  1984. 

6.  J.  Levy  &  S.  Davis  “Drag  measurements  on  a  thin  plate  in  dilute 
polymer  solutions”  International  Shipbuilding  Progress  14, 166, 1967. 

7.  G.L.  Donohue,  W.G.  Tiederman  &  MM.  Reischman  “Flow 
visualization  of  the  near-wall  region  in  a  drag-reducing  channel  flow”  J. 
Fluid  Mechanics  56,  559-575,  1972. 

8.  S.J.  Kline,  W.C.  Reynolds,  F.A  Schraub  &  P.W.  Runstadler  “The 
structures  of  turbulent  boundary  layers”  J,  Fluid  Mechanics  95,  741- 
773,  1967. 

9.  M.J.  Walsh  “Riblets”  in  D.M.  Bushnell  &  J.N.  Hefner,  eds. 
Viscous  Drag  Reduction  in  Boundary  Layers,  Progress  in  Astronautics 
and  Aeronautics  123,  AIAA,  203-261,  1990. 

10.  M.C.  Gillcrist  &  L.W.  Reidy  “Drag  and  noise  measurements  on  an 
underwater  vehicle  with  a  riblet  surface  coating”  in  R.H.J.  Sellin  &  R.T. 
Moses,  eds.  Drag  Reduction  in  Fluid  Flows ,  Ellis  Horwood  Ltd., 
Chichester,  99-106,  1989. 

11.  G.W.  Anderson,  J.J.  Rohr  &  S.D.  Stanley  “The  combined  drag 
effects  of  riblets  and  polymers  in  pipe  flow”  Journal  of  Fluids 
Engineering  115,  213-221,  1993. 

12.  E.  Koury  &  P.S.  Virk  “Drag  reduction  by  polymer  solutions 

in  a  riblet-lined  pipe”  Applied  Scientific  Research  54,  323-347,  1995. 

13.  H.  Mizunuma,  K.  Ueda  &  Y.  Yokouchi  “Synergistic  effects  in 
turbulent  drag  reduction  by  riblets  and  polymer  additives”  in  J.W.  Hoyt 
et  al. ,  eds.  Proceedings  of  the  Fluids  Engineering  Division  Summer 
Meeting  2,  Turbulence  Modification  and  Drag  Reduction,  107-114, 
1996. 

14.  T.  Theodorsen  “Mechanism  of  turbulence”  Proceedings  of  the  2nd 
Midwestern  Conference  on  Fluid  Mechanics,  Ohio  State  University, 
Columbus,  Ohio,  1952. 

15.  J.  Zhou,  C.D.  Meinhart,  S.  Balachandar  &  R.J.  Adrian  “Formation 
of  coherent  hairpin  packets  in  wall  turbulence”  in  R.L.  Panton,  ed.  Self- 
Sustaining  Mechanisms  of  Wall  Turbulence,  Computational  Mechanics 
Publications,  Southampton,  109-134,  1997. 

16.  C.R.  Smith  &  J.D.A  Walker  “Sustaining  mechanisms  of  turbulent 
boundary  layers:  the  role  of  vortex  development  and  interactions”  in 
R.L.  Panton,  ed.  Self-Sustaining  Mechanisms  of  Wall  Turbulence, 
Computational  Mechanics  Publications,  Southampton,  13-47,  1997. 

17.  J.W.  Hoyt  &  R.H.J.  Sellin  “A turbulent-flow  dye-streak  technique” 
Experiments  in  Fluids  20,  38-41,  1995. 

18.  J.W.  Hoyt  &  R.H.J.  Sellin  “Three-dimensional  visualization  of 
large  structures  in  the  boundary  layer”  submitted,  1998. 


19.  C.R.  Smith,  J.D.A  Walker,  A.H.  Haidari  &  U.  Sobrun  “On  the 
dynamics  of  near-wall  turbulence”  Phil  Trans.  R.  Soc.  London  A  336, 
131-175,  1991. 

20.  J.M.  Chacin,  B.J.  Cantwell  &  S.J.  Kline  “Study  of  turbulent 
boundary  layer  structure  using  the  invariants  of  the  velocity  gradient 
tensor”  Experimental  Thermal  and  Fluid  Science  13,  308-317, 1996. 

21.  J.B.  Anders  Jr.  “Outer-layer  manipulators  for  turbulent  drag 
reduction”  in  D.M.  Bushnell  &  J.N.  Hefner,  eds..  Viscous  Drag 
Reduction  in  Boundary  Layers,  Progress  in  Astronautics  and 
Aeronautics,  123,  AIAA,  263-284,  1990. 

22.  S.J.  Barker  “Radiated  noise  from  turbulent  boundary  layers  in 
dilute  polymer  solutions”  Physics  of  Fluids  16,  1387,  1973. 

23.  J.F.  Brady  “An  experimoital  study  of  the  vibration,  noise,  and  drag 
of  a  cylinder  rotating  in  water  and  certain  polymer  solutions”  Ph.D. 
Thesis,  University  of  Rhode  Island,  1973. 


5 


DRAG  REDUCTION  “DESIGNER  FLUID  MECHANICS”— AERONAUTICAL  STATUS  AND  ASSOCIATED 

HYDRODYNAMIC  POSSIBILITIES 
(an  “embarrassment  of  technical  riches”) 


Dennis  M.  Bushnell 
Chief  Scientist 

NASA  -  Langley  Research  Center 
11  Langley  Boulevard,  MS  110 
Hampton,  Virginia  23681-0001 
d.m.bushnell@larc.nasa.gov 

Abstract  -  Paper  addresses  aeronautical  drag  reduction  areas,  purposes  and  approaches  and  provides  a  status  regarding  both  individual 
and  combinational  techniques.  Emphasis  is  placed  upon  emerging/re-emerging  approaches  and  consequent  near(er)  and  farther)  term 
techniques  of  potential  interest  for  hydrodynamic  applications.  Paper  considers  mitigation/amelioration  technologies  for  pressure  drag, 
drag-due-to-lift,  wave  drag  and  viscous  drag. 


I.  INTRODUCTION 

Drag  per  se  is  among  the  major  requisites  for  energy  utilization 
by  humankind  in  the  20th  Century,  the  most  blatant  examples  being 
vehicles  of  all  types  (land,  sea,  air)  and  pipeline  transport.  Drag  is 
usually  dissected  into  the  major  components  of  pressure  or  form  drag, 
drag-due-to-lift,  wave  drag  and  attached  friction  or  viscous  drag. 
Which  particular  components  are  present/dominant  is  a  function  of  the 
particular  application  and  extant  design  sophistication. 

Due  to  their  extreme  importance  (tens  of  billions  of  dollars/year) 
drag  reduction  techniques  and  technology  have  been  worked  for 
essentially  the  entire  20th  Century-this  is  far  from  a  new  area  of 
engineering  research  and  development.  Considerable  progress  has 
been  made,  primarily  in  the  minimization  of  form  or  pressure  drag 
[e.g.,  refs.  1  and  2].  The  other  drag  sources  have  also  been  worked  by 
the  research  community  but,  as  a  general  statement,  there  are  few  (and 
these  usually  quite  limited)  examples  of  deployed  drag  reduction 
approaches  for  friction  drag,  drag  due  to  lift  and  wave  drag  other  than 
simple  “shape  change.”  There  are  a  great  many  techniques  extant  in 
terms  of  invention  and  technical  evaluation  success  but  from  a 
technology  viewpoint  they  simply  have  not  offered  enough  payoff  in 
the  “real  world”  of  economics  and  the  “illities.”  [ref.  3] 

General  characteristics  of  those  drag  reduction  approaches 
which,  at  least  thus  far,  have  “transitioned”  from  the  laboratory  to 
application  include  simplicity,  very  favorable  economics,  generally 
passive/rigid/retrofittable,  reliable/“foolproof,”  we  11- understood  and 
simulatable  in  laboratory  facilities  at  application  scale/conditions,  [ref. 

3] 

The  course  of  drag  reduction  research  has  historically  been  one 
of  “ebb  and  flow,”  with  the  more  active  periods  corresponding  to  the 
conjunction  of  the  emergence  of  some  new  technical  opportunities/ 
inventions/approaches  to  the  problem  and  reemphasis  of  various 
societal  (including  military)  requirements  for  drag  reduction.  We  are 
currently  entering  again  into  such  a  conjunction,  this  time  engendered 
by  a  combination  of  economic/  affordability/  environment  drivers  and 
the  computing/  electron  ics/smart  structures/  miniaturization 
“revolutions.” 

The  purpose  of  the  present  paper  is  to  briefly  summarize  the 
status  of  drag  reduction  research  and  technology  in  each  of  the  drag 
component  areas  within  the  aeronautical  world  [see  also  refs.  4-9]  and 
provide,  as  a  surrogate  for  a  conclusions  section,  a  summary  of 
emerging  approaches  and  “best  bets”  for  hydrodynamic 
R&D/application. 

II.  PRESSURE/FORM  DRAG  REDUCTION 

(SEPARATION/VORTEX  CONTROL) 

As  a  general  rule,  pressure  or  form  drag  is,  or  has  the  potential  to 
be,  the  largest  of  the  drag  components  when  exacerbated  by  steady  or 
dynamic  large  scale  flow  separation.  A  remnant  of  pressure  drag 
exists  even  in  fully  attached  flow,  due  to  surface  decambering  by  the 
attached  viscous  flow.  However,  this  level  is  relatively  benign,  the 
order  of  20  percent  or  less  of  the  integrated  skin  friction,  and  is 
addressable  via  either  boundary  layer  thinning  or  systems  approaches 
(especially  propulsive  synergisms).  Separated  flow  is  the  major 
pressure  drag  problem  area  and  therefore  separated  flow  control,  for 
both  2-D  and  3-D  separated  flows,  is  the  key  R&D  arena  for  pressure 


drag  reduction.  3-D  separation  can  be  either  “closed”  (e.g.,  analogous 
to  the  2-D  case)  or  open— the  latter  resulting  in  organized,  generally 
longitudinal,  vorticity  and  requiring  vortex  control  [e.g.,  refs.  10  and 
11]  which  therefore  becomes  a  subset  of  separation  control.  Canonical 
approaches  to  separation  control  include  mitigation  of 
imposed/causative  pressure  gradients,  removal  of  near  wall  low 
momentum  fluid,  addition  of  higher  momentum  fluid  into  the  wall 
region  and/or  imposition  of  a  wall  “slip  layer.”  Classical  approaches  to 
longitudinal  vortex  control  include  minimization  of  causative  transverse 
pressure  gradients,  production  of  spatially-phased  counter  vorticity, 
segmented  vorticity  production,  setup/excitation  of  vortex  instability 
modes,  control  vortices  to  interact  with/alter  the  vortex  and  energy 
extraction  from  the  vortex. 

The  importance  of  separation  control  was  recognized  early  on  in 
aviation  and  assiduously  developed  and  practiced  for  the  fixed-wing 
aircraft  cruise  condition  in  essentially  two  stages— addressing  first  large 
scale  separated  regions  and  later,  in  a  stage  called  “drag  cleanup,” 
smaller  scale  separated  flow  regimes  associated  with  skin  roughness 
and  waviness,  appurtenances  and  intersection  regions.  The  dominant 
approach  was  to  remove/mitigate  the  pressure  gradients  responsible  for 
the  flow  separation  via  geometry  alterations,  resulting 
in“streamlining”/smooth(er)  surfaces  and  fillets  [e.g.,  refs.  10  and  12]. 
A  variant  of  this  approach  was  also  utilized  for  “high  lift”— variable 
geometry  (slats  and  flaps). 

Over  the  years  a  multitude  of  other  separation  control  approaches 
have  been  invented/discovered,  researched  and  in  some  specific 
instances,  applied.  These  include  blown  flaps  for  fighters,  imbedded 
boundary  layer  vortex  generators  (control  by  vortices,  ref.  10,  see  also 
ref.  13),  circulation  control  [ref.  14],  base  burning  (for  projectiles), 
“fences”  and  passive  bleed.  An  enduring  large  scale  vortex  generator 
separation  control  approach  has  been  the  use  of  leading  edge 
extensions  etc.  for  improved  fighter  agility  [ref.  10],  All  of  these 
approaches  satisfy  the,  at  least  thus  far,  common  characteristics  of 
deployed  drag  reduction  devices  stated  previously. 

This  almost  century- long  increasing  attention  to  detail  has 
reduced  the  pressure  or  form  drag  on  aircraft  to  a  level  which  is,  in  the 
aggregate,  the  order  of  half  or  less  of  the  other  drag  components.  For 
modem  transport  aircraft  at  the  cruise  condition,  the  drag  breakdown  is 
approximately  45  percent  skin  friction,  40  percent  drag  due  to  lift  and 
15  percent  pressure  drag— made  up  of  attached  flow  “decambering,” 
“crud  drag”  associated  with  residual  skin  roughness  and  antennas, 
joints,  windshield  wipers,  intersections,  etc.  as  well  as  some  small 
“accepted”  level  of  shock  wave  drag  at  the  higher  (subsonic)  speeds. 

It  should  be  noted  that  the  list  of  alternative,  and  generally  in 
some  manner  “active,”  separation  control  approaches  studied  is  quite 
extensive  (e.g.,  trapped/stabilized  transverse  vortices  [refs.  15-17], 
pneumatic/  actuated  strake  vortex  control  [ref.  10],  passive  porous  wall 
control  of  wave-induced  separation,  spanwise  blowing,  pulse  blowing 
[refs.  18-21],  mission-adaptive  wings,  jet  vortex  generators,  etc.  etc.). 
As  noted  previously  historically  there  has  been  a  strong  penchant  to 
eschew,  operationally,  such  active  approaches  in  favor  of  passive 
ones— based  upon  valid  systems/  application  metrics  rationale. 

III.  DRAG-DUE-TO-LIFT  REDUCTION 

The  status  of  drag-due-to-lift  reduction  for  aircraft  parallels  that 
of  form  drag  reduction— the  (linear)  theoretically  obvious  and  easily 


7 


implemented  have  been  adopted.  A  major  difference  is  a  relative  lack 
of  a  significant  (in  the  aggragate)  research  program  to  examine  the 
multitudinous  alternative  approaches  [see  ref.  9].  What  is  nearly 
universally  employed  are  the  tenants  of  planar  inviscid  theory  which 
dictate  an  elliptic  span  load  for  DDL  minimization  on  finite  span  wings. 
The  other  obvious  approach,  again  from  simple  theory,  is  increased 
span— obviously  limited  by  structural  considerations.  “Winglets,”  “non- 
planar”  wing-tip  devices  (essentially  thrust-producing  end  plates)  are 
often  employed  either  in  lieu  of  increased  span  or  to  mitigate  the 
effects  of  a  non-optimal  (tip-loaded)  span  load  distribution.  There  are 
a  host  of  passive  tip  approaches  to  extract  energy  from  the  tip  vortex 
which  have  been  looked  at/studied  somewhat  but,  at  this  point,  not 
employed-e.g.,  tip  turbines,  vortex  diffuser  vanes  and  tip  “sails”  or 
“feathers.”  Configurational  approaches  such  as  ring/joined  wings  and 
mass  transfer  (porous  tips,  tip  injection)  have  also  been  found  effacious 
in  the  laboratory-but  are  not  yet  employed. 

In  short,  as  in  flow  separation  control,  there  is  an  “embarrassment 
of  riches”  in  the  DDL  reduction  arena,  via  non-planer  lifting  surfaces, 
energy/thrust  extraction  from  the  vortex,  alteration  of  the  boundary 
conditions  at/  “elimination”  of  the  tip  region  and  creative  propulsion 
integration.  However,  again  none  but  the  simplest,  most 
straightforward  is  actually  utilized  or  indeed  even  studied/optimized  in 
sufficient  depth  to  allow  a  rational  systems  evaluation  for  aeronautical 
applications. 

IV.  WAVE  DRAG  REDUCTION  (VOLUME  AND  LIFT) 

(Shock)  wave  drag  is  a  potentially  serious  wing  drag  component 
for  high  subsonic  speed  transports  and  accounts  for  the  order  of  a  third 
of  the  drag  of  a  “well-designed”  supersonic  transport.  Again,  there 
are  a  plethora  of  drag  reduction  approaches,  [e.g.,  ref.  9]  varying  from 
simple/simplex  to  complex/multidisciplinary-and  again  the  simpler 
methods  are  the  ones  which  are  utilized.  These  include,  from  linear 
theory,  shock  strength  mitigation  approaches  such  as  wing  sweep,  area 
ruling,  extended  lifting  line  (onto  the  fuselage)  along  with  leading  edge 
“thrust,”  wing  twist/warp  and  reduced  thickness  and  flow  angle(s). 
More  recently  non-linear  theory,  e.g.,  CFD,  has  been  utilized  to  wring 
another  10  percent  or  so  from  such  optimizations. 

In  addition  to  these  “usual”  wave  drag  reduction  methods  there  is 
a  wealth  of  “non-conventional”  mainly  non-utilized  approaches 
including  nose  spikes,  fluid  or  particle  injection,  focusing  lasers,  heat 
addition,  nose  blunting  (“works”  due  to  presence  of  over-expansion), 
“star-bodies”  and  passive  bleed. 

There  also  exists  another  whole  class  of  alternative  approaches  to 
wave  drag  reduction  based  upon  multi-body  favorable  interference, 
the  well  known  “Busemann  Bi-plane”  being  the  reducio-ad-absurdum 
example.  Variants  include  ring  wings  and,  for  lifting  configurations, 
the  parasol  wing.  Separated  flow  control  for  shock  boundary  layer 
interactions  regions  is  probably  required  to  accrue  the  full  benefits  of 
favorable  wave  interference.  Many  of  these  unconventional 
approaches  offer  major  potential  benefits,  [ref.  9] 

V.  ATTACHED  VISCOUS  DRAG  REDUCTION 

Obvious  zeroth  order  approaches  to  viscous  drag  reduction 
include  smooth(er)  surfaces,  reduced  wetted  area  and  extended 
regions  of  laminar,  as  opposed  to  turbulent,  flow.  In  the  “air  world”  a 
recent  method  of  accomplishing  the  former  is  to  utilize  engine  thrust 
vectoring  or  load  alleviation  to  allow  reductions  in  control  surface 
“acreage.”  Alternatively,  blended  wing  body/spanloader 

configurations  can,  in  the  limit,  obviate  a  fuselage  per  se  and  the 
associated  wetted  area/friction  drag. 

The  methodology  for  transition  delay,  usually  termed  laminar 
flow  control  or  LFC,  differs  between  2-D  and  3-D  flows.  The  latter 
exhibit  boundary  layer  crossflow  which  necessitates  some  type  of 
active  (suction  is  the  usual  “approach”-of-choice)  control  whereas  in 
2-D  (including  axisymmetric)  flows  significant  drag  reduction  is 
usually  available  via  (favorable)  pressure  gradient  tailoring  (so-called 
“natural”  laminar  flow).  Multitudinous  flight  (and  laboratory)  studies 
are  available  for  both  “natural”  and  controlled  LFC/transition 
extension-up  to  Reynolds  numbers  greater  than  50  x  106  ,  and,  as  for 
many  of  the  other  drag  reduction  arenas/concepts— the  approaches 
“work,”  technically.  Thus  far  only  the  simple,  more  robust  “natural” 
approach  is  used,  often  inadvertently,  on  lower  speed  aircraft  where 
the  wings  are  largely  “2-D”/unswept.  The  economics  of  controlled 
LFC  are,  at  least  thus  far,  evidently  not  favorable  in  the  air  world- 


even  through  the  technology  has  been  amply  “demonstrated”  in  flight 
and  “production”  surface  smoothness  is  now  compatible  with 
maintenance  of  laminar  flow. 

Turbulent  drag  reduction  is  a  much  studied  and,  in  spite  of  some 
significant  technical  successes,  much  ignored  area  of  research  in  terms 
of  “air  world  “applications.  Technically  (as  opposed  to 
technologically)  successful  approaches  to  TDR  include  riblets,  slot 
injection/wall  wake  (steady  state  or  dynamic),  Stratford  closure(s), 
surface  heating  [refs.  22,  23],  nose  “swords,”  normal  injection, 
(spanwise)  oscillatory  wall  motions,  [refs.  24-33]  “inplane”  or  convex 
longitudinal  streamline  curvature  and  relaminarization  via  massive 
suction.  None  of  these  are,  at  this  point,  applied  in  the  air  world 
although  riblets  have  been  employed  in  several  Olympic  sporting 
events,  the  America’s  Cup  races  and  are  evidently  to  be  offered  on  the 
Airbus  A340  and  used  on  some  U.S.  military  aircraft  to  save  the  weight 
and  cost  of  paint  as  well  as  provide  drag  reduction.  Refs. 6,  8,  9  and 
34-37  provide  useful  entre  into  the  literature  in  this  arena. 

VI.  EMERGING  AERONAUTICAL  DRAG  REDUCTION 

APPROACHES 

There  are  two  general  areas  of  increasing  activity  in  the  arena  of 
aeronautical  drag  reduction.  Neither  of  these  can,  at  this  point,  be 
termed  even  technically  (let  alone  technologically)  successful  but  both 
have  sufficient  degrees  of  freedom  and  promise  to  bear  watching. 

The  first  of  these  is  the  use  of  surface-distributed  Mems  or 
Mems-Iike  active  sensing/logic/actuator  devices  to  either  establish  an 
alternative  (lower  drag)  set  of  dynamic  motions  near  the  wall  or,  more 
usually,  to  sense  and  attempt  to  invert/subvert  the  “pre-burst”  wall 
dynamics.  This  approach  is  currently  a  collective  “gleam-in-the  eye” 
with  some  limited  initial  successes  but  truly  immense  practical 
difficulties  [refs.38-55].  This  area  is  actually  a  subset  of  a  broader 
emerging  technology  termed  smart  structures/materials.  All  of  the 
major  technology-related  Government  Agencies/Departments  have 
significant,  and  in  many  cases  coordinated  research  programs  in  smart 
materials/structures -which  can  be  employed  either  to  control 
body/surface  motions  directly  or  used  for  flow  control  via  such  motions 
[e.g.,  refs.  56-62].  Propulsion  applications  of  this  technology  are 
relatively  far  advanced  [e.g.,  refs.63-66].  Aero  applications  include 
high  lift,  vortex  control,  buffet  control,  noise  alleviation,  vehicle  health 
monitoring/  healing,  control(s)  and  viscous  drag  reduction. 

The  other  general  approach  which  is  enjoying  increased  activity 
is  work  at  the  systems/configuration  level  utilizing  synergisms.  [e.g., 
refs.  8  and  67]  Suggestions  in  this  arena  include  (1)  multi-stage 
aircraft  of  various  persuasions  (especially  supersonic).  (2)  strut-braced 
aircraft  with  tip  engines  to  simultaneously  reduce  DDL  up  to  50 
percent  and  thin  and  unsweep  the  wing  to  allow  extensive  “natural” 
laminar  flow  as  well  as  providing  major  structural  weight  reductions 
(also  applicable  to  supersonic  cruise  machines),  (3)  blended  wing 
body/spanloader  aircraft  which,  in  the  limit,  effectively  obviate  the 
fuselage  wetted  area/associated  skin  friction,  (4)  reverse  delta  wing 
supersonic  cruise  configurations  to  provide  extensive  natural  laminar 
flow,  (5)  wing/body  propulsion  system  synergisms  which  generate 
large  additional  “static  pressure  thrust”  forces  (and  increased 
propulsive  efficiency)  which  act  to  cancel  a  sizable  fraction  of  the 
body/wing  drag  (ala  Goldschmeid),  (6)  a  front-mounted  “windmill” 
which  reduces  the  momentum  flux/drag  over  the  vehicle  and  then 
redeposits  the  momentum  into  the  wake  (e.g.,  the  momentum  is  simply 
extracted  at  the  front  and  reinserted  at  the  back  allowing  the  viscous 
drag  to  be  reduced  in  between),  and  (7)  large(r)  diameter  bodies— 
providing  reduced  surface  area/drag  per  unit  of  volume,  which 
can/m  ay  require  flow  separation  control  “at  cruise.” 

Additional  “newer”  aero  drag  reduction  approaches/research 
are,  in  many  cases,  problematical  in  terms  of  technological  and,  in 
many  cases  even  technical  feasibility.  Probably  the  most  highly 
developed,  feasible  and  interesting  of  these  is  active  (but  not  reactive) 
“synthetic  jets”  for  thrust  vectoring  [ref.  68],  vortex  control  and  other 
flow  control  applications  [e.g.,  ref.  69].  There  is  a  recent  paper  [ref. 
70]  which  indicates  that  implanted  (as  opposed  to  flowing  [e.g.,  ref.  71, 
35]  fibers/particulates  can  provide  a  net  drag  reduction  whereas 
conventional  wisdom/previous  experience  indicates  drag  increases. 
There  is  also  some  recent  work  on  an  old  concept— (downstream) 
moving  walls  [ref.  72].  There  are  obvious,  potentially  large,  skin 
friction  reductions  associated  with  such  (flow-driven)  wall  motions,  but 
the  implementation  issues  are  formidable.  There  is  now  some  recent 
further  indication  that  a  3-D  wall  mini-to-micro  roughness  can  provide 


8 


turbulent  drag  reductions  the  order  of  that  available  from  riblets  [ref. 
73,  see  also  ref.  8].  And,  finally,  there  is  even  some  indication  that 
passive  compliant  walls  are  again  being  looked  at  for  the  turbulent  case 
[refs.  74,  75].  Observed  drag  reductions  for  the  latter  are  relatively 
modest  and  their  existence  is  somewhat  surprising  in  view  of  previous 
research.  This  area  probably  deserves  another  round  of  checks, 
rechecks  and  double  checks  for  accuracy  as  well  as  alternative 
explanations  for  the  observations  obtained. 

VII.  SUGGESTIONS  REGARDING  HYDRODYNAMIC  DRAG 
REDUCTION/FLOW  CONTROL 

The  following  suggested  approaches  are  based  upon  study  of 
aero  drag  reduction  techniques  and  subsequent  extrapolation  into  the 
hydrodynamics  arena  with  some  initial  consideration  given  to  “real 
world”  hydrodynamic  operational  issues  such  as  bio-fouling  ,  etc. 
Current  and  projected  Naval  hydrodynamic  requirements  are  set  forth, 
for  example  in  refs.  76,  77  [see  also  ref.  79].  Previous/in  some  cases 
similar  applications  of  aero  drag  reduction/flow  control  research  to 
hydrodynamics  include  refs.  78-80.  There  are  obvious  physical 
differences  between  aerodynamics  and  hydrodynamics  which  provide 
major  drag  reduction  opportunities  in  the  hydro  arena  which  are 
essentially  unavailable  to  the  aero  world.  These  include  turbulent  drag 
reduction  via  polymers/surfactants,  microbubbles/2  phase  flow, 
electromagnetics  and  perhaps  even  compliant  walls  (the  latter  possibly 
enabled  by  the  closer  inertia/frequency  match  between  water  and 
vehicle  surface  dynamics  compared  to  the  air  case). 

VIII.  HYDRO  RESEARCH  SUGGESTIONS 

•  Thrust  vectoring  for  control/perhaps  employing  circulation 
control  and/or  trailing  edge  trim  tabs  on  pump  jet  stators  [see  refs. 
81-84,  also  ref.  14] 

•  “Free-wheeling”  device  ahead  of  the  propulsor  to  “homogenize” 
the  propulsor  inflow,  also  large  eddy  break-up  devices  (viscous 
flow  embedded  airfoils)  for  same  purpose  [e.g.,  ref.  85,  also  ref. 

35] 

•  Shorter/large(r)  diameter  bodies  (with  “cruise”  separation  control 
for  efficient  body  closure)-reduced  wetted  area/skin  friction  for 
a  given  volume.  Alternatively- multi-stage  vehicles  (especially 
for  weapons,  UUV’s) 

•  Automatic  controls  for  operation  in  the  doubly  stratified,  (thermal, 
salinity)  sheared  water  column  to  reduce  3-D  flow 
generation/vortex  drag/signatures  engendered  by  body  motion(s) 
and  control  surface  motions/excursions 

•  Polymers/surfactants  with  replenishment  via  on-board  culturing  of 
zo  and  phyto  plankton  filtered  from  seawater  coolant,  [see  ref. 
86  for  interesting  comments  on  polymers,  also  ref.  35] 

•  Supercavitation 

•  MHD,  multitudinous  variants  including  parallel  DC  magnetic  field 
which  “monodimensionalizes”  the  turbulence/allows  attainment 
of  any  friction  drag  level  from  turbulent  to  laminar  [refs.  87-101] 

•  Continuous  surface  curvature  in  3-space  to  minimize  longitudinal 
vortex  generation/drag  (including  obviation  of  “bilge  vortices”), 
see  ref.  10 

•  Active  body  vortex  control  (e.g.,  via  deployed  micro  VG’s)  to 
counter/alter  body  motion  induced  vorticity/provide  enhanced 
maneuverability 

•  Nose  region  “natural”  and/or  “heated”  laminar  flow  control 

•  Design  water  intakes/outlets  synergist  ically  with  body 

hydrodynamics  e.g.,  cooling  water  injection  into  tip  regions  to 
reduce  DDL/control  tip  vortex  generation,  slot  injection  drag 
reduction 

•  “Bionic”  (e.g.,  derived  from  shark/fish  study)  non-biocide  anti- 
biofouling  approaches  to  reduce  residual  “crud  drag”  (estimated 
to  be  order  of  1 5  percent  to  20  percent  of  total  submarine  body 
drag) 

•  Favorable  wave  interference  (e.g.,  utilizing  catamaran  hulls, 

swath  supports)  for  surface  wave  drag  reduction/partial 

“cancellation” 

•  Examination  of  potential  impact  of  altered  hull-water-air 

interface  (e.g.,  via  passive  porous  surfaces,  steam/bubble  layers, 
etc.)  upon  surface  wave  drag 

•  Active/smart/brilliant  materials  for  (quasi-steady)  localized  flow 
optimization  (on-going) 


•  “Afterburner”  for  burst  speed  (to  counter  drag/reduce  size  of 
propulsion  system-  if  propulsion  system  originally  sized  for  burst 
speed  metric).  Hydrogen/oxygen  rocket  is  obvious  possibility  as 
fuel  is“available”  from  seawater  (process/store  /replenish  during 
normal  “cruise”) 

•  “Controlled”/localized  cavitation  to  obtain  turbulent  drag 
reduction  via  “microbubble’Vflow  density  reduction  [see  ref.  35] 
while  obviating  direct  air  pumping/on-board  storage  penalties. 
Involves  utilization  of  one  or  more  of  the  following:  micro 
roughness,  increased  air  entrainment  at  bow,  hydrophobic 
surface  coatings,  wall  heating,  acoustic  fields  and  MHD/EHD  as 
well  as  overall  pressure  distribution  to  enhance  micro¬ 
cavitation/promote  “filmboiling” 

•  Large  scale  fillets  (as  obtained  from  studies  of  shark  dorsal  fin- 
body  intersection  regions)  for  obviation  of  intersection  region 
“necklace  vortices”  [ref.  12] 

•  “Goldschmeid”  integrated/shrouded  propulsor/body  design  to 
obtain  additional,  synergistic  “static  pressure  thrust”  thereby 
reducing  net  drag 

•  Serrated  trailing  edges  to  reduce  wake  deficits  [ref.  102,  103] 

•  Dynamic  segmented  trim  tabs  slaved  to  stanchion  internal  stress 
field  to  reduce/eliminate  oscillatory  lift  on  pump  jet  shroud  [see 
also  ref.  104] 

•  A  “manta-ray”  configuration  with  much  greater  agility/L/D 
during  maneuver  and  extensive  laminar  leading  edges  allowing 
reduced  self  noise  and  larger  array  gain  for  passive  acoustic 
sensors  [e.g.,  ref.  105] 

•  (Dynamic)  ring  vortices  for  torpedo  defense 

IX.  AN  ADDITIONAL  NOTE  REGARDING  SCALING/ 
EVALUATION  OF  “DIFFERENT”  APPROACHES 

It  should  be  noted  that,  once  shed,  organized  longitudinal  vorticity 
behavior  appears  to  be  highly  Reynolds  number  dependent  even  at  high 
Reynolds  number,  probably  due  to  the  streamline-induced  curvative 
influences  upon  the  imbedded  turbulence  fields  [ref.  10].  Since  such 
vortical  entities  have  zeroth-to-first  order  influence(s)  upon  control(s) 
and  signature(s),  as  well  as  powering  and  sensors,  it  is  essential  that 
Reynolds  number  scaling  issues  of  flow  control/drag  reduction 
approaches  be  investigated.  Current  shortfalls  in  turbulence  modelling 
(and  DNS/LES)  technology  for  such  flows  on  actual  “real  world” 
configurations  for  at  sea/at  speed  conditions  precludes  anything  other 
than  an  experimental  approach  to  such  scaling  issues. 

Efficient/effective/“useful”  examination  of  drag  reduction 
approaches,  especially  in  terms  of  ship  (as  opposed  to  localized) 
performance  and  potential  side  effects/problems  requires  the  timely 
development  of  a  small  physical  scale  (for  initial  and  test 
cost/productivity  rationales)  and  “full  scale  Reynolds  number” 
experimental  capability.  There  are  currently  two  disparate  candidate 
approaches— a  highly  pressurized  gas  facility  and  a  liquid  Helium 
(Helium  I  NOT  Helium  II,  e.g.,  a  Navier-Stokes  fluid,  order  of  2.3  to 
4.5<»  K).  The  former  passes  the  “giggle  factor”  test  better  and  has 
somewhat  less  stringent  model  smoothness  requirements  but  does  not, 
as  of  yet,  provide  as  high  a  Reynolds  number  as  the  latter.  A  strength 
of  the  liquid  Helium  approach  is  effective  utilization  of  magnetic 
suspension  to  enable  perhaps  more  accurate  measurements  of 
powering,  control  and  signature(s). 

Until  such  a  relatively  inexpensive  “whole  vehicle”  high 
Reynolds  number  test  capability  is  made  available/utilized  much  of  the 
drag  reduction  technical  research  will  remain  just  that— research. 
Applications  involving  significant  deviation  from  current  paradigms  are 
simply  too  risky/expensive  given  the  current  experimental 
facility /approach  suite  [ref.  3]. 

X.  REFERENCES 

1.  Gad-el-Hak,  Mohamed,  and  Bushnell,  Dennis  M.  “Separation 
Control:  Review,”  Journal  of  Fluids  Engineering.  March  1991,  Vol. 
113,  pp.  5-30. 

2.  Viswanath,  P.  R.,  “Flow  Management  Techniques  for  Base  and 
Afterbody  Drag  Reduction,”  Prog.  Aerospace  Sci..  Vol.  32,  pp.  70-129. 
1995. 

3.  Bushnell,  Dennis  M.,  “Application  Frontiers  of  ‘Designer  Fluid 
Mechanics’-Visions  versus  Reality  Art  Attempt  to  Answer  the 
Perennial  Question  Why  Isn’t  It  Used?”'  AIAA  97-2110,  28TH 


9 


AIAA  Fluid  Dynamics  Conference,  4th  AIAA  Shear  Flow  Control 
Conference,  June  29- July  2,  1997,  Snowmass  Village,  CO. 

4.  “Drag  Reduction  Devices  for  Aircraft,”  1910900  NTIS 

Accession  Number:  PB96-863576/XAB,  National  Technical 

Information  Service,  Springfield,  VA,  February  1996. 

5.  Poisson-Quinton,  Ph.,  “Flow  Control  Systems  Around  Airplanes,” 
Francaise  de  Mecaniaue,  No.  2,  1995,  p.  127-137. 

6.  Joslin,  Ronald  D.,  “Overview  of  Laminar  Flow  Control,” 
NAS A/RP-97- 1407,  December  1997. 

7.  Gad-el- Hak,  Mohamed,  “Modem  Developments  in  Flow 
Control,”  Appl.  Mech.  Rev..  Vol.  49,  No.  7,  July  1996,  pp.  365-379. 

8.  Bushnell,  Dennis  M.,  “Viscous  Drag  Reduction  in  Aeronautics,” 
ICAS  ‘94  Guggenheim  Lecture,  ICAS  Paper  94.-0. 1,  pp.  1-24. 

9.  Bushnell,  Dennis  M.,  “Supersonic  Drag  Reduction,”  AIAA  21st 
Fluid  Dynamics,  Plasma  Dynamics  and  Lasers  Conference,  June  1 8- 
20,  1990,  Seattle,  WA,  AIAA  90-1596. 

10.  Bushnell,  Dennis  M.,  “Longitudinal  Vortex  Control-Techniques 
and  Applications,  The  32nd  Lanchester  Lecture,  Aeronautical  Journal. 
October  1992,  pp.  293-312. 

11.  Zhuang,  F.  G.,  “Vortex  Control  Technology,”  ICAS  Proceedings. 
September  20-25,  1992,  18th  Congress  of  the  Internationa!  Council  of 
the  Aeronautical  Sciences,  Beijing,  People’s  Republic  of  China,  pp. 
XXXI-XLI. 

12.  Lakshmanan,  B.,  Tiwari,  S.  N.,  “Study  of  Supersonic  Intersection 
Flowfield  at  Modified  Wing-Body  Junctions,”  AIAA  Journal,  V.  31, 
No.  5,  May  1993,  pp.  877-883. 

13.  Lin,  John  C„  Robinson,  Stephen  K.,  McGhee,  Robert  J.,  Valarezo, 
Walter  O.,  “Separation  Control  on  High-Lift  Airfoils  Via  Micro-Vortex 
Generators,”  Journal  of  Aircraft,  Vol.  31,  No.  6,  Nov-Dec  1994,  pp. 
1317-1323. 

14.  Nielsen,  Jack  N.  ^Compiler!  Proceedings  of  the  Circulation^ 
Control  Workshop  1986.  NASA  Conference  Publication  2432, 
February  19-21,  1986. 

15.  Juhasz,  Albert  J.,  and  Smith,  John  M.,  “Performance  of  High- 
Area-Ratio  Annular  Dump  Diffuser  Using  Suction-Stabilized- Vortex 
Flow  Control,”  NASA  Technical  Memorandum  X-3535,  May  1977. 

16.  Woollett,  Richard  R.,  “Preliminary  Investigation  of  Short  Two- 
Dimensional  Subsonic  Diffusers,”  NACA  Research  Memorandum  RM 
E56C02,  May  25,  1956. 

17.  Haight,  Charles  H.,  “Experimental  Mating  of  Trapped  Vortex 
Diffusers  with  Large  Area  Ratio  Thrust  Augmentors,”  Final  Report 
June  1973  -  January  1974,  ARL  TR  74-0115,  AD-A003493,  September 
1974. 

18.  Wygnanski,  I.,  and  Seifert,  A.,  “The  Control  of  Separation  by 
Periodic  Oscillations,  AIAA  94-2608,  18th  AIAA  Aerospace  Ground 
Testing  Conference,  June  20-23,  1994,  Colorado  Springs,  CO. 

19.  Masuda,  Shigeaki,  Obi,  Shinnosuke  and  Aoki,  Kenta,  “Control  of 
Turbulent  Separating  and  Reattaching  Flow  by  Periodic  Perturbations,” 
Turbulence  Control.  FED  Vol.  193,  1994  ASME  Fluids  Engineering 
Division  Summer  Meeting,  Lake  Tahoe,  Nevada,  June  19-23,  1994. 

20.  Seifert,  A.,  Bachar,  T.,  Koss,  D.,  Shepshelovich,  M.,  and 
Wygnanski,  I.,  “Oscillatory  Blowing:  A  Too!  to  Delay  Boundary- 
Layer  Separation,”  AIAA  Journal.  Vol.  31,  No.  11,  November  1993, 
pp.  2052-2060. 

21.  Seifert,  A.,  Darabi,  A.,  and  Wygnanski,  I.,  “Delay  of  Airfoil  Stall 
by  Periodic  Excitation,”  Journal  of  Aircraft  Vol.  33,  No.  4,  July- 
August  1996,  pp.  691-698. 

22.  Kazakov,  A.  V.,  Kogan,  M.  N.,  and  Kuryachii,  A.  P.,  “Reduction 

of  Turbulent  Friction  under  Local  Surface  Heating.”  Journal _ of 

Applied  Mechanics  and  Technical  Physics.  Vol.  37,  No.  6,  1996,  pp. 
832-838. 

23.  Kazakov,  A.  V.,  Kogan,  M.  N.,  and  Kuryachii,  A.  P.,  “The  Effect 
of  the  Thermal  Properties  of  a  Body  Being  Flown  about  on  Friction  and 
Heat  Transfer  under  Conditions  of  Local  Heat  Input  to  a  Turbulent 
Boundary  Layer,”  High  Temperature.  Vol.  35,  No.  1,  1997,  pp.  58-63. 

24.  Laadhari,  F.,  Skandaji,  L.,  and  Morel,  R„  “Turbulence  Reduction 
in  a  Boundary  Layer  by  a  Local  Spanwise  Oscillating  Surface,”  fhys. 
Fluids  6  HOY  October  1994,  pp.  3218-3220. 

25.  Akhavan,  R.,  Jung,  W.,  Mangiavacchi,  N.,  “Control  of  Wall 
Turbulence  by  High  Frequency  Spanwise  Oscillations,”  AIAA  93- 
3282,  AIAA  Shear  Flow  Conference,  July  6-9.  1993,  Orlando,  FL. 

26.  Hu,  H.-C.,  and  Kelly,  R.  E.,  “Stabilization  of  Longitudinal  Vortex 
Instabilities  by  Means  of  Transverse  Flow  Oscillations,”  Phvs.  Fluids  £ 
(3),  March  1997. 


27.  Trujillo,  Steven  M.,  Bogard,  David  G.,  Ball,  Kenneth  S., 
“Turbulent  Boundary  Layer  Drag  Reduction  Using  an  Oscillating 
Wall,”  A97-33308,  AIAA  Shear  Flow  Control  Conference,  4th, 
Snowmass  Village,  Co.,  June  29- July  2,  1997,  11  pp. 

28.  Baron,  Arturo  and  Quadrio,  Maurizio,  “Turbulent  Drag 
Reduction  y  Spanwise  Wall  Oscillations,”  Annlied  Scientific  Research 
55?  311-326,  1996. 

29.  Miyake,  Yutaka,  Tsujimoto,  Koichi,  Takahashi,  Masayuki,  “On 
the  Mechanism  of  Drag  Reduction  of  Near- Wall  Turbulence  by  Wall 

Oscillation.”  Transactions  of  the  Japan _ Society  Qf  Mechanical 

Engineers.  Part  B,  Vol.  63,  No.  605,  January  1997,  pp.  16-23. 

30.  Baron,  A.,  and  Quadrio,  M.,  “Turbulent  Drag  Reduction  by 
Spanwise  Wall  Oscillations.”  Appl.  Sci.  Res..  Vol.  55,  No.  4,  pp.  311- 
26. 

31.  Satake,  Sin-ichi,  Kasagi,  Nobuhide,  “Turbulence  Control  with 
Wall- Adjacent  Thin  Layer  Damping  Spanwise  Velocity  Fluctuations,” 
International  Journal  of  Heat  and  Fluid  Flow.  Vol.  17,  No.  3,  June  1996, 
pp.  343-352. 

32.  Choi,  Kwing-So,  Roach,  Paul  E.,  DeBisschop,  Jean-Robert, 
Clayton,  Brian  R.,  ‘Turbulent  Boundary- Layer  Control  by  Means  of 
Spanwise- Wall  Oscillation”  97-1795,  AIAA  Fluid  Dynamics 
Conference,  28th,  Snowmass  Village,  Co.,  June  29- July  2,  1997,  9  pp. 

33.  Akhavan,  R.,  Jung,  W.  J.,  Mangiavacchi,  N.,  ‘Turbulence  Control 
in  Wall-Bounded  Flows  by  Spanwise  Oscillations.”  Advances  in 
Turbulence  IV  (A95-20275  04-34Y  Fluid  Mechanics  and  Its 
Applications.  Vol.  18,  1993,  pp.  299-303  and  Applied  Scientific 
Research.  Vol.  51,  No.  1-2,  1993,  pp.  299-303. 

34.  Bechert,  D.  W.,  Bruse,  M.,  Hage,  W.,  Van  der  Hoeven,  J.  G.  T., 
and  Hoppe,  G.,  “Experiments  on  Drag-Reducing  Surfaces  and  their 

Optimization  with  an  Adjustable  Geometry^] _ Fluid 

Mechanics.  1997,  Vol.  338,  pp.  59-87. 

35.  Bushnell,  Dennis  M.,  and  Hefner,  Jerry  N.  f Editors!  Viscous 
Drag  Reduction  in  Boundary  Lavers.  Vol.  123,  Progress  in  Astronautics 
and  Aeronautics,  1990. 

36.  Choi,  K-S,  Prasad,  K.  K.,  and  Truong,  T.  V.  (Editors),  Emerging 
Techniques  in  Drag  Reduction.  1996,  Mech.  Engng.  Publications  Ltd., 
London. 

37.  “Special  Course  on  Skin  Friction  Drag  Reduction,”  AGARD 
Report  786,  March  1992. 

38.  Gunzburger,  Max  D.  (Editor),  Flow  Control,  The  IMA  Volumes 
in  Mathematics  and  its  Applications— Volume  68,  1995,  Springer- 
Verlag. 

39.  Fan,  Xuetong,  Hofman,  Lorenz,  and  Herbert,  Thorwald,  “Active 
Flow  Control  with  Neural  Networks,”  AIAA  Paper  93-3273,  AIAA 
Shear  Flow  Conference,  Orlando,  FL,  July  6-9,  1993. 

40.  Kimura,  Motoaki,  Tung,  Steve,  Ho,  Chih-Ming,  Jiang,  Fukang, 
Tai,  Yu-Chong,  “MEMS  for  Aerodynamic  Control,”  AIAA  Paper  No. 
97-21 18,  AIAA  Fluid  Dynamics  Conference,  28th,  Snowmass  Village, 
Co,  June  29-July  2,  1997.  9  pp. 

41.  Koumoutsakos,  Petros,  Bewley,  Thomas  R.,  Hammond,  Edward 
P.,  Moin,  Parviz,  “Feedback  Algorithms  for  Turbulence  Control-Some 
Recent  Developments,”  AIAA  Paper  97-2009,  AIAA  Fluid  Dynamics 
Conference,  28th,  Snowmass  Village,  Co.,  June  29-July  2,  1997,  13  p. 

42.  Choi,  H.,  Moin,  P.,  Kim,  J.,  “Active  Turbulence  Control  for  Drag 
Reduction  in  Wall-Bounded  Flows,”  Journal  of  Fluid  Mechanics.  Vol. 
262,  p.  75-1 10,  March  10,  1994. 

43.  McMichael,  James  M.,  “Progress  and  Prospects  for  Active  Flow 
Control  Using  Microfabricated  Electromechanical  Systems  (MEMS), 
AIAA  Paper  No.  96-0306,  AIAA  Aerospace  Sciences  Meeting  and 
Exhibit,  34th,  Reno,  NV,  January  15-18,  1996,  21  p. 

44.  Ho,  Chih-Ming,  Tung,  Steve,  Tai,  Yu-Chong,  “Interactive  Control 
of  Wall  Structures  by  MEMS-based  Transducers.”  Advances  in 
Turbulence  VI:  Proceedings  of  the  6th  European  Turbulence 
Conference.  Lausanne,  Switzerland,  July  2-5,  1996. 

45.  Choi,  H.,  Moin,  P.,  Kim,  J.,  “Active  Turbulence  Control  for  Drag 
Reduction  in  Wall-Bounded  Flows,”  Journal  of  Fluid  Mechanics.  Vol. 
262,  March  10,  1994,  pp.  75-110. 

46.  Carlson,  H.  A.,  Lumley,  J.  L.,  “Active  Control  in  the  Turbulent 
Wall  Layer  of  a  Minimal  Flow  Unit,”  Journal  of  Fluid  Mechanics.  Vol. 
329,  December  25,  1996,  pp.  341-71. 

47.  Ho,  Chih-Ming,  Tai,  Yu-Chong,  “REVIEW:  MEMS  and  its 
Applications  for  Flow  Control,”  Journal  of  Fluids  Engineering. 


10 


Transactions  of  the  AS  ME.  Vol.  118,  No.  3,  September  1996,  pp.  437- 
446. 

48.  Parekh,  D.  E.,  Agarwal,  R.  K.,  “Control  of  Transitional  and 
Turbulent  Flows.”  Proceedings  of  the  1996  ASME  Fluids  Engineering 
Division  Summer  Meeting  (Part  2  of  3),  San  Diego,  CA,  1996. 

49.  Joslin,  R.  D.,  Nicolaides,  R.  A.,  Erlebacher,  G.,  Hussaini,  M.  Y., 
Gunzburger,  M.  D.,  “Active  Control  of  Boundary-Layer  Instabilities: 
Use  of  Sensors  and  Spectral  Controller,”  AIAA  Journal.  Vol.  33,  No.  8, 
August  1995,  pp.  1521-3. 

50.  Ho,  Chih-Ming,  “Control  of  Fluid  Flows  by  Micro  Transducers,” 
MHS  ‘96,  Proceedings  of  the  Seventh  International  Symposium  on 
Micro  Machine  and  Human  Science,  pp.  29-33. 

51.  Rathnasingham,  R.,  Breuer,  K.  S.,  “System  Identification  and 
Control  of  a  Turbulent  Boundary  Layer,”  Physics  of  Fluids.  Vol.  9,  No. 
7,  July  1997,  pp.  1867-9. 

52.  Moin,  P.,  “Active  Turbulence  Control  in  Wall  Bounded  Flows 
Using  Direct  Numerical  Simulation,”  AD-A267  261,  N94- 17286, 
November  6,  1992. 

53.  Jacobson,  Stuart  A.,  and  Reynolds,  William  C.,  “Active  Control  of 
Boundary  Layer  Wall  Shear  Stress  Using  Self-Learning  Neural 
Networks,”  AIAA  93-3272,  AIAA  Shear  Flow  Conference,  Orlando, 
FI,  July  6-9, 1993. 

54.  Gad-el-Hak,  Mohamed,  “Interactive  .Control  of  Turbulent 
Boundary  Layers:  A  Futuristic  Overview,”  AIAA  Journal.  Vol.  32, 
No.  9,  September  1994,  pp.  1753-1765. 

55.  Moin,  P.,  and  Bewley,  Thomas,  “Feedback  Control  of 
Turbulence,”  Appl  Mech  Rev.  Vol.  47,  No.  6,  Part  2,  June  1994,  pp. 
S3-13. 

56.  Hardy,  Robin  C.,  and  Simpson,  Joycelyn  O.  (Editors),  Proceedings 
of  the  4th  Annual  Workshop:  Advances  in  Smart  Materials  for 
Aerospace  Applications.  NASA  Conference  Publication  10185,  March 
1996. 

57.  Quackenbush,  T.  R.,  Bilanin,  A.  J.,  McKillip,  R.  M.,  “Vortex 
Wake  Control  Via  Smart  Structures  Technology,”  Proceedings  of  the 
SPIE--the  International  Society  for  Optical  Engineering  Conference, 
Vol.  2721,  pp.  78-92. 

58.  Barrett,  Ron,  Farokhi,  Saeed,  “Subsonic  Aerodynamics  and 
Performance  of  a  Smart  Vortex  Generator  System,”  Journal  of 
Aircraft.  Vol.  33,  No.  2,  March-April  1996,  pp.  393-398. 

59.  Saddoughi,  S.  G.,  “Experimental  Investigations  of  On-Demand 
Vortex  Generators,”  NTIS  Accession  Number:  N95-22451/5/XAB, 
December  1994,  7  pp. 

60.  Austin,  Fred,  Siclari,  Michael  J.,  Van  Nostrand,  William, 
Weisensel,  G.  N.,  Kottamasu,  Vishnu,  Volpe,  Giuseppe,  “Comparison 
of  Smart-Wing  Concepts  for  Transonic  Cruise  Drag  Reduction,”  Smart 
Structures  and  Materials  1997:  Industrial  and  Commercial  Applications 
of  Smart  Structures  Technologies:  Proceedings  of  the  Meeting.  San 
Diego,  CA,  March  4-6,  1997,  pp.  33-40. 

61.  Loewy,  Robert  G.,  “Recent  Developments  in  Smart  Structures 
with  Aeronautical  Applications,”  American  Institute  of  Aeronautics 
and  Astronautics,  1997,  (A97-29150),  55  pp. 

62.  Sater,  Janet  M.  (Editor),  “Smart  Structures  and  Materials  1997: 
Industrial  and  Commercial  Applications  of  Smart  Structures 
Technologies;  Proceedings  of  the  Meeting,  San  Diego,  CA,  March  4-6, 
1997  ”  490  pp. 

63.  de  Jager,  Bram,  “Rotating  Stall  and  Surge  Control:  A  Survey,” 
Proceedings  of  the  1995  34th  IEEE  Conference  on  Decision  and 
Control.  Part  2  of  4,  New  Orleans,  LA. 

64.  “Sensing,  Actuation,  and  Control  in  Aeropropulsion,”  Proceedings 
of  the  S PIE- Tli e  International  Society  for  Optical  Engineering.  Vol. 
2494. 

65.  Day,  I.  J.,  “Review  of  Stall,  Surge  and  Active  Control  in  Axial 
Compressors,”  Eleventh  International  Symposium  on  Air  Breathing 
Engines,  September  20-24,  1993,  Tokyo,  Japan,  pp.  97-105. 

66.  Dugundji,  J.,  Epstein,  A.  H.,  Gamier,  V.,  Greitzer,  E.  M., 
Guenette,  G.,  Paduano,  J.,  Silkowski,  P.,  Simon,  J.,  Valavani,  L.,  “A 
Progress  Report  on  Active  Control  of  Flow  Instabilities:  Rotating  Stall 
Stabilization  in  Axial  Compressors,”  AIAA-89-1008,  AIAA  2nd  Shear 
Flow  Conference,  March  13-16,  1989,  Tempe,  AZ. 

67.  Bushnell,  Dennis  M.,  “Frontiers  of  the  ‘Responsibly  Imaginable’ 
in  (Civilian)  Aeronautics,  AIAA  Paper  98-0001,  1998  AIAA  Dryden 
Lecture  presented  at  the  36th  Aerospace  Sciences  Meeting  and 
Exhibit,  January  12-15,  1998,  Reno,  NV. 


68.  Smith,  Douglas  R.,  Parekh,  David  E.,  Kibens,  Valdis,  Glezer,  Ari, 
“Thrust  Vectoring  with  Hybrid  Synthetic  Jet  Actuators.”  Proceedings 
of  the  1997  ASME  Fluid  Engineering  Division  Summer  Meeting. 
FEDS M’ 97.  Part  8  of  24,  Vancouver,  Can. 

69.  Roos,  Frederick  W.,  “Synthetic- Jet  Microblowing  for  Vortex 
Asymmetry  Management  on  a  Hemisphere-Cylinder  Forebody,”  AIAA 
Paper  97-1973,  AIAA  Shear  Flow  Control  Conference,  4th,  Snowmass 
Village,  Co,  June  29- July  2,  1997,  5  pp. 

70.  Takata,  Tashi,  Kyogoku,  Keiji,  Nakahara,  Tsunamistu, 
“Turbulent  Drag  Reduction  (Effect  of  Implanted  Fiber),”  Transactions 
of  the  Japan  Society  of  .Mechani cal  Engineers.  Part  B,  Vol.  62,  No. 
596,  April  1996,  pp.  1383-1387. 

71.  Wamser,  C.,  Lykossov,  V.  N.,  “On  the  Friction  Velocity  During 
Blowing  Snow,”  Contributions  to  Atmospheric  Physics.  Vol.  68,  No.  1, 
pp.  85-94. 

72.  Bechert,  D.  W.,  Hage,  W.,  and  Brusek,  M.,  “Drag  Reduction  with 
the  Slip  Wall,”  AIAA  Journal.  Vol.  34,  No.  5:  Technical  Notes,  pp. 
1072-1074. 

73.  Sirovich,  L.,  and  Karlsson,  S.,  “Turbulent  Drag  Reduction  by 
Passive  Mechanisms.”  Nature.  Vol.  388,  August  21,  1997,  pp.  753-755. 

74.  Lee,  T.,  Fisher,  M.,  and  Schwarz,  W.  H.,  “Investigation  of  the 
Stable  Interaction  of  a  Passive  Compliant  Surface  with  a  Turbulent 
Boundary  Layer,”  Journal  Fluid  Mechanics.  Vol.  257,  1993,  pp.  373- 
401. 

75.  Choi,  K.-S.,  Yang,  X.,  Clayton,  B.  R.,  Glover,  E.  J.,  Atlar,  M., 
Semenov,  B.  N.,  and  Kulik,  V.  M.,  “Turbulent  Drag  Reduction  Using 
Compliant  Surfaces,”  Proc.  R.  Soc.  Lond.  A.  1997,  453,  pp.  2229-2240. 

76.  Technology  for  the  United  States  Navy  and  Marine  Corps.  2 QQQz 
2035— Volume  6  Platforms.  National  Academy  Press,  Washington  DC, 
1997. 

77.  “  DOD  Compiles  Submarine  Technology  Program  Wish  List,” 
Aerospace  Daily.  November  27,  1996,  pp.  312-313. 

78.  Moore,  K.  J.,  Jones,  Gary,  and  Ndefo,  Ejike,  “Vortex  Control  in 
Submarine  Design,”  Roval  Institute  of  Naval  Architects  Symposium. 
May  13-15,  1991,  London  UK. 

79.  Bushnell,  Dennis  M.,  and  Donaldson,  C.  D.,  “Control  of 
Submersible  Vortex  Flows,”  NASA  Technical  Memorandum  102693, 
June  1990. 

80.  Report  jon  the  DARPA  Advanced  Flow  Control  Techniques 
Workshop.  November  19-22,  1991. 

81.  Gal-Or,  Benjamin,  “Civilizing  Military  Thrust  Vectoring  Flight 
Control.”  Aerospace  America.  Vol.  34,  No.  4,  April  1996,  pp.  20-21. 

82.  Schneider,  W.  E.,  “Marine  Propulsion  Unit  with  Controlled  Cyclic 
and  Collective  Blade  Pitch,”  Patent-5  249  992. 

83.  Flynn,  Billie,  Smith,  Rogers  E.,  Schneider,  Ed,  “Thrust  Vectoring: 
A  New  Dimension.”  Canadian  Aeronautics  and  Space  Journal  Vol.  41, 
No.  4,  December  1995,  7  pp. 

84.  Czamowski,  J.,  Cleary,  R.,  Kreamer,  B.,  “Exploring  the  Possibility 
of  Placing  Traditional  Marine  Vessels  Under  Oscillating  Foil 
Propulsion,”  Proceedings  of  the  1997  7th  International  Offshore  and 
Polar  Engineering  Conference.  Part  2  of  4,  Honolulu,  HI. 

85.  Sluchak,  Vladimir,  “The  Thin  Ring  Wing  as  a  Means  of  Flow 
Improvement  Upstream  of  a  Propeller,”  SNAME  Propellers/Shafting 
‘97  Symposium,  September  23-24,  1997,  Virginia  Beach,  VA. 

86.  Motier,  John  F.,  Chou,  Lu-Chien,  Kommareddi,  Nagesh, 
“Commercial  Drag  Reduction  Past,  Present  and  Future.”  American 
Society  of  Mechanical  Engineers.  Fluids  Engineering . Division  FED, 
Vol.  237,  No.  2,  1996,  pp.  229-234. 

87.  Krakov,  M.  S.,  and  Nikiforov,  I.  V.,  “Control  of  Flow  Separation 
in  a  Plane  Channel  by  Means  of  a  Magnetic  Fluid,” 
Magnetohvdrodvnamics.  Vol.  26,  No.  4,  October- December  1990,  pp. 
469-74. 

88.  Crawford,  Catherine  H.,  and  Kamiadakis,  George  Em,  “Reynolds 
Stress  Analysis  of  EMHD-Controlled  Wall  Turbulence.  Part  1. 
Streamwise  Forcing,”  Phvs.  Fluids  9  (3),  March  1997,  pp.  788-806 

89.  Meng,  James  C.  S.,  “Magnetohydrodynamic  Boundary  Layer 
Control  System,”  Patent  Number  5,273,465,  December  28,  1993. 

90.  Henoch,  C.,  and  Stace,  J.,  “Experimental  Investigation  of  a  Salt 
Water  Turbulent  Boundary  Layer  Modified  by  an  Applied  Streamwise 
Magnetohydrodynamic  Body  Force.”  Phvs.  Fluids  7  (6),  June  1995. 

91.  Meng,  James  C.  S.,  Huyer,  Stephen  A.,  Castano,  John  M., 
Thivierge,  Daniel  P.,  Hendricks,  Peter  J.,  “Experimental  Study  of  the 
Span  wise  Vortex  Resonance  Hypothesis  for  Turbulent  Drag  Reduction 


11 


Over  a  Flat  Plate  in  Salt  Water,”  NUWC-NPT  Technical  Report 
10,680,  March  1,  1997. 

92.  Meng,  J.  C.  S.,  “Wall  Layer  Microturbulence  Phenomenology  and 
a  Markov  Probability  Model  for  Active  Electromagnetic  Control  of 
Turbulent  Boundary  Layers  in  an  Electrically  Conducting  Medium,” 
NUWC-NPT  Technical  Report  10,434,  June  1,  1995. 

93.  Cattaneo,  Fausto,  “On  the  Effects  of  a  Weak  Magnetic  Field  on 
Turbulent  Transport,”  The  Astrophvsical  Journal.  434:200-205, 
October  10,  1994. 

94.  Meng,  James  C.  S.,  “Active  Turbulence  Control  Using 
Microelectrodes,  Permanent  Magnets  in  Microgrooves,”  Patent 
Number  5,359,951,  November  1,  1994. 

95.  Meng,  J.  C.  S.,  Henoch,  C.  W.„  and  Hrubes,  J.  D.,  “Seawater 

Electromagnetohydrodynamics:  A  New  Frontier.”  Magnitnava 

Gidrodinamika  Conference.  Vol.  30,  No.  4,  October-December  1994, 
pp.  483-506. 

96.  Krai,  Linda  D.,  and  Donovan,  John  F.,  “Numerical  Simulation  of 
Turbulence  Control  Using  Electromagnetic  Forces.”  American  Society 
of  Mechanical  Engineers.  Fluids  Engineering  Division  FED,  Vol.  237, 
No.  2,  1996,  pp.  319-329. 

97.  Qhoi,  Haecheon,  Lee,  Donghoon,  Lim,  Junwoo,  and  Kim,  John, 
“Control  of  Near  Wall  Streamwise  Vortices  Using  an  Electromagnetic 
Force  in  a  Conducting  Fluid,”  AIAA  Paper  97-2059,  AIAA  Shear  Flow 
Control  Conference,,  4th,  Snowmass  Village,  CO,  June  29- July  2,  1997, 

12  pp. 

98.  Krakov,  M.  S.,  and  Kamiyama,  S.,  “Steady  Flow  Past  a  Circular 
Cylinder  Coated  with  Magnetic  Fluid:  Flow  Structure,  Drag  Reduction 


and  Coating  Deformation,”  Journal  of  Fluid  Mechanics.  Vol.  295,  July 
25,  1995,  pp.  1-22. 

99.  Budingen,  G.  V.,  Frenzel,  H.,  Steger,  R.,  Vorwerk,  J.,  Brunn,  P. 
O.,  “Simultaneous  Drag  Reduction  and  Heat  Transfer  Enhancement 
for  Slit  Flow  by  Means  of  Coating  One  Wall  with  a  Magnetic  Fluid,” 
Journal  of  Intelligent  Material  Systems  and  Structures,  Vol.  5,  No.  6, 
November  1994,  pp.  776-86. 

100.  Zhang,  W.,  Diamond,  P.  H.,  “Turbulence  Suppression  and  Drag 
Reduction  by  External  Magnetic  Field.  Proceedings  of  International 
Sherwood  Fusion  Theory  Conference.  Dallas,  TX,  March  14-16,  1994. 

101.  Orlandi,  P.,  “Drag  Reduction  in  Turbulent  MHD  Pipe  Flows,” 
NTIS  Accession  Number:  N1 99700 14679/XAB,  December  1996,  10 

pp. 

102.  Hunter,  Craig,  Delore,  Pasquale,  and  Presz,  Walter  M.,  “Drag 
Reduction  and  Wake  Minimization  on  Marine  Vehicles,”  Final  Report, 
Office  of  Naval  Research,  Grant  No.  0014-89-J-1883,  AD-A241  270, 
July  1991. 

103.  Vijgen,  P.,  Howard,  F.  G.,  Bushnell,  D.  M.,  Holmes,  B.  J., 
“Serrated  Trailing  Edges  for  Improving  Lift  and  Drag  Characteristics 
of  Lifting  Surfaces,”  U.S.  Patent  5,088,665,  1992. 

104.  Akin,  O.,  and  Rockwell,  D.,  “Actively  Controlled  Radial  Flow 
Pumping  System;  Manipulation  of  Spectral  Content  of  Wakes  and 

Wake-Blade  Interactions,”  Transactions  of  the  ASME, _ Journal  of 

Fluids  Engineering.  Vol.  116,  No.  3,  September  1994,  pp.  528-37. 

105.  August,  Henry,  Carapezza,  Edward,  “Ring  Wing  for  an 
Underwater  Missile,”  AIAA  Atmospheric  Flight  MEchanics 
Conference,  Monterey,  CA,  August  9-11,  1993,  Technical  Paper  A93- 
4830120-08. 


12 


EUROPEAN  DRAG  REDUCTION  RESEARCH  - 
RECENT  DEVELOPMENTS  AND  CURRENT  STATUS 


Kwing-So  Choi 

Department  of  Mechanical  Engineering 
The  University  of  Nottingham 
Nottingham  NG7  2RD,  United  Kingdom 
kwing-so.choi@nottingham.ac.uk 


Abstract  -  The  recent  developments  and  current  status  of  the  drag  reduction  research  in  Europe  have  been  described  here  with  an  overview  of 
European  Research  Community  on  Flow,  Turbulence  and  Combustion  (ERCOFTAC)  where  a  large  amount  of  research  work  has  been  coordinated. 
The  research  activity  in  Europe  is  unique  in  a  sense  that  the  research  areas  are  diverse  with  a  mixture  of  new  and  traditional  themes.  This  is  due  to 
various  funding  mechanisms  available  in  Europe  mainly  through  national  funding  schemes  in  each  country.  There  is  an  obvious  disadvantage  in 
this  arrangement,  however,  that  it  is  difficult  to  gather  momentum  on  a  particular  work  as  the  research  funds  are  spread  very  thinly  across  Europe. 
ERCOFTAC ’s  main  aim  is,  therefore,  to  stimulate  coordinated  European-wide  research  efforts  on  special  topics  in  flow,  turbulence  and  combustion. 
The  European  Drag  Reduction  Meetings,  which  are  organised  as  a  part  of  activities  within  ERCOFTAC’s  Drag  Reduction  Special  Interest  Group 
have  been  a  driving  force  for  research  coordination  on  drag  reduction  within  Europe. 


I.  INTRODUCTION 

The  purpose  of  this  paper  is  firstly  to  give  an  overview  of  European 
Research  Community  on  Flow,  Turbulence  and  Combustion 
(ERCOFTAC)  where  a  large  amount  of  research  work  has  been 
coordinated  in  recent  years.  The  Drag  Reduction  Special  Interest  Group 
is  one  of  well  established  research  groups  within  ERCOFTAC,  which  has 
organised  10  specialised  meetings  -  European  Drag  Reduction  Meetings 
-  on  drag  reduction  since  1986.  Initially  the  European  Drag  Reduction 
Meeting  was  a  very  informal  gathering  of  only  a  dozen  or  so  researchers, 
and  most  of  discussions  were  centred  around  the  use  of  passive  devices, 
such  as  riblets  and  LEBUs  and  their  results.  As  the  time  goes  by,  this 
informal  meeting  has  developed  to  a  semi -formal  meeting  of  delegates 
from  all  over  the  Europe,  including  researchers  from  Russia,  Ukraine  and 
Czech  Republic. 

Secondly,  a  description  of  recent  developments  and  current  status  of 
the  drag  reduction  research  in  Europe  is  given  with  a  view  to  highlight  the 
efforts  expended  by  the  European  researchers  in  recent  years.  Discussions 
of  some  of  the  recent  results  on  riblets,  compliant  coating,  drag  reduction 
in  nature,  polymer  additives  and  wall  oscillation  are  given  with  an 
emphasis  on  the  drag-reduction  mechanisms  involved.  Some  descriptions 
on  the  emerging  techniques  for  drag  reduction  such  as  passive  porous 
surface  and  slip  wall  are  also  given.  It  is  not  within  the  scope  of  this  paper, 
however,  to  summarise  all  the  recent  research  activities  on  drag  reduction 
in  Europe.  Therefore,  the  discussions  of  some  of  the  topics,  such  as  the 
polymer  additives  for  drag  reduction,  are  limited  only  to  those  presented 
at  the  European  Drag  Reduction  Meetings. 

II.  ERCOFTAC 

The  ERCOFTAC  (European  Research  Community  on  Flow, 
Turbulence  and  Combustion)  Association  was  created  as  an  international 
association  with  scientific  objectives  according  to  Belgian  law  on  June  3, 
1988  in  Paris.  The  main  objectives  of  ERCOFTAC  are: 

•  to  promote  joint  efforts  of  European  research  institutes  and  industries 
who  are  active  in  all  aspects  of  flow,  turbulence  and  combustion, 
with  the  objective  of  exchanging  technical  and  scientific  information 
concerning  basic  and  applied  research  and  the  development, 
validation  and  maintenance  of  numerical  codes  and  databases 

•  to  promote  centres,  called  ERCOFTAC  Pilot  Centres,  in  many 
European  countries  to  act  as  centres  for  collaboration,  stimulation 
and  application  of  research 

•  to  promote  industrial  application  of  research  by  means  of  novel 
kinds  of  collaborations  between  industry,  governments,  professional 
societies  and  research  groups 

•  to  stimulate,  through  the  creation  of  Special  Interest  Groups,  well- 
coordinated  European-wide  research  efforts  on  specific  topics  in 
flow,  turbulence  and  combustion 

•  to  stimulate  the  creation  of  advanced  training  activities  in  all  fields 
related  to  flow,  turbulence  and  combustion. 


ERCOFTAC  membership  is  open  to  research  groups  in  academic  or 
governmental  organisations  and  to  industrial  corporations  located  in  the 
EC  and  EFTA  countries.  The  ERCOFTAC  Association  is  managed  by  the 
Managing  Board  which  is  composed  of  elected  representatives  of  the 
voting  members.  The  Managing  Board  elects  among  its  members  the 
Executive  Committee  composed  of  the  Chairman,  two  Vice  Chairmen  and 
the  Treasurer.  Either  the  Chairman  or  the  two  Vice  Chairmen  are  from 
industry.  The  Executive  Committee  is  responsible  for  the  daily  course  of 
affairs.  The  General  Assembly  established  the  Scientific  Programme 
Committee,  which  recommends  the  research  goals  of  ERCOFTAC  and 
proposes  special  activities.  The  Managing  Board  has  recently  approved 
the  creation  of  an  Industrial  Advisory  Committee,  which  advises  the 
Board  on  matters  of  Industrial  relevance. 

The  ERCOFTAC  Pilot  Centre  network  forms  one  of  the  pillars  of  the 
ERCOFTAC  Association.  ERCOFTAC  Pilot  Centres  are  composed  of 
ERCOFTAC  members  in  a  region  or  a  country.  ERCOFTAC  Pilot  Centres 
coordinate  the  research  in  flow,  turbulence  and  combustion  on  a  regional 
or  national  scale,  while  at  the  same  time  being  linked  to  all  other  Pilot 
Centres  via  the  ERCOFTAC  Pilot  Centre  network.  In  1997,  the  following 
16  ERCOFTAC  Pilot  Centres  exist:  Belgium,  France  PEPIT,  France 
South,  France  West,  Germany  North,  Germany  South,  Germany  West, 
Greece,  Italy,  Netherlands,  Nordic,  Portugal,  Spain,  Switzerland,  UK 
North  and  UK  South. 

ERCOFTAC  Special  Interest  Groups  form  the  second  pillar  of  the 
Association.  ERCOFTAC  Special  Interest  Groups  are  composed  of 
ERCOFTAC  members  working  together  on  a  well-defined  specific  topic 
on  flow,  turbulence  and  combustion.  Activities  of  Special  Interest  Groups 
are  organising  workshops,  comparison  of  codes,  exchange  of  research 
results,  creation  of  experimental  and/or  numerical  data  bases,  organisation 
of  courses,  etc.  ERCOFTAC  Special  Interest  Groups  are  associated  with 
at  least  two  Pilot  Centres,  and  have  an  international  organising  committee. 


13 


Currently,  ERCOFTAC  Special  Interest  Groups  exist  on  the 
following  topics.  The  numbers  are  specific  to  each  individual  group  and 
those  groups  not  listed  here  have  ceased  their  activities. 

1 .  Large  Eddy  Simulation 

2.  Turbulent  Boundary  Layers 

3.  Identification  Schemes  for  Eddy  Structures  in  Free  Turbulent  Shear 
Flows 

4.  Turbulence  in  Compressible  Flows 

5.  Atmospheric  Boundary  Layer  Turbulence  and  Diffusion  over 
Complex  Terrain 

6.  Turbulence  and  Dispersion  in  Urban  Atmosphere 

7.  Atmospheric  Dispersion 

8.  Turbomachineiy 

10.  Laminar  to  Turbulent  Transition  and  Retransition 

12.  Dispersed  Turbulent  Two  Phase  Flow 

13.  Grid  Generation  and  Adaptivity 

14.  Stably  Stratified  and  Rotating  Turbulence 

15.  Turbulence  Modelling 

1 7  Shock/Boundary  Layer  Interaction 

1 9.  Parallel  Computing  in  CFD 

20.  Drag  Reduction 

21.  Vortex  Dynamics 

24.  Variable  Density  Turbulent  Flows 

25.  CFD  for  Ship  Hydrodynamics 

28.  Aerodynamics  and  Steady  State  Combustion  in  Furnaces  and 
Combustion  Chambers 
30.  Wind  over  Waves 

32.  Particle  Image  Velocimetry 

33.  Laminar-Turbulent  Transition  Mechanisms,  Prediction  and  Control 
101.  Quality  and  Trust  in  Industrial  CFD 

Flow,  Turbulence  and  Combustion  (formally  Applied  Scientific 
Research)  is  an  international  journal  published  in  association  with 
ERCOFTAC.  Further  details  of  ERCOFTAC  Association  can  be  found  on 
World  Wide  Web  (http://imhefwww.epfl.ch/lmf/ERCOFTAC/). 

III.  drag  reduction  special  interest  group 

Drag  Reduction  Special  Interest  Group  (SIG)  is  one  of  the  founding 
groups  of  ERCOFTAC  Association  when  it  was  established  in  1988, 
although  a  drag  reduction  group  in  Europe  existed  before  then.  A 
coordination  of  experimental,  numerical  and  analytical  research  into  drag 
reduction  and  flow  management  using  passive  and  active  techniques  is 
carried  out  by  the  group,  which  include  riblets,  LEBUs,  polymer  additives, 
compliant  coating,  boundary  layer  structures  and  drag  reduction 
mechanisms.  The  Group’s  main  objectives  are: 

•  to  bring  together  active  researchers  in  an  area  of  drag  reduction 
and  flow  management  to  discuss  the  latest  results 

•  to  identify  area  of  passive  and  active  devices  in  terms  of  industrial 
applications  and  technology  transfer 

•  to  encourage  collaborations  among  researchers  in  Europe 

The  International  Organising  Committee  of  Drag  Reduction  SIG  consists 
of: 

D. W.  Bechert,  DLR,  Germany 

K.-S.  Choi,  University  of  Nottingham,  U.K.  (convenor) 

E.  Coustols,  ONERA/CERT,  France 
P.  Luchini,  University  of  Milan,  Italy 

K.  K.  Prasad,  T.U.  Eindhoven,  The  Netherlands 
A.M.  Savill,  University  of  Cambridge,  U.K. 

T.V.  Truong,  EPFL,  Switzerland 

Recent  meetings  were  held  in  1993  in  Lausanne,  Switzerland  (8th 
European  Drag  Reduction  Meeting  and  Workshop  on  Drag-reduction 
Mechanisms)  and  in  1995  in  Naples,  Italy  (9th  European  Drag  Reduction 
Meeting  and  Workshop  on  Active  Control).  The  last  meeting  (10th 
European  Drag  Reduction  Meeting)  was  held  in  1997  in  Berlin,  Germany. 
Several  publications  [1-4]  were  made  as  a  result  of  these  meetings.  The 
latest  monograph  “Emerging  Techniques  in  Drag  Reduction”  (edited  by 
K.-S.  Choi,  K.K.  Prasad  and  T.V.  Truong)  was  published  in  June  1996  by 


Mechanical  Engineering  Publication.  Reports  on  these  meetings  as  well 
as  the  activities  on  drag  reduction  can  be  found  in  ERCOFTAC  Bulletin. 

IV.  EUROPEAN  DRAG  REDUCTION  RESEARCH 

Riblets 

The  study  of  riblets  has  been  one  of  the  focused  research  activities 
in  turbulent  drag  reduction  in  the  last  two  decades.  There  is  still  so  much 
interest  in  this  passive  device  in  Europe  in  controlling  turbulent  as  well  as 
laminar  boundary  layers.  At  the  University  of  Nottingham,  studies  were 
conducted  in  a  low-speed  boundary  layer  tunnel  to  investigate  a  heat- 
transfer  enhancement  over  the  heated  riblet  surface  and  a  delay  in 
transition  to  turbulence  of  laminar  boundary  layer  by  riblets.  The  results 
of  heat-transfer  measurement  over  the  heated  triangular  riblets  [5-7] 
indicate  that  the  heat  transfer  coefficient  is  increased  as  much  as  10% 
within  the  drag-reducing  regime  of  riblets,  say  s+  <  30.  This  apparent 
breakdown  of  the  Reynolds  analogy  seems  to  result  from  a  difference  in 
the  turbulence  length  scale  of  momentum  and  thermal  boundary  layers  due 
to  their  difference  in  initial  conditions  and  molecular  diffusivities.  It  has 
been  demonstrated  that  the  transition  to  turbulence  of  an  excited  laminar 
boundary  layer  over  the  riblet  surface  can  be  delayed  very  significantly 
[8].  The  growth  rate  of  the  momentum  thickness  during  the  non-linear 
stage  of  the  transition  has  been  reduced  over  the  riblet  surface 
accompanied  by  a  reduction  in  the  turbulence  intensity.  The  shape  factor 
of  the  boundary  layer  over  the  riblet  surface  is  lower,  supporting  that  the 
rate  of  transition  has  indeed  been  reduced.  It  seems  that  the  mechanism  of 
transition  delay  by  riblets  is  similar  to  that  of  turbulent  drag  reduction, 
where  the  longitudinal  grooves  interact  with  the  legs  of  hairpin  vortices 
to  hinder  their  development. 

A  research  group  at  DLR  Berlin  has  been  investigating  riblets  for 
turbulent  drag  reduction  using  an  oil  channel,  which  is  accurate  to  ±0.3% 
of  the  measured  drag  force  [9-12].  A  considerable  improvement  in  drag 
reduction  was  obtained  in  recent  years  by  optimising  the  shape  of  riblets 
systematically.  They  have  tested  riblets  of  many  configurations  including 
triangular,  semi-circular,  blade,  “brother  and  sister”  and  three-dimensional 
riblets.  As  a  result,  the  maximum  drag  reduction  as  much  as  10%  can  be 
achieved.  Bechert  and  his  colleagues  have  tested  a  combination  of  blade 
riblets  and  “ejection”  slits  in  an  effort  to  increase  the  amount  of  drag 
reduction  further  more.  It  was  expected  that  the  fluctuating  pressures  in  a 
turbulent  boundary  layer  drive  the  fluid  in  and  out  of  small  slits  like  a  jet 
flow,  thereby  generating  a  thrust  force.  With  this  configuration  of  riblets, 
a  maximum  drag  reduction  of  nearly  9%  was  achieved. 

The  technique  and  theoretical  explanation  for  riblet  optimisation  is 
described  by  a  group  of  researchers  at  the  University  of  Milan  [13-16], 
who  suggested  that  the  drag  reduction  can  be  maximised  by  increasing  the 
difference  in  protrusion  height  between  the  longitudinal  and  cross  flows. 
This  will  maximise  the  impedance  to  the  cross  flow  with  a  minimum  drag 
on  the  longitudinal  flow.  Luchini  also  investigated  the  effects  of  riblets  on 
the  boundary  layer  stability.  His  results  using  the  eN  method  show  that  the 
Tollmien-Schlichting  (T-S)  waves  over  the  triangular  riblet  surface  are 
found  to  be  excited  at  a  lower  critical  Reynolds  number.  The  conditional 
analysis  of  ejections  in  the  turbulent  boundary  layer  over  riblets  was 
carried  out  by  Baron  and  Quadrio  [17-19],  who  confirmed  that  the 
frequency  of  ejections  is  increased  and  the  duration  reduced  by  the 
presence  of  riblets.  They  observed  that  the  average  number  of  ejections  in 
each  burst  is  greater  over  riblets  than  that  over  a  flat  plate. 

Experimental  studies  of  riblets  in  laminar  boundary  layers  have  been 
carried  out  by  a  group  at  the  Institute  of  Theoretical  and  Applied 
Mechanics,  Russia  [20-23].  The  experimental  results  show  that  the  riblets 
can  delay  the  transformation  of  the  A-vortices  into  turbulent  spots  and 
shift  the  point  of  transition  further  downstream.  When  the  riblets  are  used 
in  the  linear  stage  of  transition,  the  growth  rate  of  T-S  waves  is  increased 
agreeing  well  with  the  numerical  results  obtained  by  Luchini.  The 
effectiveness  of  riblets  in  controlling  the  transitional  three-dimensional 
flow  was  also  investigated  by  Kozlov  and  his  colleagues.  This  was  carried 
out  by  exciting  the  streamwise  vortices  in  the  swept-wing  boundary  layer 
using  a  vortex  generator.  The  results  seem  to  indicate  that  the  riblets  can 
suppress  the  development  of  laminar-turbulent  transition  of  three- 
dimensional  boundary  layers.  It  was  also  demonstrated  experimentally  that 
the  riblets  can  substantially  affect  the  way  the  vortices  develop  in  the 
wake  behind  a  single  roughness  element,  leading  to  a  delay  in  transition 
to  turbulence. 


14 


Effectiveness  of  riblets  in  turbulent  boundary  layers  under  pressure 
gradient  was  investigated  at  the  Delft  University  of  Technology.  Through 
a  direct  measurement  of  drag  and  velocity,  DeBisschop  and  Nieuwstadt 
[24]  were  able  to  show  that  a  greater  drag  reduction  of  up  to  13%  can  be 
obtained  by  using  riblets  in  a  boundary  layer  under  an  adverse  pressure 
gradient.  This  is  to  confirm  the  result  of  previous  study  by  Choi  [25]  who 
carried  out  a  detailed  measurement  of  velocity  profiles  of  turbulent 
boundary  layer  over  a  riblet  surface  under  different  pressure  gradient 
conditions. 

Review  papers  on  riblets  were  written  by  many  researchers  [26-29]. 
Compliant  coating 

A  research  group  at  the  University  of  Warwick  has  been  engaged  in 
the  study  of  compliant  coating  in  delaying  transition  of  boundary  layers 
to  turbulence  [30-35].  They  demonstrated  that  in  theory,  at  least, 
substantial  transition  delays  were  possible  with  Kramer’s  coatings.  This 
numerical  study  was  supported  by  a  series  of  towing  tank  experiments  by 
Gaster  [36].  Recent  effort  has  been  directed  towards  the  optimisation  of 
compliant  coating  for  maximum  reduction  in  skin-friction  drag,  such  as  by 
using  multiple  compliant  panels  and  anisotropic  coatings.  Effects  of 
compliant  rotating  disc  on  the  boundary-layer  transition  were  also 
investigated  by  the  same  group.  It  was  shown  that  a  compliant  wall  has  a 
stabilising  effect  on  the  Type  I  inviscid  instability,  while  the  Type  II 
viscous  instability  is  stabilised  only  when  the  compliance  of  the  wall 
coating  is  increased.  Although  the  experimental  work  was  not  conclusive 
in  showing  an  increase  in  the  critical  Reynolds  number  with  compliant 
rotating  disc,  there  was  an  indication  that  this  can  be  done  with  an  increase 
in  the  wall  compliance. 

Over  the  past  forty  years,  there  have  been  intensive  investigations 
into  the  use  of  compliant  coating  to  obtain  turbulent  drag  reduction  in 
boundary-layer  flows.  Although  positive  results  were  found  in  some  of  the 
studies  carried  out  in  Russia,  none  of  these  had  been  successfully 
validated  by  independent  researchers.  Recently,  a  series  of  tests  were 
carried  out  at  the  University  of  Nottingham  to  verify  the  experimental 
results  of  Semenov  and  Kulik  [37-39],  who  successfully  demonstrated  the 
ability  of  compliant  coatings  in  reducing  the  skin-friction  drag  and 
surface-flow  noise  in  a  turbulent  boundary  layer.  The  results  obtained  by 
Choi  et  al  [40,  41]  clearly  demonstrate  that  the  turbulent  skin  friction  is 
reduced  for  one  of  the  compliant  coatings  tested,  indicating  a  drag 
reduction  of  up  to  7  percent  within  the  entire  speed  range  of  the  tests.  The 
intensities  of  skin-friction  and  wall-pressure  fluctuations  measured 
immediately  downstream  from  the  compliant  coating  show  reductions  in 
the  intensities  of  up  to  7  percent  and  19  percent,  respectively.  The  results 
also  indicate  reductions  in  turbulence  intensity  by  up  to  5  percent  across 
almost  the  entire  boundary  layer.  Furthermore,  an  upwards  shift  of  the 
logarithmic  velocity  profile  is  evident  indicating  that  the  thickness  of  the 
viscous  sublayer  is  increased  as  a  result  of  turbulent  drag  reduction  by  the 
compliant  coating. 

Drag  reduction  in  nature 

Experimental  studies  on  live  penguins  were  carried  out  by  Bannasch 
[42,  43]  at  the  Technical  University  of  Berlin  with  measurements  using 
life-sized  models  in  a  water  tank.  An  axisymmetric  body  based  on  three 
medium-sized  penguin  species  was  found  to  be  an  excellent  low-drag 
laminar  body.  When  the  transition  from  laminar  to  turbulent  flow  was 
triggered  at  5  %  of  the  body  length,  the  surface  drag  coefficients  remained 
even  lower  than  those  of  a  turbulent  flat  plate  of  equal  length,  and  they 
declined  at  a  higher  rate  with  increasing  Reynolds  numbers.  Viscous  drag 
was  reduced  by  the  characteristic  “stepwise”  pressure  and  the  velocity 
distribution  developed  along  the  multiple-curved  (wave-like)  contour  of 
that  body.  Turbulent  velocity  fluctuations  in  the  boundary  layer  remained 
at  a  low  level  even  with  the  rigid  model.  The  wavy  contour  and  compliant 
wall  of  penguin  body  are  considered  to  be  the  main  reasons  for  the 
excellent  swimming  efficiency.  In  most  cases,  a  regular  pattern  of 
transverse  waves  (wavelength  of  2  -3  cm)  was  observed  over  the  plumage. 

A  passive  flow-separation  control  method  to  mimic  the  bird  feathers 
was  tested  in  a  wind  tunnel  at  DLR  Berlin  [12].  The  results  of  the  test  of 
self-activated  movable  flap  over  a  laminar  wing  section  revealed  that  the 
maximum  lift  of  the  airfoil  was  increased  by  20%  without  perceivable 
deleterious  effects  under  cruise  condition.  This  was  confirmed  by  a  flight 
test  with  a  motor  glider  by  recording  the  reduction  in  minimum  speed 
before  stall.  Replica  of  shark  skin  was  tested  in  a  Berlin  Oil  Channel  for 


turbulent  drag  reduction  [12].  For  this  experiment,  800  individually 
movable  scales  were  carefully  produced  and  they  were  anchored  on 
adjustable  springs.  This  allowed  each  artificial  scale  to  move  freely, 
interacting  with  the  near-wall  flow  field  of  the  turbulent  boundary  layer. 
Although  there  were  obvious  difficulties  in  optimizing  all  the  parameters 
involved  in  this  experiment,  Bechert  and  his  colleagues  were  able  to 
obtain  a  modest  drag  reduction  of  3%.  The  same  group  has  tested  the  hairy 
surfaces  for  drag  reduction  [12],  which  were  exhibited  by  otters  and  sea 
leopards.  Again  only  a  marginal  drag  reduction  (1 .5%)  was  observed  when 
the  hairs  were  placed  either  on  the  flat  surface  or  very  close  to  it. 

Polymer  additives 

A  series  of  experiments  were  carried  out  by  Choi  and  his  colleagues 
[44-46]  using  a  towing  tank  at  British  Maritime  Technology,  where  a 
combined  use  of  riblets  with  polymer  coating  was  investigated  for 
turbulent  drag  reduction.  A  one-third  scale  model  of  America’s  Cup 
winning  yacht,  the  Australia  II  was  used  for  this  test  and  the  total 
hydrodynamic  resistance  was  measured  at  various  towing  speeds.  The 
results  indicated  that  the  riblets/polymer  combination  offered  an  overall 
improvement  in  drag  reduction  characteristics  over  either  riblets  or 
polymer  coating  alone,  with  a  maximum  reduction  in  total  flow  resistance 
of  3.5%  at  s+  -  8  (Re  =  3.8xl06). 

Drag  reduction  mechanism  of  turbulent  boundary  layers  with 
polymer  additives  has  been  studied  recently.  Orlandi  [47]  investigated  into 
the  constitutive  equation  of  dilute  polymer  solution,  relating  the 
elongation  viscosity  to  the  local  flow  properties.  Here,  the  viscosity  of  the 
solution  becomes  large  when  the  strain  rate  is  greater  than  the  vorticity. 
The  accuracy  of  this  method  was  tested  against  other  numerical  methods. 
The  study  at  the  Delft  University  of  Technology  involved  a  direct 
numerical  simulation  and  Laser  Doppler  anemometry  of  a  turbulent  pipe 
flow  with  polymer  additives  [48].  The  results  show  that  the  viscous 
anisotropic  stresses  introduced  by  extended  polymers  play  a  key  role  in 
the  drag  reduction. 

Wall  oscillation 

Laadhari  and  his  colleagues  [49]  at  Ecole  Centrale  de  Lyon  carried 
out  an  experimental  study  to  look  at  the  problem  of  spanwise-wall 
oscillation  in  a  turbulent  boundary  layer.  This  is  to  experimentally  confirm 
the  results  of  recent  direct  numerical  simulation  suggesting  that  the 
turbulent  skin-friction  drag  can  be  reduced  by  a  wall  oscillation.  With 
detailed  measurements  using  hot-wire  anemometry  they  were  able  to  show 
that  the  mean  velocity  gradient  of  the  boundary  layer  is  reduced  near  the 
oscillating  wall.  They  also  demonstrated  that  there  are  reductions  in 
turbulence  intensities,  suggesting  that  the  skin-friction  drag  of  the 
turbulent  boundary  layer  may  be  reduced  by. the  spanwise-wall  oscillation. 

An  investigation  into  the  changes  in  the  turbulent  boundary-layer 
structure  with  a  spanwise-wall  oscillation  was  carried  out  by  Choi  et  ah 
[50,  51]  at  the  University  of  Nottingham  using  hot-wire  anemometry  and 
flow  visualization  Their  results  clearly  indicate  that  the  logarithmic 
velocity  profiles  are  shifted  upwards  and  turbulence  intensities  reduced  by 
the  spanwise-wall  oscillation.  When  the  wall  oscillation  was  optimised 
with  a  non-dimensional  wall  speed,  the  skin-friction  reductions  as  much 
as  45%  were  observed  within  five  boundary  layer  thicknesses  downstream 
of  the  start  of  wall  oscillation.  The  mechanism  of  drag  reduction  seems  to 
strongly  relate  to  the  spanwise  vorticity  generated  by  the  periodic  Stokes 
layer  over  the  oscillating  wall,  which  affects  the  boundary  layer  profile  by 
reducing  the  mean  velocity  gradient  within  the  viscous  sublayer.  The 
longitudinal  vortices  in  the  near-wall  region  are  also  realigned  into  the 
spanwise  direction,  reducing  the  intensity  of  streamwise  vorticity 
fluctuations  across  the  boundary  layer. 

The  effect  of  wall-oscillation  amplitude  on  the  total  energy  balance 
was  investigated  by  Baron  and  Quadrio  at  the  University  of  Milan  using 
a  direct  numerical  simulation  [52].  Although  no  net  savings  were  found 
when  the  amplitude  of  wall  oscillation  was  greater  than  3QJ%h,  net  energy 
savings  were  obtained  at  smaller  amplitudes.  Here,  Qx is  the  flow  rate  and 
h  is  the  half  height  of  turbulent  channel  flow.  Indeed,  there  was  up  to  10% 
of  net  energy  saving  at  the  wall -oscillation  amplitude  of  QJ4h.  This  study 
was  carried  out  at  a  fixed  non-dimensional  period  of  V  -  100,  therefore 
there  may  be  a  scope  of  further  net  energy  savings.  They  also  confirmed 
the  basic  conclusions  of  earlier  numerical  study. 

An  experimental  study  of  turbulent  pipe  flows  was  conducted  by 
Choi  and  Graham  [53]  with  a  view  to  reduce  the  friction  drag  by 


15 


oscillating  a  section  of  the  pipe  in  a  circumferential  direction.  The  results 
indicated  that  the  friction  factor  of  the  pipe  is  reduced  by  as  much  as  25% 
as  a  result  of  active  manipulation  of  near-wall  turbulence  structure  by 
circular-wall  oscillation.  An  increase  in  the  bulk  velocity  was  clearly 
shown  when  the  pipe  was  oscillated  at  a  constant  head,  supporting  the 
measured  drag  reduction  in  the  present  experiment.  The  percentage 
reduction  in  pipe  friction  was  found  to  be  better  scaled  with  the  non- 
dimensional  velocity  of  the  oscillating  wall  than  with  its  non-dimensional 
period,  confirming  a  suggestion  [50,  51]  that  the  drag  reduction  seem  to 
be  resulted  from  the  realignment  of  longitudinal  vortices  into 
circumferential  direction  by  the  wall  oscillation. 

Direct  numerical  simulation  of  turbulent  flow  in  a  rotating  pipe  was 
carried  out  by  Orlandi  at  the  University  of  Rome  [54,  55].  A  drag 
reduction  was  observed  accompanied  by  a  reduction  of  turbulent  kinetic 
energy  when  the  pipe  rotates  about  its  axis,  which  seems  to  result  from  the 
modification  of  the  vortical  structure  near  the  wall.  A  spiral  motion  is  seen 
in  the  flow  at  high  pipe  rotation,  transporting  the  streamwise  vorticity 
away  from  the  wall.  The  DNS  results  were  used  to  study  how  the  hilicity 
fluctuations,  turbulent  energy  production  and  dissipation  change  as  the 
solid  body  rotation  is  applied  to  the  pipe  flow.  The  results  seem  to  suggest 
that  the  energy  dissipation  takes  place  in  the  region  where  the  helicity 
density  is  very  low. 

DNS  studies  conduced  at  the  University  of  Madrid  on  turbulent 
boundary  layer  structure  [56-58]  seem  to  suggest  that  there  is  a 
regenerating  cycle  of  quasi-streamwise  vortices  (QSVs).  This  cycle  is 
local  to  the  near-wall  region  and  does  not  depend  on  the  outer  boundary- 
layer  structure.  The  wall  turbulence  is  maintained  by  this  regenerating 
cycle  where  QSVs  extract  energy  from  the  mean  flow  to  create  the  near¬ 
wall  streaks,  and  these  streaks  in  turn  give  rise  to  the  quasi-streamwise 
vortices.  Since  QSVs  are  directly  responsible  for  the  turbulent  skin- 
friction  drag,  attempts  have  been  made  to  weaken  these  vortices  to  obtain 
a  drag  reduction.  Jimenez  and  Pinelli  suggested  that  any  part  of  this 
regenerating  cycle  can  be  interrupted  for  a  drag  reduction,  which  is  similar 
to  an  argument  previously  put  forward  by  Choi  [59].  An  oscillating 
velocity  was  applied  to  the  near-wall  streaks  of  the  boundary  layer  in  an 
effort  to  disturb  the  cycle.  This  brought  a  decay  of  the  streaks  and 
laminarisation  of  the  boundary  layer,  supporting  the  hypothesis  being 
made.  This  numerical  experiment  is  reminiscent  of  the  spanwise-wall 
oscillation  of  the  turbulent  boundary  layer,  which  gave  a  turbulent  drag 
reduction  of  up  to  45%.  Preliminary  results  suggest  that  the  relevant  time 
scales  of  this  numerical  experiment  are  comparable  to  those  of  spanwise- 
wall  oscillation. 

Passive  porous  surface 

A  group  at  the  University  of  Warwick  investigated  into  the  effects 
of  passive  porous  walls  on  laminar-turbulent  transition  [60,  61].  This  is  the 
first  combined  theoretical  and  experimental  study  of  the  effects  of  such 
walls  similar  to  those  found  over  wings  and  in  other  aeronautical 
applications.  The  theoretical  work  suggested  that  passive  porous  walls 
with  the  appropriate  characteristics  could  have  a  markedly  favourable 
effect  on  transition,  provided  that  the  streamwise  pressure  gradient  is  not 
adverse.  Broadly,  this  conclusion  holds  for  both  two-dimensional  flows 
and  the  three-dimensional  flows  over  infinitely  swept  wedges,  the  latter 
being  a  simple  model  flow  representative  of  flows  over  swept  wings. 

The  experiments  carried  out  by  Carpenter  and  Porter  did  not  provide 
a  completely  reliable  test  of  the  theoretical  predictions.  They  did, 
however,  lead  to  the  discovery  of  a  novel  phenomenon.  For  sufficiently 
porous  walls  and  when  a  certain  threshold  flow  speed  had  been  exceeded, 
strong  highly-coherent  structures  were  self-excited  in  the  boundary  layer. 
These  appeared  to  have  the  form  of  A-vortices.  This  phenomenon  is  very 
robust  and  could  not  be  suppressed  by  modifying  the  cavity's  trailing 
edge,  installing  baffles  or  changing  the  cavity  depth.  A  simple  theoretical 
model  and  the  experimental  evidence  suggest  that  the  generation  of  the 
coherent  disturbances  is  due  to  a  feedback  mechanism,  where  the 
fluctuations  of  cavity  air  mass  generate  pressures  in  phase  with  the 
disturbance  generated  at  the  leading  edge  of  the  panel. 

Slip  wall 

For  rigid  bodies  immersed  in  a  flow,  the  non-slip  condition  must 
hold  on  the  wall  surface.  The  basic  idea  pursued  by  Bechert  at  DLR  Berlin 
was  to  release  this  non-slip  condition  in  order  to  reduce  drag  [62].  This 
was  attempted  with  a  rolling  belt  driven  by  the  wall  shear  stress  of  the 


boundary  layer  itself.  Drag  measurement  of  the  slip  wall  in  an  oil  channel 
suggests  that  there  is  as  much  as  9%  of  net  drag  reduction.  The  system  has 
a  further  scope  for  optimization,  therefore,  it  may  be  possible  to  achieve 
a  greater  drag  reduction  by  improving  the  mechanism. 

V.  CONCLUSIONS 

The  recent  developments  and  current  status  of  the  drag  reduction 
research  in  Europe  have  been  described  here  with  an  overview  of 
European  Research  Community  on  Flow,  Turbulence  and  Combustion 
(ERCOFTAC)  where  a  large  amount  of  research  work  has  been 
coordinated.  The  research  activity  in  Europe  is  unique  in  a  sense  that  the 
research  areas  are  diverse  with  a  mixture  of  new  and  traditional  themes. 
This  is  due  to  various  funding  mechanisms  available  in  Europe  mainly 
through  national  funding  schemes  in  each  country.  The  obvious 
disadvantage  for  this  arrangement  is  that  it  is  difficult  to  gather 
momentum  on  a  particular  work  as  the  research  funds  are  spread  very 
thinly  across  Europe.  ERCOFTAC’s  main  aim  is,  therefore,  to  stimulate 
coordinated  European-wide  research  efforts  on  special  topics  in  flow, 
turbulence  and  combustion,  in  which  drag  reduction  is  one  of  well 
established  subject  areas. 

The  author  would  like  to  acknowledge  the  support  from  the 
Leverhulme  Trust. 

VI.  REFERENCES 

1 .  Coustols,  E.,  “Turbulence  Control  by  Passive  Means”,  Kluwer,  1 990. 

2.  Choi,  K.-S.,  “Recent  Developments  in  Turbulence  Management”, 
Kluwer,  1991. 

3.  Prasad,  K.K.,  “Further  Developments  in  Turbulence  Management”, 
Kluwer,  1993. 

4.  Choi,  K.-S.  et  al ,  “Emerging  Techniques  in  Drag  Reduction”, 
Mechanical  Engineering  Publications,  1996. 

5.  Choi,  K.-S.,  “Breakdown  of  the  Reynolds  Analogy  over  Drag- 
reducing  Riblets  Surface”,  Appl.  Sci.  Res.,  51,  1993,  149-155. 

6.  Choi,  K.-S.  and  Orchard,  D.M.,  “The  Structure  of  Thermal  Boundary 
Layer  over  Drag-reducing  Riblets”,  Proc.  10th  European  Drag 
Reduction  Meeting,  Berlin,  1997. 

7.  Choi,  K.-S.  and  Orchard,  D.M.,  “Turbulence  Management  Using 
Riblets  for  Heat  and  Momentum  Transfer”,  Int.  J.  Exp.  Thermal 
Fluid  Set,  15(2),  1997,  109-124. 

8.  Starling,  I.  and  Choi,  K.-S.  “Non-linear  Laminar-Turbulent 
Transition  over  Riblets”,  Proc.  Laminar  Flow  Workshop ,  Queen 
Mary  and  Westfield  College,  London,  1997. 

9.  Bechert,  D.W.  et  al,  “The  Berlin  Oil  Channel  for  Drag  Reduction 
Research”,  Exp.  in  Fluids ,  12,  1992,  251-260. 

10.  Bruse,  M.  et  al.  “Experiments  with  Conventional  and  with  Novel 
Adjustable  Drag-reducing  Surfaces”  in  Near-wall  Turbulent  Flows 
(eds.  R.M.S.  So  et  al.)  Elsevier,  1993,  pp.  719-738. 

1 1 .  Bechert,  D.W.  et  al,  “Experiments  on  Drag-Reducing  Surfaces  and 
their  Optimisation  with  an  Adjustable  Geometry”,  J  Fluid  Mech. 
338, 1997, 59-87. 

12.  Bechert,  D.W.,  “Biological  Surfaces  and  their  Technological 
Application  -  Laboratory  and  Flight  Experiments  on  Drag  Reduction 
and  Separation  Control”,  AIAA  Paper  97-1960, 1997. 

13.  Luchini,  P.  et  al,  “Resistance  of  a  Grooved  Surface  to  Parallel  Flow 
and  Cross-flow”,  J.  Fluid  Mech.  228,  1991, 87-109. 

14.  Luchini,  P.  et  al. ,  “Viscous  Eddies  over  a  Grooved  Surface 
Computed  by  a  Gaussian-Integration  Galerkin  Boundary-Element 
Method”,  AIAA  J.  30(8),  1992,  2168-2170. 

15.  Luchini,  P.  and  Trombetta,  G.,  “Effects  of  riblets  upon  flow 
stability”,  Appl.  Sci.  Res.  54,  1995,  313-321. 

16.  Luchini,  P.,  Pozzi,  A.,  “Computation  of  Three-dimensional  Stokes 
Flow  over  Complicated  Surfaces  (3D  Riblets)  using  a  Boundary- 
Independent  Grid  and  Local  Corrections”,  10th  European  Drag 
Reduction  Meeting,  Berlin,  1997. 

1 7.  Baron,  A.,  “On  the  Boundary  Layer/Riblets  Interaction  Mechanisms 
and  the  Prediction  of  Turbulent  Drag  Reduction”,  International  J. 
Heat  Fluid  Flow,  14,  1993,  324-332. 

18.  Baron,  A.  and  Quadrio,  M.,  “Turbulent  Boundary  Layer  over 
Riblets:  Conditional  Analysis  of  Ejection -like  Events”,  International 
J.  Heat  Fluid  Flow,  18(2),  1997,  188-196. 


16 


19.  Baron,  A.  and  Quadrio,  M.,  “On  The  Accuracy  of  Wall  Similarity 
Methods  in  Determining  Friction  Velocity  over  Smooth  and 
Ribletted  Surfaces”,  J.  Fluids  Engr.,  Trans.  ASME ,  119(4),  1997, 
1009-1011. 

20.  Grek,  G.R.  et  al,  “Experimental  Study  of  the  Influence  of  Riblets  on 
Transition”,/.  Fluid Mech.  315,  1996,  31-49. 

2 1 .  Grek,  G.R.  et  al ,  “Effects  of  Riblets  on  Vortex  Development  in  the 
Wake  Behind  a  Single  Roughness  Element  in  the  Laminar  Boundaty 
Layer  on  a  Flat  Plate”,  La  Recherche  Aerospatiale,  1,  1996,  1-9. 

22.  Boiko,  A.V.  et  al. ,  “Transition  Control  By  Riblets  in  a  Swept  Wing 
Boundary  Layer  with  an  Embedded  Streamwise  Vortex”,  European 
J.  Mechanics,  B/Fluids ,  16(4),  1997,  465-482. 

23.  Kozlov,  V.V.,  “Effect  of  Riblets  on  Flow-structures  at  Laminar- 
turbulent  Transition  and  Simulation  of  their  Influence  on  Turbulent 
Boundary  Layer”,  Proc.  10th  European  Drag  Reduction  Meeting , 
Berlin,  1997. 

24.  DeBisschop,  J.R.  and  Nieuwstadt,  F.T.M.,  “Turbulent  Boundary 
Layer  in  an  Adverse  Pressure  Gradient”,  AIAA  J.  34(5),  1996,  932- 
937. 

25.  Choi,  K.-S.,  “Effects  of  Longitudinal  Pressure  Gradients  on 
Turbulent  Drag  Reduction  with  Riblets”  in  Turbulence  Control  by 
Passive  Means  (ed.  E.  Coustols),  Kluwer,  1990,  pp.  109-121. 

26.  Coustols,  E.  and  Savill,  M.,  “Turbulent  Skin-Friction  Drag 
Reduction  by  Active  and  Passive  Means”,  AGARD  Report  786, 
1992. 

27.  Coustols,  E.,  “Riblets:  Main  Know  and  Unknow”  in  Emerging 
Techniques  in  Drag  Reduction  (eds.  K.-S.  Choi  et  al. ),  Mechanical 
Engineering  Publications,  1996. 

28.  Choi,  K.-S.,  “Turbulent  Drag  Reduction  Strategies”  in  Emerging 
Techniques  in  Drag  Reduction  (eds.  K.-S.  Choi  et  al),  Mechanical 
Engineering  Publications,  1996. 

29.  Tardu,  S.F.  “Coherent  Structure  and  Riblets”,  Appl.  Sci .  Res.  54, 
1995,349-385. 

30.  Lucey,  A.D.  and  Carpenter,  P.W.,  “A  Numerical  Simulation  of  the 
Interaction  of  a  Compliant  Wall  and  Inviscid  Flow”,  J.  Fluid  Mech., 
234,  1992, 121-146. 

3 1 .  Carpenter,  P.W.,  “Optimisation  of  Multiple-Panel  Compliant  Walls 
for  Delay  of  Laminar-Turbulent  Transition”,  AIAA  J,  31,  1993, 
1187-1188. 

32.  Dixon,  A.E.  et  al,  “Optimisation  of  Viscoelastic  Compliant  Walls 
for  Transition  Delay”,  AIAA  J . ,  32,  1 994,  256-267. 

33.  Davies,  C.  and  Caipenter,  P.W.,  “Numerical  Simulation  of  the 
Evolution  of  Tollmien-Schlichting  Waves”,  J.  Fluid  Mech .  335, 
1997,361-392. 

34.  Cooper,  A  .J.  and  Carpenter,  P.W.,  “Stability  of  Rotating-disc 
Boundary-layer  Flow  over  a  Compliant  Wall.  Part  1.  Type  I  and  II 
Instabilities”,/.  Fluid  Mech.  350,  1997,231-259. 

35.  Cooper,  A.J.  and  Carpenter,  P.W.,  “Stability  of  Rotating-disc 
Boundary-layer  Flow  over  a  Compliant  Wall.  Part  2.  Absolute 
Instability”,/.  Fluid  Mech.  350,  1997,  261-270. 

36.  Gaster,  M.,  “Is  the  Dolphin  a  Red  Herring?”  in  Turbulence 
Management  and  Relamianalisation  (eds.  H.W.  Liepmann  and  R. 
Narasimha),  Springer- Verlag,  1987,  pp.  285-304. 

37.  Kulik,  V.M.  et  al,  “Experimental  Investigation  of  One-layer 
Viscoelastic  Coatings  Action  on  Turbulent  Friction  and  Wall 
Pressure  Pulsations”  in  Recent  Developments  In  Turbulence 
Management  (ed.  K.-S.  Choi),  Kluwer,  1991,  pp.  263-289. 

38.  Semenov,  B.N.,  “On  Conditions  of .  Modelling  and  Choice  of 
Viscoelastic  Coatings  for  Drag  Reduction”  in  Recent  Developments 
in  Turbulence  Management  (ed.  K.-S.  Choi),  Kluwer,  1991,  pp.  241  - 
262. 

39.  Kulik,  V.M.  and  Semenov,  B.N.,  “The  Measurement  of  Dynamic 
Properties  of  Viscoelastic  Materials  for  Turbulent  Drag  Reduction” 
in  Emerging  Techniques  in  Drag  Reduction  (ed.  K.-S.  Choi  et  al), 
Mechanical  Engineering  Publications,  1996,  pp.  207-217. 

40.  Choi,  K.-S.  et  al,  “Experiments  on  Turbulent  Drag  Reduction  using 
Compliant  Surface”,  Proc.  1st  Int.  Conf.  on  Flow  Interaction ,  Hong 
Kong,  1994. 

41.  Choi,  K.-S.  et  al. ,  “Turbulent  Drag  Reduction  using  Compliant 
Surfaces”,  Proc.  Royal  Society,  Ser.  A.,  453,  1997,  2229-2240. 


42.  Bannasch,  R,,  “Hydrodynamics  Of  Wave-like  Curvature  on  Bodies 
of  Swimming  Animals”,  Proc.  International  Symposium  on 
Seawater  Drag  Reduction,  Newport,  RI,  1998. 

43.  Bannasch,  R.,  “Experimental  Investigations  on  the  Boundary  Layer 
Development  in  Swimming  Penguins:  Mechanisms  of  Drag 
Reduction  and  Turbulence  Control”,  Proc.  10th  European  Drag 
Reduction  Meeting,  Berlin,  1997. 

44.  Choi,  K.-S.  et  al,  “Tests  of  Drag  Reducing  Polymer  Coated  on 
Riblet  Surface”,  Appl  Sci.  Res.  46,  1989,  209-217. 

45.  Choi,  K.-S.  et  al.,  “Drag  Reduction  with  a  Combined  Use  of  Riblets 
and  Polymer  Coating”  in  Drag  Reduction  in  Fluid  Flows  (eds. 
R.H.J.  Sellin  and  R.T.  Moses),  Ellis  Horwood,  1989,  pp.  271-277. 

46.  Choi,  K.-S.,  “Drag  Reduction  by  Riblets  for  Marine  Applications”, 
Trans.  Royal  Inst.  Naval  Arch.,  PartB,  133,  1991,  129-143. 

47.  Orlandi,  P.,  “Tentative  Approach  to  the  Direct  Simulation  of  Drag 
Reduction  by  Polymers”,  J.  Non-Newtonian  Fluid  Mech.  60(2/3), 
1995,277-301. 

48.  DenToonder,  J.M.J.  et  al,  “Drag  Reduction  by  Polymer  Additives 
in  a  Turbulent  Pipe  Flow”,  J.  Fluid  Mech.  337,  1997,  193-231. 

49.  Laadhari,  F.  et  al,  “Turbulence  Reduction  in  a  Boundary  Layer  by 
a  Local  Spanwise  Oscillating  Surface”,  Phys.  Fluids,  A6(10),  1994, 
3218-3220. 

50.  Choi,  K.-S.  et  al,  “Turbulent  Boundary-Layer  Control  by  Means  of 
Spanwise-wall  Oscillation”,  AIAA  Paper  97-1795,  presented  at  the 
28th  AIAA  Fluid  Dynamics  Conf.,  Snowmass,  Co.,  USA,  1997. 

51 .  Choi,  K.-S.  et  al,  “Turbulent  Boundary-Layer  Control  by  Means  of 
Spanwise-Wall  Oscillation”,  to  appear  in  AIAA  /.,  1998. 

52.  Baron,  A.,  and  Quadrio,  M.,  “Turbulent  Drag  Reduction  by 
Spanwise  Wall  Oscillations”,  Appl.  Sci.  Res.,  55,  1996,  311-326. 

53.  Choi,  K.-S.  and  Graham,  M.,  “Drag  Reduction  of  Turbulent  Pipe 
Flows  by  Circular-wall  Oscillation”,  Phys.  Fluids,  10(1),  1998,  7-9. 

54.  Orlandi,  P.  and  Fatica,  M.,  “Direct  Simulations  of  Turbulent  Flow  in 
a  Pipe  Rotating  about  its  Axis”,  /.  Fluid  Mech.  343,  1997,  43-72. 

55.  Orlandi,  P.,  “Helicity  Fluctuations  and  Turbulent  Energy  Production 
in  Rotating  and  Non-Rotating  Pipes”,  Phys.  Fluids  9(7),  1997,  2045- 
2056. 

56.  Jimenez,  J.  and  Pinelli,  A.,  “Controlling  the  Structures  of  the 
Turbulent  Wall  Region”,  Proc.  Euromech  Colloquium  -  361,  Berlin, 

1997. 

57.  Jimenez,  J.  and  Pinelli,  A.,  “Wall  Turbulence:  How  It  Works  and 
How  to  Damp  It”,  AIAA  Paper  97-2112,  1997. 

58.  Jimenez,  J.  and  Pinelli,  A.,  “The  Role  of  Coherent  Structure 
Interactions  in  the  Regeneration  of  Wall  Turbulence”,  Proc.  7th 
European  Turbulence  Conference,  Saint  Jean  Cap  Ferrat,  France, 

1998. 

59.  Choi,  K.-S.,  “Near-wall  Structure  of  Turbulent  Boundary  Layer  with 
Riblets”,/  Fluid  Mech.,  208,  1989,  417-458. 

60.  Carpenter,  P.W.  and  Porter,  L.J.,  “Further  Developments  in  the  Use 
of  Passive  Porous  Walls  for  Drag  Reduction”,  Proc.  9,h  European 
Drag  Reduction  Meeting,  Naples,  1995. 

61 .  Carpenter,  P.W.,  “The  Feasibility  of  Using  Passive  Porous  Walls  for 
Drag  Reduction”  in  Emerging  Techniques  in  Drag  Reduction  (eds. 
Choi,  K.-S.  et  al).  Mechanical  Engineering  Publications,  1996. 

62.  Bechert,  D.W.  et  al,  “Drag  Reduction  with  The  Slip  Wall”,  AIAA  J. 
34(5),  1996,  1072-1074. 


17 


DRAG  REDUCTION  RESEARCH  IN  JAPAN 


Keizo  Watanabe 

Department  of  Mechanical  Engineering 
Tokyo  Metropolitan  University 
1-1,  Mmami  Ohsawa,  Hachiooji-shi,  Tokyo,  192-0397 
keizo@ecomp  metro-u.ac.jp 


Abstract  -  This  paper  is  a  review  of  recent  water  drag  reduction  research  and 
its  practical  applications  proposed  in  Japan.  The  methods  of  drag  reduction  which 
are  the  subjects  of  this  research  are  surfactant  additives,  bubble  mixing  and  highly 
water-repellent  walls.  Problems  that  may  arise  in  industrial  applications  are  examined. 


I.  INTRODUCTION 

Since  the  reduction  of  friction  in  turbulent  flow  was 
first  achieved  by  Toms  [1]  in  1948,  much  of  the  reported 
work  on  drag  reduction  has  been  related  to  hydrodynamic 
drag  reduction  using  polymer  additives.  In  spite  of  extensive 
research  on  drag  reduction,  industrial  applications  are  few 
because  of  the  degradation  of  polymer  solutions,  such  as 
the  breakdown  of  polymer  molecules  by  mechanical  shearing 
of  the  flow  fields.  Of  the  various  types  of  drag  forces  which 
arise,  viscous,  or  skin  friction,  drag  is  one  of  the  most 
significant.  The  reduction  of  drag  is  important  from  the 
point  of  view  of  conserving  energy. 

After  the  oil  shock  in  1970,  drag  reduction  research 
led  to  the  discovery  of  new  merits  in  application,  and  new 
drag  reduction  techniques  were  reported.  For  example,  the 
effects  of  longitudinally  ribbed  surfaces  on  drag  were  studied 
in  an  attempt  to  contain  wall  bursts,  and  the  results  indicated 
that  drag  reductions  as  large  as  7%  occur  with  certain 
V-groove  riblets. 

Drag  reduction  has  recently  been  associated  with  the 
reduction  of  carbon  gas  emissions  which  are  linked  to  global 
warming,  and  industrial  application  of  drag  reduction  for 
such  purposes  has  been  expected. 

In  this  paper,  the  current  research  on  drag  reduction 
in  Japan  is  reviewed  and  potential  industrial  applications 
are  surveyed  and  future  research  directions  are  discussed. 

fl  .  CLASSIFICATION  OF  DRAG  REDUCTION 

We  can  classify  drag  reduction  according  to  the  flow 
behavior  and  the  method  used,  as  shown  in  Fig.  1.  It 
is  well-known  that  hydrodynamic  drag  reduction  using  a 
mixture  of  bubbles  and  fine  solid  particles  is  achieved  through 
laminar  flow  control,  wherein  the  transition  from  laminar 
to  turbulent  flow  is  delayed  such  that  it  occurs  at  a  higher 
Reynolds  number.  Generally,  examination  of  the  characteristics 
of  drag  reduction  and  fluid  flow  is  required  to  enable  the 
application  of  drag  reduction  to  fluid  engineering  technology. 

In  many  of  these  practical  applications,  the  importance 
of  polymer  degradation  has  been  recognized  but  only  a  limited 
amount  of  data  on  it  is  available.  Thus  there  are  high 
expectations  from  the  methods  which  involve  surfactant  addition, 
bubble  mixtures  and  highly  water-repellent  coatings  for  drag 
reduction. 


[5]  .  Although  work  on  the  characteristics  of  surfactant 
solutions  is  still  basic,  it  is  necessary  to  develop  new  surfactant 
additives  in  order  to  use  high-density  thermal  energy 
transportation  in  a  wide-area  energy  supply  network  system. 

It  is  important  to  create  a  municipal  energy  system 
with  low  environmental  load  to  allow  the  coexistence  of 
urban  as  well  natural  environments  along  with  human  activity. 
Under  these  circumstances,  the  energy  supply  network  system. 
The  Eco -Energy  City  Project  which  is  part  of  the  New 
Sunshine  Project  of  the  Agency  of  Industrial  Science  and 
Technology  within  the  Ministry  of  International  Trade  and 
Industry,  is  being  developed  in  Japan  [6]  .  The  New  Energy 
and  Industrial  Technology  Development  Organization  (NEDO) 
assigned  the  research  and  development  to  the  Energy 
Conservation  Center,  Japan,  for  the  period  from  fiscal  1993 
to  2000.  Thus  we  anticipate  a  practical  application  of  surfactant 
solutions  for  reduction  of  the  pumping  costs  of  the  transport 
station  in  this  system 

Figure  2  shows  the  schematic  of  one  possible  example 
for  such  a  reduction  of  pumping  energy  costs  in  this  project. 
The  development  of  a  vacuum  thermally-insulated  heat  transport 
piping  system  will  enable  high-efficiency  heat  transport  and 
help  realize  the  cascade  use  of  heat  in  industrial  areas 
and  the  transport  of  heat  derived  from  waste  heat  to 
heat-requiring  areas,  thus  contributing  to  the  effective  use 
of  waste  heat  while  promoting  energy-savings  and  reducing 
environmental  problems.  As  described  above,  the  practical 
application  of  drag  reduction  by  surfactant  addition  is  related 


-(Turbulent  Flow] 

-(Addition  or  Mixture] 

1 .  High-Molecular— Weight  Polymer 

2.  Surfactant 

3.  Bubble 

4.  Fine— Solid— Particle 

5.  Fiber 


|  Drag  Reduction  1 — i 


H  Surface] 


1.  Riblets 


fll.  APPLICATION  OF  DRAG  REDUCTION 

(1)  Surfactant  additives 

Experimental  results  on  drag  reduction  by  the  addition 
of  surfactants  have  been  reported  for  a  method  of  predicting 
the  drag  that  reduces  pipe  flow  J2]  ,  the  characteristics  of 
low-speed  streaks  in  turbulent  channel  flow  [3]  ,  the  flow 
resistance  and  heat  transfer  of  cold  water  pipe  flow  [4] 
and  the  possibility  of  actively  controlling  reduced  drag  flow 


‘ — [Laminar  Flow! 

L-j  Surfeit 

1.  Highly  Water— Repellent  Wall 


Fig.  1  Classification  for  Drag  Reduction 


19 


Fig.  2  Heat  Transport  Systems  with  Vacuum  Thermally-Insulated  Heat  Transport  [6] 


to  the  reduction  of  the  pressure  loss  of  waste  heat  200^' 
or  lower,  from  various  sources,  during  its  transport  to  areas 
requiring  heat,  through  the  use  of  highly-insulated  heat  transport 
piping. 

It  is  well-known  that  special  kinds  of  surfactants  that 
form  rodlike  micelles,  are  also  effective  for  the  drag  reduction 


l.Pump  2. Motor  3. Honeycomb  4. Diffuser 
5. Gauze  screen  6. Bubble  generator  7. Nozzle 
8. Reservoir  tank  9.  Orifice 

Fig.  3  Test  Tunnel  [7] 


of  turbulent  flow.  However,  there  is  the  problem  that  the 
water  mixed  with  such  a  surfactant  cannot  be  discarded 
freely  because  of  its  toxicity  and  the  corrosive  property  of 
halide  ions. 

If  new  surfactants  which  can  prevent  the  aggregation 
of  ice  and  plugging  due  to  ice  slurry  in  pipes,  can  he 
developed,  they  may  be  put  to  use  for  easy  heat  storage 
at  low  temperatures  as  well  as  high-density  thermal  energy 
transportation,  in  the  future. 


Fig.  4  Drag  Coefficient  Distribution  Associated 
with  Void  Fraction  [7] 


20 


Fig.  5  Schematic  of  3-Dimensional  Models  [10] 


Fig.  6  Details  of  Part  A  in  the  Model  [10] 


without  bubbles 


(top  :  without  bubbles,  bottom  :  with  bubbles 
flow  rate:  6.5  x  10  * m3/s,  gauge  pressure:  2 
kgf/cm2,  F„  =  0.28 1(1.6  m/s) 

Fig.  7  Bow  Wave  Patterns  around  Navigating  Ship  [10] 


(2)  Bubble  mixing  or  injection 

The  study  of  drag  reduction  of  a  bubbly  flow  has 
been  reported  for  flows  around  a  circular  cylinder  [7]  .  Figures 
3  and  4  show  the  test  tunnel  used  in  the  experiment 
and  the  experimental  result  of  drag  coefficient  distribution 
associated  with  void  fraction,  respectively.  The  diameter  of 
the  test  cylinder  is  20mm  and  the  experiment  was  performed 
in  the  regions  where  the  Reynolds  number  was  in  the 


poo  (J  oo 


Air  Injection 


Spoiler 


Sailing  Body 


/Water  Surface 


U°°+  u« 


Fig.  8  Principle  of  Drag  Reduction  for  the  Model  [11] 


_  24.0 

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CO 

£  12.1 
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0) 

£  8-° 
CO 

°  4.0 
0 


:m 

T 

TTTT\ 

TTTTJ 

1 1 1 1  p= 

- 

S 

w 

6  [deg.] 

- 

_ 

A 

0.03 

5 

- 

— 

o 

0.03 

15 

— 

— 

• 

0.05 

15 

□  — 

_ 

rr 

0.03 

20 

- 

jj 

0.05 

20 

□  — 

— 

c 

f 

— 

□D 

/.* 

- 

□D«» 

™  w  — — 

• 

•  .  A — 

'LLL- 

llI 

i  in^  oft  l^jLilr 

0  0.5  1.0  1.5  2.0 

Flow  Velocity(m/s] 


Fig.  9  Drag  Reduction  Ratio  [11] 


4  5 

range  of  1.1x10  to  3.5x10  and  the  void  fraction  was  is 
the  range  of  0  to  8%.  In  Fig.4,  a  drag  reduction  of  up 
to  50%  is  shown  at  a  velocity  of  4m/s  and  a  void  fraction 
of  4%.  The  reduction  occurs  in  the  unstable  laminar  boundary 
layer  and  the  point  of  separation  of  the  flow  around  the 
circular  cylinder  then  moves  downstream  from  the  midsection 
due  to  bubble  mixing.  In  the  case  of  for  fine  solid  particle 
suspensions,  it  has  been  reported  that  a  similar  drag  reduction 
phenomenon  occurs  in  flows  around  a  sphere  [8]  or  a  circular 
cylinder  [9]  in  dilute  carbon  black  suspensions. 

We  can  expect  the  practical  application  of  the  injection 
of  microbubbles  into,  or  covering  microbubbles  over  the  surface, 
of,  a  body  immersed  or  floating  in  fluid  flow,  for  drag 
reduction.  Doi  et  al.  [  10]  formed  a  microbubble  covering 
by  injecting  air  through  a  porous  pipe  with  pore  size  of 
15  ii  m. 

Figures  5  and  6  show  the  overall  view  of  the  3-dimensional 
model  of  a  cylindrical  body  and  the  details  of  the  experimental 
apparatus,  respectively.  In  Fig.  5,  microbubbles  are  injected 
through  the  porous  pipe,  and  the  drag  of  the  model  is 
measured  by  a  load  cell  which  is  set  at  the  column  as 
shown  in  Fig.  6.  They  studied  the  effects  of  the  microbubble 
injection  on  wave-making  resistance  by  visualizing  the  bow 
wave  patterns.  Figure  7  shows  these  bow  wave  patterns 
around  the  bows  of  a  navigating  ship  model  in  a  towing 
tank.  There  are  very  few  differences  observed  between  the 
wave  patterns  of  Figs  7(a)  and  7(b).  They  reported  that 
it  is  possible  to  reduce  the  resistance  of  a  3-dimensional 
body  by  using  microbubbles  if  the  body  is  well  covered 
by  microbubbles.  They  found  that  the  local  frictional  resistance 
is  reduced  by  more  than  20%  when  microbubbles  cover 
the  body,  although  the  wave-making  resistance  increases  slightly 
when  microbubbles  are  injected.  The  total  resistance  is  reduced 
by  more  than  5%. 


21 


Fig.  11  Moment  Coefficient  of  an  Enclosed  Rotating  Disk  [14] 

On  the  other  hand,  the  expansion  of  air  entrained 
in  the  water  flow  generates  a  high-speed  two-phase  water 
jet  and  drag  reduction  of  a  ships  hull  is  caused  by  this 
reaction  force.  Therefore,  fluid  drag  can  be  reduced  without 
the  addition  of  external  energy.  The  principle  of  drag  reduction 
of  a  ship’s  hull,  which  is  achieved  by  injecting  air  under 
atmospheric  pressure  into  the  water  flow,  has  been  proposed 
by  Tsutahara  and  Sakamoto  [11]  .  The  principle  of  drag 
reduction  in  the  proposed  model  is  shown  in  Fig.  7. 
Although  the  principle  of  the  acceleration  of  water  flow 
is  similar  to  that  in  an  underwater  ramjet  [12]  ,  it  has 
not  been  reported  in  the  literature  as  a  drag  reducing 
system. 

Their  experimental  setup  consists  of  a  spoiler  located 
at  the  bottom  of  the  propulsion  equipment,  a  sailing  body 
and  an  air  injection  nozzle  as  shown  in  Fig.  8.  Three 
types  of  sailing  bodies  with  different  spoilers  were  set  in 


00 


Fig.  12  Micrographs  of  the  Highly  Water-Repellent  Wall 

a  towing  tank,  and  the  amount  of  drag  reduction  was  determind 
using  various  parameters  such  as  sailing  velocity,  opening 
angle  of  the  rear  plate,  and  the  depth  of  the  sailing  body 
in  the  water.  Figure  9  shows  an  example  of  the  experimental 
results.  It  is  seen  that  the  drag  decreases  monotonically 
with  increasing  sailing  velocity  and  increasing  opening  angle 
of  the  rear  plate. 

(3)  Highly  water-repellent  wall 

The  initial  experiments  to  clarify  laminar  skin  friction 
reduction  were  conducted  in  the  spring  of  1994  by  Watanabe 
et  al.  [13]  using  ducts  with  highly  water-repellent  walls. 
Figure  10  shows  an  example  of  the  experimental  results 
of  the  friction  factor  obtained  in  the  study.  X  and  Re  are 
the  friction  factor  of  the  duct  and  the  Reynolds  number, 
respectively,  e  is  the  aspect  ratio,  and  its  value  for  a 
square  duct  is  e  =1.  It  was  seen  that  drag  reduction  occurs 
in  the  laminar  region  and  the  drag  reduction  ratio  of  the 
square  duct  is  about  22%. 

Figure  11  shows  the  experimental  results  of  moment 
coefficient  of  an  enclosed  rotating  disk  [14]  with  highly 
water-repellent  wall  in  tap  water.  In  the  case  of  the  highly 
water-repellent  wall  disk,  the  moment  coefficient  decreased 
compare  with  that  of  smooth  plane  disk,  and  the  value 
of  drag  reduction  rate  increases  progressively  with  increasing 
the  clearance  ratio  (s/a).  We  can  reduce  the  disk  friction 
loss  of  an  impeller  and  the  skin  friction  of  casing  of  a 
turbomachine  by  applying  the  highly  water-repellent  coating. 

The  aim  of  the  experiment  was  to  investigate  what 
kind  of  solid  surface  would  exhibit  fluid  slip  with  significantly 
less  skin  friction  than  a  smooth  wall.  In  general,  the  largest 
contact  angles  recorded  for  a  smooth  surface  are  1 12° 
~115°  .  Thus  we  need  a  useful  method  for  producing  a 


22 


Fig.  13  Model  of  Drag  Reduction  Systems  for  a  Ship  [18] 


surface  with  a  contact  angle  of  120°  or  larger,  since  it 
is  necessary  not  only  to  reduce  the  free  surface  energy 
but  also  to  change  the  surface  morphology.  Figures  12(a) 
and  12(b)  show  micrographs  of  the  tested  highly  water-repellent 
wall  obtained  using  a  microscope  and  a  SEM.  The  surface 
has  many  narrow  grooves  that  increase  the  water  repellency. 

Drag  reduction  of  a  circular  pipe  [15]  and  two  coaxially 
rotating  cylinders  [16]  has  been  reported.  Then,  it  was 
experimentally  shown  that  fluid  slip  [17]  occurs  at  the  wall. 
We  conclude  that  fluid  slip  described  in  that  paper  occurs 
due  to  the  existence  of  air  in  the  grooves,  as  shown  in 
Fig.  6(b).  In  other  words,  water  cannot  come  into  contact 
with  the  wall  because  of  the  surface  tension  when  air 
exists  in  the  grooves.  Thus  it  can  be  inferred  that  drag 
reduction  is  poor  in  the  case  of  the  flow  of  surfactant 
solutions  having  low  surface  tension. 

Since  certain  highly  water-repellent  walls  can  reduce 
laminar  flow  friction  in  both  internal  and  external  flows, 
it  is  expected  that  they  would  affect  the  heat  exchanger 
or  the  ship’s  performance.  For  the  heat  exchanger  of  a 
car,  down-sizing  and  efficient  operation  are  necessary  to  reduce 
fuel  consumption.  Since  flow  in  the  tube  of  the  heat  exchanger 
is  laminar,  the  industrial  application  of  coatings  is  well  within 
the  bounds  of  the  possibility  of  efficiency  improvement. 

A  practical  application  in  the  case  of  an  external 
flow  is  for  the  reduction  of  the  skin  friction  which  contributes 
to  about  60%  of  the  total  drag,  of  a  ship.  Greater  drag 
reduction  in  the  friction  of  a  ship  may  be  achieved  with 
a  system  that  combines  bubbly  flow  for  the  bottom  of  a 
ship  with  highly  water-repellent  walls.  Figure  13  shows 
a  model  of  drag  reduction  for  such  a  system  [18]  developed 
by  Mitsui  Engineering  &  Shipbuilding  Co..  The  bottom  of 
the  ship  is  coated  with  a  highly  water-repellent  material 
and  air  is  supplied  by  a  compressor  located  in  the  ship. 
Tests  using  a  model  have  been  carried  out,  and  the  performance 
test  for  a  real  ship  may  be  conducted  in  two  or  three 
years.  Although  the  problem  of  coating  durability  still  remains, 
drag  reduction  of  a  ship  is  one  of  the  interesting  potential 
applications  of  drag  reduction  techniques. 

IV.  CONCLUSIONS  N 

Drag  reduction  techniques  have  been  applied  to  few 
industrial  applications  because  the  utility  is  still  limited  in 
terms  of  the  flow  range  or  the  cost  performance.  Surfactant 
addition  or  bubble  mixing  in  liquids  and  the  use  of  highly 
water-repellent  walls  can  be  expected  to  be  increasingly  applied 
to  industrial  and  actual  flow  fields  in  the  future.  However, 
it  must  be  emphasized  that  we  should  also  develop  and 
study  effective  new  drag  reduction  methods. 


V.  REFERENCES 

1 .  B..  A.  Toms  “Some  Observations  on  the  Flow  of  Linear 
Polymer  Solution  through  Straight  Tube  at  Large  Reynolds 
Numbers”,  Proceedings  of  the  First  International  Congress 
on  Rheology,  July  1948. 

2.  H.  Usui,  T.  Itoh  and  T.  Saeki  “Drag  Reduction  Pipe 
Flow  of  Surfactant  Solutions”,  Proceedings  of  the  ASME  Fluids 
Engineering  Division,  FED-Vol.  237,  July  1996  pp.  159-163. 

3.  M.  Itoh,  S.  Tmao  and  K  Sugiyama  “Characteristics  of 
Low-Speed  Streaks  in  the  Flow  of  Drag-Reducing  Surfactant 
Solution”,  Transaction  of  the  JSME,  Series  B,  Vol.  63,  No. 
605,  August  1997,  pp.40-46  (in  Japanese). 

4.  H.  Iaba  and  N.  Haruki  “Flow  Resistance  and  Heat  Transfer 
Characteristics  of  Cold  Water  Pipe  Flow  with  Surfactant 
for  Cold  Heat  Energy  Transport”,  Transaction  of  the  JSME, 
Series  B,  Vol.  63,  No.  608,  October  1997,  pp.  1336-1343 
(in  Japanese). 

5.  Y.  Kawaguchi  et  al.  “Active  Control  of  Turbulent  Drag 
Reduction  in  Surfactant  Solutions  by  Wall  Heating”,  Proceedings 
of  the  ASME  Fluids  Engineering  Division,  FED-Vol.  237, 
July  1996  pp.  47-52. 

6.  Report  on  Element  Technology  Development  Program,  NEDO 
&  ECC,  1997. 

7.  Y.  Ichikawa,  K.  Sugiyama  and  Y.  Matsumoto  “Characteristics 
of  Bubbly  Flow  around  a  Circular  Cylinder”,  Proceedings 
of  Symposium  on  Multiphase  Flow  ’95,  July  1995,  pp.  132-135 
(in  Japanese). 

8.  K  Watanabe  and  H.  Kui  “Drag  of  a  Sphere  in 

High-Reynolds-Number  Range  in  Water/Fine  Solid  Particle 
Suspension”,  Proceedings  of  the  ASME  Fluids  Engineering 
Division,  FED-Vol.  221,  August  1995,  pp. 127-132. 

9.  K.  Watanabe,  Y.  Chang  and  T.  Fujita  "Drag  Reduction 

in  Flow  Past  a  Circular  Cylinder  in  Water/Fine  Solid  Particle 
Suspension”,  Trans,  of  the  JSME,  Series  B,  November  1996, 
Vol.  62,  No.  603,  pp.  3818-3823  (in  Japanese). 

10.  Y.  Doi,  K.  Mori  and  T.  Hatta  “Frictional  Drag  Reduction 
by  Microbubbles”,  Journal  of  Soc.  Naval  Arch,  of  Japan, 
July  1991,  Vol.  170.  pp.  55-63  (in  Japanese). 

11.  M.  Tsutahara  and  M.  Sakamoto  M.  “Study  of  Drag 

Reduction  on  Ship  Hull  by  Expansion  of  Entrained  Air  in 

Water  Flow”,  Trans,  of  the  JSME,  Series  B,  Vol.  .61,  N 
o.  586,  June  1995,  pp.  2088-2094  (in  Japanese). 

12.  E.  Motlard  and  C.  J.  Shoemaker  “Preliminary  Investigation 
of  an  Underwater  Ramjet  Powered  by  Compressed  Air”,  NASA 
Tech.  N.,  D-991,  1961,  pp.1-36. 

13.  K  Watanabe,  Yanuar,  K  Okido  and  H.  Mizunuma  "Drag 
Reduction  in  Flow  through  Square  and  Rectangular  Ducts 
with  Highly  Water  Repellent  Wall”,  Proceedings  of  the  ASME 
Fluids  Engineering  Division,  FED  Vol.  237,  July  1996,  pp. 
115-119. 

14.  K  Watanabe  and  S.  Ogata  "Drag  Reduction  for  a  Rotating 
Disk  with  Highly  Water  Repellent  Wall”,  Proceedings  of  the 
ASME  Fluids  Engineering  Division,  FEDSM-3380,  June  1997, 
pp.  1-5. 

15.  K.  Watanabe,  Yanuar  and  H.  Udagawa  ”Drag  Reduction 
of  Newtonian  Fluids  in  a  Circular  Pipe  with  Highly  Water 
Repellent  Wall”,  Proceedings  of  3rd  International  Symposium 
on  Performance  Enhancement  for  Marine  Applications,  May 
1997,  pp.  157-162. 

16.  K.  Watanabe  and  T.  Akino  "Drag  Reduction  in  Laminar 
Flow  between  Two  Coaxial  Cylinders”,  Proceedings  of  the 
ASME  Fluids  Engineering  Division,  June  1998,  pp.  1-6. 

17.  K.  Watanabe,  Yanuar  and  H.  Mizumuma  "Slip  of  Newtonian 
Fluids  at  Solid  Boundary”,  Proceedings  of  International 
Conference  on  Fluid  and  Thermal  Energy  Conversion  ’97, 
July  1997,  pp.  401-406. 

18.  Asahi  Shinbun,  March  27,  1997  (in  Japanese). 


23 


Wall  Turbulence  Physics 


25 


Near  wall  turbulence:  a  rememberance  of  Steve  Kline 


by 

Brian  Cantwell 

Department  of  Aeronautics  and  Astronautics 
Stanford  University 
Stanford,  CA  94305 


Abstract 

I  would  like  to  thank  the  organizers  of  this  meeting  for  inviting  me  to  speak  on  the  subject  of  wall  turbulence  and 
in  memory  of  my  good  friend  and  Stanford  colleague  Steve  Kline.  My  presentation  today  is  not  intended  to  be  a  tribute 
to  Steve.  For  that  I  highly  recommend  the  article  by  Bob  Dean  which  appeared  in  the  March  1998  issue  of  the  Journal  of 
Fluids  Engineering  [1].  I  could  not  be  more  eloquent!  Rather,  I  would  like  to  use  the  opportunity  to  recall  my 
acquaintance  with  Steve  Kline  and  his  work  on  wall  turbulence  and  to  review  our  common  and  differing  views  of  the 
subject. 


Our  acquaintance 

It  is  fitting  that  Steve  Kline  is  remembered  at  a 
meeting  where  the  subject  is  that  which  was  nearest  and 
dearest  to  his  heart.  Steve  made  pioneering 
contributions  to  our  knowledge  of  the  stability  of  flow 
in  wide  angle  diffusers  and  the  development  of  standards 
for  measurement  accuracy.  His  fluid  mechanics  film  on 
flow  visualization  is  one  of  the  classics.  In  his  later 
years  he  wrote  prolifically  and  provocatively  on  the 
relationship  between  innovation  and  technology.  But  it 
was  the  structure  of  turbulence  near  a  wall  which  held 
his  constant  interest  for  over  forty  years  virtually  up  to 
the  last  days  before  his  death.  Watching  him  struggle 
through  his  difficult  illness  oyer  the  past  several  years, 
with  his  health  improving  at  times  and  then  worsening, 
I  was  convinced  that  part  of  the  reason  he  survived  so 
long  was  simply  that  he  still  had  work  to  do  -  the 
problem  of  turbulence  was  not  yet  solved!  At  one  point 
about  a  year  and  a  half  ago  I  visited  him  at  home  during 
a  particularly  bad  stretch.  He  had  called  me  on  a  Sunday 
afternoon  and  asked  me  to  come  over  not,  it  turned  out, 
to  commiserate  about  his  illness  but  to  discuss  a  series 
of  technical  reports  written  by  an  young  entrepreneur 
whom  he  had  been  mentoring.  At  the  end  of  an 
afternoon  of  technical  discussions  we  said  our  goodbyes 
and  I  think  both  of  us  felt  that  we  would  not  see  each 
other  again.  In  fact  he  rallied  from  that  episode  and  I 
visited  him  several  more  times  in  similar  circumstances 
until  his  death  about  a  year  later.  Throughout  this 
difficult  period  I  could  not  help  but  stand  in  amazement 
at  his  tenacious  dedication  to  his  research. 

I  first  got  to  know  Steve  when  I  came  to  Stanford 
in  1978.  He  was  in  the  throes  of  organizing  a  follow- 
on  to  the  1968  Stanford  Conference  on  turbulent 
boundary  layers  -  the  first  Kline  Olympics  [2].  The  new 
conference  had  a  much  more  ambitious  theme  to 
consider:  the  computation  of  complex  turbulent  flows. 


As  always,  Steve  was  thinking  in  totally  new  ways  and 
he  conceived  a  conference  which  which  would  actually 
run  over  two  years  with  data  presented  in  the  first 
conference  and  computed  results  presented  a  year  later, 
including  computations  of  hidden  cases  with  data  which 
was  to  be  taken  in  the  intervening  year.  The  result  was 
the  1980-81  Stanford- AFOSR  Conference  on  Complex 
Turbulent  Flows  -  the  second  Kline  Olympics  [3].  One 
of  Steve's  requirements  for  the  conference  was  the 
creation  of  a  digital  data  library  of  critically  evaluated 
cases  which  was  also  a  relatively  new  idea  at  the  time. 
The  results  of  the  conference  were  mixed.  What  was 
clear  was  that,  at  that  point  in  time,  there  was  no  way 
to  fully  distinguish  between  model  errors  and  numerical 
errors.  Grids  were  too  coarse  and  solvers  did  not  have 
adequate  accuracy.  So  the  original  goal  to  evaluate 
models  was  never  realized.  Nevertheless  the  conference 
presented  a  clear  picture  of  the  state-of-the-art  at  the 
time  and  Kline's  ideas  about  zonal  modeling  which 
were  set  forth  at  that  conference  have  wound  their  way 
into  many  of  the  advances  in  turbulence  modeling  since 
that  time.  Both  the  68  and  80-81  conferences  were 
quintessential  examples  of  Steve’s  intellectual 
leadership.  This  is  where  his  loss  will  be  felt  most 
acutely  by  the  turbulence  community. 

Kline's  work  on  near  wall  turbulence 

Although  I  met  Steve  in  1978,  I  knew  of  his 
work  much  earlier.  Don  Coles  and  I  had  been  doing 
some  research  at  Caltech  on  turbulent  spots,  measuring 
the  ensemble-averaged  large  scale  structure  [4].  In  the 
process,  we  did  some  visualization  and  scaling  of  the 
sublayer  streaks  beneath  the  spot.  Don  referred  to  the 
normalization  of  the  sublayer  structure  as  "Kline 
scaling"  and  I  was  prompted  to  go  back  and  read  Kline's 
classic  1959  and  1967  papers  on  the  visualization  of 
the  sequence  of  events  surrounding  bursting  [5],  [6]. 
The  results  of  this  work  are  well  known  to  everyone 


29 


here  and  so  I  will  not  spend  a  lot  of  time  repeating 
them.  Kline's  sketches  of  what  they  saw  in  their 
visualizations  have  been  reproduced  in  a  number  of 
papers  including  by  1981  Annual  Reviews  paper  [7]. 
Rather,  I  would  like  to  take  the  opportunity  to  briefly 
consider  what  the  real  significance  of  this  work  was  and 
why  it  inspired  so  much  research  that  followed.  In  the 
mid  1950’s  the  prevailing  picture  of  turbulence  was  in 
fact  no  picture  at  all!  What  I  mean  by  this  is  that  no 
one  had  seriously  considered  that  turbulence  might  be 
something  that  was  picturable.  Townsend  had  used 
correlation  data  to  sketch  the  mean  large  scale  motion 
in  shear  layers  and  wakes  and  deserves  credit  as  the  first 
to  clearly  show  that  part  of  the  turbulent  motion  is 
coherent.  But  Kline  went  a  step  further  and  recognized 
that  the  instantaneous  motion  was  an  important  object 
of  study.  He  had  developed  hydrogen  bubble 
visualization  methods  was  able  to  use  this  technique  to 
discover  basic  flow  elements  of  turbulence  in  the 
sublayer.  Kline  was  willing  to  directly  address  the 
dynamics  of  turbulent  motion  on  its  own  terms.  This 
was  a  turning  point  in  turbulence  research  which  then 
began  to  emphasize  the  use  of  visualization  as  a 
primary  measurement  tool.  This  emphasis  persists 
today  in  the  way  we  use  DNS  data  and  PIV 
measurements  to  enhance  our  understanding  of  the 
physics  of  turbulence. 

During  the  1960's  and  70’s  dozens  of  papers  were 
published  devoted  to  the  visual  identification  of 
turbulent  structure  in  an  effort  to  fill  out  and 
unambiguously  define  the  picture  of  wall  structure  and 
especially  the  dynamics  of  the  bursting  process  which 
was  known  to  be  a  primary  contributer  to  the  Reynolds 
stress  in  the  near  wall  region.  A  wide  variety  of 
techniques  were  developed,  some  based  on  direct 
visualization,  some  on  sophisticated  methods  of 
processing  records  of  instantaneous  velocity  data.  By 
the  late  1970's  low  Reynolds  number  simulation  data 
began  to  be  available.  But  as  the  research  proliferated  a 
variety  of  competing  pictures  of  the  turbulent  motion 
began  to  emerge.  By  the  mid  1980's  it  was  clear  that 
the  whole  effort  was  not  converging.  Researchers 
looking  at  the  same  flow  were  seeing  different  things 
and  having  a  hard  time  understanding  one  another.  The 
whole  subject  was  in  danger  of  descending  to  the  level 
of  what  Feynman  once  called  "cargo  cult  science" 
where,  in  the  absence  of  fundamental  understanding,  the 
mere  association  of  events  in  time  or  space  is  used  to 
infer  cause  and  effect. 

This  prompted  Kline  in  the  late  1980's  to 
undertake,  with  his  student  Steve  Robinson,  a  study  of 
all  the  different  pictures  that  people  were  using.  The 
idea  was  to  reconcile  them  and  to  see  if,  at  the  end  of 
the  day,  one  overall  picture  would  emerge.  The  first 
step  was  to  survey  all  the  workers  in  the  field  and  to 
produce  a  kind  of  taxonomy  of  turbulent  structure.  At 
first  I  had  misgivings  about  the  whole  approach  which 
looked  to  me  like  science  carried  out  by  vote.  In  fact 


they  carried  out  a  rigorous  study  and  in  the  end  a  good 
many  scientific  issues  were  resolved.  They  included  in 
their  study  the  turbulent  boundary  layer  simulation  data 
of  Phillipe  Spalart  [8]  which  was  just  then  becoming 
available.  This  gave  them  access  to  quantitative 
information  of  a  kind  which  had  never  been  available 
before  to  an  experimentalist  like  Steve.  Difficult  to 
measure  field  variables  such  as  vorticity  and  pressure 
could  be  analyzed  in  a  variety  of  new  ways.  The  upshot 
of  this  work  was  an  updated  picture  of  turbulent  wall 
structure  in  the  form  of  streamwise  leaning  arches  of 
low  pressure  [9].  In  the  most  symmetric  cases  the  feet 
of  the  arch  attached  to  the  wall  with  the  head  leaning 
downstream  near  the  edge  of  the  layer.  In  a  few 
instances  both  feet  could  be  observed  but  in  most  cases 
the  arch  tended  to  be  unsymmetrical  with  one  foot  at 
the  wall  and  the  termination  of  the  opposite  foot  some 
distance  away  from  the  wall.  This  was  the  first  work  I 
am  aware  of  that  used  in-situ  static  pressure  to  identify 
the  basic  flow  structure.  One  of  the  big  advantages  of 
this  approach  was  that  pressure,  like  vorticity,  did  not 
suffer  from  the  lack  of  Galilean  invariance  which  tended 
to  plague  visualizations  of  the  velocity  field. 

Recent  work 

However  this  was  not  altogether  satisfying  to  Steve 
who  felt  that  any  identifier  of  the  flow  structure  had  to 
be  non-local  in  nature  and  based  in  some  way  on  an 
integration  of  the  velocity  field.  In  his  view  the 
pressure  was  an  outcome  of  some,  as  yet  undefined, 
dynamical  process.  This  led  him  to  focus  his  interest 
on  bringing  a  rigorous  definition  to  the  concept  of  a 
vortex.  To  pursue  this  problem  he  took  on  two  new 
PhD  students  who  were  to  follow  the  work  of  Steve 
Robinson.  In  the  early  1990's  he  began  working  with 
Luis  Portela  and  then  a  couple  of  years  later  Juan 
Chacin  came  on  board.  Both  continued  to  study  the 
Spalart  boundary  layer  simulation,  in  effect  rerunning 
the  simulation  as  various  ideas  were  tried. 

About  three  years  ago,  as  his  health  began  to  fail, 
Steve  recognized  that  he  would  not  be  able  to  provide 
adequate  advising  and  he  asked  Jim  Johnston,  Peter 
Bradshaw  and  me  to  help.  Peter  and  Jim  helped  advise 
Luis  and  I  advised  Juan.  The  effect  of  this  was  to  put 
the  two  of  them  on  somewhat  separate  tracks  toward 
the  PhD.  Luis  continued  to  focus  on  flow  patterns  near 
the  wall  and  the  question  of  defining  a  vortex  while 
Juan  began  to  investigate  the  structure  of  the  velocity 
gradient  tensor  near  the  wall.  The  results  of  both  of 
these  studies  are  reported  in  the  recent  volume  on  Self- 
Sustaining  Mechanisms  in  Wall  Turbulence  [10],  [11]. 

Chacin’s  research  led  to  what  I  consider  to  be  an 
important  advance  in  the  identification  of  turbulent  wall 
structure.  Following  some  earlier  work  by  Blackburn  et 
al  [12],  he  found  that  the  cubic  discriminant  of  the 
velocity  gradient  tensor  provided  a  very  useful,  Galilean 
invariant,  scalar  descriptor  of  the  flow  structure 
especially  near  the  wall  where  visualizations  of  the 


30 


vorticity  and  dissipation  and  especially  the  velocity 
field  are  full  of  ambiguities  and  very  difficult  to 
interpret  [13],  [14].  But  I  could  never  convince  Steve  of 
the  value  of  this  approach  which  he  regarded  as  a  "point 
method"  lacking  the  non-local  character  he  deemed 
essential.  We  argued  the  point  back  and  forth  several 
times  and  in  the  end  we  simply  agreed  to  disagree.  I 
miss  those  debates,  I  wish  I  could  work  on  him  just 
once  more. 

References 

1.  Bob  Dean  "A  tribute  to  Steve  Kline",  J. .  Fluids  Eng. 
Vol.  120,  March  1998,  pp  2-3. 

2.  S.  Kline,  M.  Morkovin,  G.  Sovran  and  D.  Cockrell, 
Proceedings:  Computation  of  turbulent  boundary  layers 
-  1968  AFOSR-IFP-Stanford  conference  Vol  I. 

3.  S.  Kline,  B.  Cantwell,  and  G.  Lilley  1981. 
Proceedings:  1980-81  AFOSR  -  HTTM  -  Stanford 
conference  on  complex  turbulent  flows. 

4.  B.  Cantwell,  D.  Coles  and  P.  Dimotakis,  1978. 
Structure  and  entrainment  in  the  plane  of  symmetry  of 
a  turbulent  spot,  J.  Fluid  Mech.  87:  641-72. 

5.  S.  Kline  and  P.  Runstadler  1959.  Some  preliminary 
results  of  visual  studies  of  the  flow  model  of  the  wall 
layers  of  the  turbulent  boundary  layer.  Trans  AS  ME 
Series  E  2:  166-70. 

6.  S.  Kline,  W.  Reynolds,  F.  Schraub  and  P  Runstadler 
1967.  The  structure  of  turbulent  boundary  layers.  J. 
Fluid  Mech.  30:741-73. 

7.  B.  Cantwell  1981.  Organized  motion  in  turbulent 
flow.  Ann.  Rev.  Fluid  Mech.  13:457-515. 

8.  P.  Spalart  1986.  Direct  simulation  of  a  turbulent 
boundary  layer  up  to  Re0  =1410.  J.  Fluid  Mech. 
187:61-98 

9.  S.  Robinson  1991.  The  kinematics  of  turbulent 
boundary  layer  structure.  NASA  TM  103859. 

10.  S.  Kline  and  L.  Portela  1997.  A  view  of  the 
structure  of  turbulent  boundary  layers.  In  self 
sustaining  mechanisms  of  wall  turbulence.  Adv.  in 
Fluid  Mech.  75,  ed.  by  R.  Panton  ,  Comp.  Mech.  Inc. 

11.  B.  Cantwell,  J.  Chacin  and  P.  Bradshaw  1997.  On 
the  dynamics  of  turbulent  boundary  layers.  In  self 
sustaining  mechanisms  of  wall  turbulence.  Adv.  in 
Fluid  Mech.  75,  ed.  by  R.  Panton  ,  Comp.  Mech.  Inc. 

12.  H.  Blackburn,  N.  Mansour  and  B.  Cantwell  1996. 
Topology  of  fine  scale  motions  in  turbulent  channel 
flow.  J.  Fluid  Mech.  310:  269-292. 


13.  J.  Chacin,  B.  Cantwell  and  S.  Kline  1996.  Study 
of  turbulent  boundary  layer  structure  using  the 
invariants  of  the  velocity  gradient  tensor.  J.  Exp. 
Thermal  Fluid  Sci.  13:  308-317. 

14.  J.  Chacin  and  B.  Cantwell  1997.  Study  of 
turbulence  structure  using  the  invariants  of  the  velocity 
gradient  tensor.  Report  TF-70,  Flow  physics  and 
computation  division,  dept,  of  Mech.  Eng.,  Stanford 
Univ. 


31 


VORTEX  PACKETS  AND  THE  STRUCTURE  OF  WALL  TURBULENCE 


Ronald  J.  Adrian 

Department  of  Theoretical  and  Applied  Mech. 
University  of  Illinois  at  Urbana-Champaign 
216  Talbot  Lab,  Urbana,  IL  61801 
r-adrian@uiuc.edu 


S.  Balachandar 

Department  of  Theoretical  and  Applied  Mech. 
University  of  Illinois  at  Urbana-Champaign 
216  Talbot  Lab,  Urbana,  IL  61801 
s-bala@uiuc.edu 


Abstract  -  Experimental  evidence  in  low  to  moderate  Reynolds  number  wall  flows  shows  that  hairpin  vortices  (including  asymmetric  inclined  vortices) 
occur  in  groups  that  propagate  as  a  whole  with  relatively  slow  dispersion.  These  groups,  or  “packets”,  grow  upwards  from  the  buffer  layer  to  about 
one-half  of  the  thickness  of  the  boundary  layer.  Direct  numerical  simulations  of  the  growth  of  a  single  hairpin  eddy  in  a  clean  background  flow  show 
how  these  packets  may  be  formed  in  the  near  wall  (low  Reynolds  number)  region  by  a  viscous  autogeneration  mechanism  that  is  similar  in  many 
regards  to  the  mechanism  proposed  by  Smith  and  co-workers  [1].  The  organization  of  hairpin  eddies  into  packets  and  the  interactions  of  those  packets 
is  an  important  feature  of  wall  turbulence  that  provides  a  new  paradigm  by  which  many  seemingly  unconnected  aspects  of  wall  turbulence  can  be 
explained.  These  include  the  inordinately  large  amount  of  streamwise  kinetic  energy  that  resides  in  very  long  streamwise  wavelengths,  the  occurrence 
of  multiple  Q2  events  per  turbulent  burst,  the  formation  of  new  streamwise  vorticity,  and  the  characteristic  angles  of  inclination  of  fronts.  The 
autogeneration  process  may  also  explain  the  formation  of  long  quasi-streamwise  vortices  in  the  buffer  layer  and  the  associated  low-speed  streaks. 


I.  INTRODUCTION 

Hairpin  shaped  vortices  are  thought  by  many  to  be  a  central  feature 
of  turbulent  wall  layers.  An  idealized  hairpin  vortex  consists  of  a  pair  of 
counter-rotating  quasi-streamwise  vortices  that  are  tilted  upwards  along  the 
downstream  direction  and  a  hairpin  head  that  connects  to  the  quasi- 
streamwise  vortices  at  their  downstream  ends,  as  shown  in  Figure  1. 
Haiipin  vortices  observed  in  experiments  and  computations  seldom  possess 
perfect  spanwise  symmetry;  more  often  they  are  asymmetric,  left-  or  right- 
handed  cane-like  vortices,  which  consist  of  a  head,  a  neck  and  one 
dominant  quasi-streamwise  leg  [2,3].  Nevertheless,  a  picture  of  the 
turbulent  wall  layer  as  a  distribution  of  hairpin  vortices  provides  a 
reasonable  model  for  many  of  the  flow  features  that  have  been  observed 
and  documented  in  the  past  (c.f.  [4]  for  example.). 

In  the  streamwise  wall  normal  (x-y)  plane,  the  velocity  signature  of  a 
hairpin  vortex  is  characterized  by  a  circular  vortex  core  and  a  strong 
outward  pumping  of  low  momentum  fluid.  This  hairpin  vortex  signature  is 
relatively  insensitive  to  the  degree  of  asymmetry  of  the  hairpin.  Recent  PIV 
measurements  [5-7]  in  a  turbulent  boundary  layer  over  a  range  of  Reynolds 
numbers  clearly  show  numerous  hairpin  vortex  signatures  within  the 
boundary  layer,  providing  strong  evidence  that  the  turbulent  wall  layer  at 
moderate  Reynolds  numbers  is  thickly  populated  with  hairpin  vortices. 

In  the  experimental  measurements  cited  above  the  hairpin  vortices 
were  often  observed  to  occur  one  behind  the  other  as  a  train  in  the 
streamwise  direction  forming  a  coherent  group  or  packet  of  hairpin 
vortices.  Although  the  shapes  and  sizes  of  the  packet  varied,  the  tendency 
to  form  group  of  hairpins  was  observed  at  all  instances.  The  streamwise 
coherence  of  the  near-wall  hairpin  vortices  persisted  even  at  higher 
Reynolds  numbers.  The  hairpin  vortices  within  a  packet  were  observed  to 
work  cooperatively  passing  low-speed  fluid  from  the  downstream  most 
vortex  to  its  upstream  neighbor  and  so  on  over  several  hairpin  vortices  to 
form  a  low-speed  streak  of  length  significantly  longer  than  a  single  hairpin 
vortex.  As  a  result,  transport  properties,  such  as  Reynolds  stresses,  of  the 
packet  could  significantly  exceed  a  simple  sum  of  the  contribution  from 
each  individual  hairpin  within  the  packet.  Thus  the  arrangement  of  hairpin 
vortices  into  packets  with  definite  distribution  of  size,  age  and  spatial 
separation  has  a  potentially  large  effect  on  the  overall  momentum  and  heat 
transport  from  the  wall.  For  instance,  significant  drag  reduction  can  be 
anticipated  by  disturbing  the  streamwise  alignment  of  hairpins  within  a 
packet. 

The  present  paper  will  focus  on  the  following  issues:  (a)  A  brief 
review  of  all  experimental  evidence  supporting  the  existence  of  hairpins; 
(b)  a  review  of  computational  results  on  the  autogeneration  of  new  hairpin 
vortices;  (c)  explanation  on  the  basis  of  the  hairpin  packet  paradigm  of 
experimental  observations  that  cannot  be  explained  by  single  hairpin 
models;(d)  the  implications  of  hairpins  occurring  as  packets,  instead  of 
being  randomly  scattered  throughout  the  boundary  layer. 

Hairpin  vortices  have  a  long  history.  Theodorsen  [8]  was  the  first  to 
suggest  the  importance  of  hairpin-type  vortices  in  turbulent  wall  layers.  His 
original  proposal  consisted  of  horseshoe  vortices  with  omega-shaped  head 
and  neck  region  that  extended  spanwise  to  form  spanwise  vortex  legs.  The 
visualization  experiments  of  Head  and  Bandyopadhyay  [9]  inferred  that 
stretched  vortex  loops  (or  hairpin  vortices)  inclined  at  about  45°  are  a 
major  component  of  the  turbulent  wall  layer.  There  are  two  major  pieces  of 
experimental  evidence  showing  that  hairpins  occur  in  groups.  First,  the  side 
view  smoke  flow  visualizations  of  Head  and  Bandyophadhyay  [9]  revealed 


large  scale  structures,  inclined  at  a  characteristic  angle  of  about  20°,  that 
marked  the  outer  edge  of  the  turbulent  boundary  layer.  They  inferred  that 
this  structure  was  a  group  of  individual  hairpin  vortices,  each  stretching 
from  the  wall  to  the  outer  edge  of  the  boundary  layer,  Figure  2(a).  (See 
also  the  model  of  Bandyopadhyay  [10])  The  angle  of  envelope  of  the  group 
was  approximately  18°.  Second,  based  on  experimental  observations  of 
hydrogen  bubble  pattern  in  the  near-wall  region  of  a  low  Reynolds  number 
turbulent  boundary  layer,  Smith  [11]  reported  that  the  results  are  consistent 
with  at  least  three  hairpin  vortices  forming  with  alignment  along  the 
streamwise  direction.  Figure  2(b).  Subsequent  work  by  Smith  and 
coworkers  demonstrated  the  formation  of  sequences  of  hairpins  by  a 
stationary  hemispherical  bump  on  the  wall  [12,13]  and  by  impulsive 
injection  of  fluid  [14]  in  a  laminar  boundary  layer.  More  recent  direct 
numerical  simulations  by  Zhou,  Adrian  &  Balachandar  [15]  and  Zhou, 
Adrian,  Balachandar  &  Kendall  [16]  on  the  evolution  of  a  single  initial 
hairpin  vortex  in  a  unidirectional  mean  turbulent  channel  flow  have 
.identified  the  mechanistic  details  behind  the  autogeneration  of  secondary 
hairpin  vortices  in  the  near-wall  region  leading  to  the  formation  of  a 
hairpin  packet.  A  significant  outcome  of  these  simulations  is  that  new 
hairpins  are  formed  both  on  the  upstream  and  downstream  sides  of  the 
initial  hairpin  resulting  in  a  half-diamond  or  tent-like  hairpin  packet.  This 
shape  for  the  hairpin  packet  is  consistent  with  recent  experimental 
measurements  [7]  schematically  represented  in  Figure  2c.  The 
computations  also  show  that  the  autogeneration  process  is  robust  and 
occurs  more  readily  in  the  case  of  an  asymmetric  initial  hairpin,  eventually 
forming  a  staggered  array  of  one-sided  hairpin  vortices.  This  is  in 
accordance  with  the  predominantly  one-sided  hairpins  noted  by  Guezennec 
&  Choi  [2]  and  Robinson  [3]. 

II.  EXPERIMENTAL  EVIDENCE  FOR  PACKETS 

The  velocity  signature  of  a  hairpin  vortex  in  a  spanwise-wall  normal 
(y-z)  plane  passing  through  the  quasi-streamwise  vortex  legs  is 
characterized  by  a  pair  of  counter  rotating  vortices  pumping  fluid  away 
from  the  wall.  On  the  other  hand,  in  a  streamwise-wall  normal  (jt-y)  plane 
the  hairpin  vortex  is  characterized  by  (a)  a  strong  outward  pumping  of  low 
momentum  fluid  on  the  in-board  side  of  the  quasi-streamwise  vortices.  This 
quadrant-two  (Q2)  flow  encounters  the  high-speed  free-stream  and  forms  a 
shear  layer  which  is  inclined  45°  to  the  horizontal;  and  (b)  closed/spiraling 
streamlines  corresponding  to  the  circular  vortex  core  of  the  hairpin  head  in 
a  frame  of  reference  traveling  downstream  with  the  hairpin  vortex. 

The  schematic  shown  in  Figure  1  clearly  illustrates  the  typical 
hairpin  vortex  signature  in  the  x-y  plane,  provided  it  passes  between  the 
quasi-streamwise  legs.  However,  it  must  be  emphasized  that  this  hairpin 
signature  is  relatively  insensitive  to  the  degree  of  asymmetry  of  the  hairpin. 
The  hairpin  vortex  signature  will  then  allow  reasonably  accurate 
identification  of  hairpin  vortices  from  quantitative  measurement  of  the 
velocity  field  within  the  turbulent  wall  layer.  It  should  be  emphasized  that 
the  Q2  vectors  exhibit  a  maximum  somewhere  below  the  vortex  head  and 
that  it  is  characteristic  of  the  combined  induction  associated  with  the 
proximity  of  the  vortex  head  and  legs.  This  peak  in  the  Q2  velocity 
provides  a  clear  evidence  for  the  existence  of  a  three-dimensional  vortex,  as 
a  two-dimensional  vortex,  such  as  a  vortex  line,  is  in  general  incapable  of 
generating  such  a  local  velocity  maximum. 

Figure  3a  shows  a  velocity  vector  plot  in  the  streamwise-wall  normal 
(jt-y)  plane  obtained  from  high  resolution  PIV  measurement  of  a  zero 


33 


pressure  gradient  boundary  layer  with  Re0  =  1015  [7].  A  constant 
convection  velocity  of  Uc  =  0.9  (  U„  is  the  free  stream  velocity)  has 

been  subtracted  from  the  streamwise  velocity  in  order  to  bring  out  the 
packet  of  hairpins,  whose  heads  are  clearly  identified  in  the  figure.  The 
hairpins  within  the  packet  are  observed  to  extend  from  the  wall  up  to 
y  /  8  ~  0.5  to  0.6,  where  S  defines  the  edge  of  the  boundary  layer.  From 
the  convection  velocity  it  can  be  inferred  that  the  hairpin  packet  propagates 
along  the  streamwise  direction  at  0.6  to  0.9  U „  .  The  PIV  measurements 
cover  a  wide  streamwise  range  of  up  to  3.05  and  over  this  extended 
streamwise  range  Tomkins  [7]  observed  different  geometric  shapes  for  the 
hairpin  packet  including:  uninterrupted  streamwise  growth,  sawtooth 
shape,  half-diamond  or  tent  shape  and  constant  height.  Figure  3a  might  fit 
the  description  of  a  packet  of  constant  height.  In  the  case  a  ramp-like 
envelope  for  the  hairpin  packet,  as  in  uninterrupted  growth,  sawtooth  and 
half-diamond  shape,  the  mean  angle  of  the  ramp  is  observed  to  be  about 
15°,  which  is  consistent  with  earlier  observations  of  Head  & 
Bandyopadhyay  [9].  Furthermore,  over  the  Reynolds  number  (  Re0  )  range 
form  1000  to  7705,  the  packet  is  observed  to  contain  from  about  4  hairpins 
to  as  many  as  nine  hairpins. 

The  cooperative  action  of  the  streamwise  aligned  hairpins  within  the 
packet  can  be  clearly  observed  in  figure  3a  as  the  zone  of  strong  negative 
velocity  that  lies  below  the  hairpin  vortex  heads.  This  zone  of  low 
momentum  also  exists  at  higher  Reynolds  numbers,  as  shown  in  figure  3b 
for  Ree  =  7705  but  is  restricted  closer  to  the  wall  in  terms  of  outer  units. 

At  higher  Reynolds  number  multiple  zones  of  almost  uniform  momentum 
can  be  observed  [5,6].  The  interface  between  any  two  adjacent  zones  is 
marked  by  a  sequence  of  vortex  cores,  which  contributes  to  the  near 
uniform  velocity  jump  across  them.  These  vortex  cores  can  be  identified  as 
the  heads  of  nearly  streamwise  aligned  hairpin  vortices  and  thus  the 
interface  between  the  different  uniform  momentum  zones  can  be  interpreted 
as  the  envelop  of  a  hierarchical  hairpin  packet. 

The  uniform  momentum  zone  observed  close  to  the  wall  in  figures  3a 
and  3b  extends  over  more  than  one  thousand  viscous  wall  units  along  the 
streamwise  direction.  While  it  resembles  the  low  speed  streak  that  occurs  in 
the  buffer  layer,  it  is  a  new  and  quite  distinct  phenomenon  as  it  occurs  well 
above  the  buffer  layer  and  extends  past  the  logarithmic  layer  [6].  However 
the  low  momentum  zones  are  associated  with  near  wall  streaks,  since  the 
hairpin  vortices  and  hairpin  packets  are  believed  to  grow  out  of  the  near¬ 
wall  streaks,  at  least  in  the  first  zone  closest  to  the  wall.  The  packets  are 
also  not  the  conventional  bulges,  but  the  largest  packets  in  the  hierarchy  of 
hairpin  packets  might  cause  the  bulges.  The  organization  of  the  bulges 
appears  to  be  less  coherent  than  the  packets,  suggesting  that  the  packets 
interact  in  a  complex  way. 

III.  GENERATION  OF  HAIRPIN  VORTEX  PACKETS 

The  frequent  occurrence  of  vortex  packets  in  the  experiments  requires 
explanation.  The  kernel  experiments  of  Acarlar  &  Smith  [12,13]  followed 
the  process  of  continuous  generation  of  a  train  of  hairpin  vortices  behind  a 
hemispherical  bump  in  a  laminar  boundary  layer.  Subsequent  experiments 
by  Haidari  &  Smith  [14]  considered  the  more  relevant  case  of  a  single 
hairpin  vortex  generated  by  an  impulsive  injection  of  fluid  into  the 
boundary  layer  and  the  subsequent  generation  of  secondary  hairpins  to 
form  a  packet.  This  process  of  initial  hairpin  formation  from  fluid  injection 
and  its  subsequent  evolution  and  formation  of  additional  vortical  structures 
was  studied  numerically  by  Singer  &  Joslin  [17].  Based  on  the 
experimental  observations  and  inviscid  computations.  Smith  et  al.  [1] 
offered  a  conceptual  inviscid  model  for  the  mechanism  by  which  new 
hairpins  can  be  naturally  generated  out  of  a  single  hairpin.  While  the  above 
cited  investigations  all  pertain  to  the  formation  of  a  hairpin  packet  in  a 
laminar  boundary  layer  flow,  the  experimental  evidence  [6,7,9,11] 
suggests  that  once  a  hairpin  is  formed  by  a  localized,  low  momentum 
agency  near  the  wall,  it  can,  under  a  range  of  circumstances,  proceed  to 
generate  a  sequence  of  new  vortices  forming  a  coherent  packet  of  hairpin 
vortices.  A  fundamentally  similar  general  mechanism  may  occur  in 
turbulent  flow  as  well,  but  if  so,  it  needs  to  be  understood  in  that  context. 

The  numerical  simulations  of  the  growth  of  a  single  hairpin  vortex  in 
the  background  of  a  low  Reynolds  number  unidirectional  mean  turbulent 
channel  flow  [15,16]  offer  additional  insight  into  the  mechanisms,  which 
could  explain  the  formation  of  new  hairpin  vortices,  and  their  spatial 
arrangement  into  packets.  These  studies  differ  from  the  work  described 
above  in  that  the  initial  field  was  a  viscous,  hairpin  vortex-like  structure 
that  was  extracted  from  the  full  two-point  turbulent  correlation  tensor  of  a 


Rer  = 180  channel  flow  direct  numerical  simulation  of  Kim,  Moser  and 

Moin  [18]  by  the  process  of  stochastic  estimation  (c.f.  [19]),  rather  than 
created  by  external  forcing.  By  appropriately  choosing  the  event  vector  in 
the  stochastic  estimation  process,  the  structure  of  the  initial  vortex  can  be 
varied  over  a  wide  range  in  a  systematic  manner  to  represent  form  an 
idealized  symmetric  hairpin  to  a  more  realistic  asymmetric  or  one-sided 
hairpin. 

Zhou  et  al.  [15,16]  considered  both  symmetric  and  asymmetric  Q2 


event  vectors  given 


by  a  second  quadrant  velocity  ( u  =  a^l- p2 um  , 


v  =  a^\  -  p2  vm  ,  w  =  p(ul  +  )  specified  at  a  single  point  within 

the  channel.  Here  (wm,vm)  is  chosen  to  maximize  the  product 
umvm  weighted  by  the  probability  density  of  its  occurrence  /(wm,vm) 
and  thereby  maximize  the  contribution  to  mean  Reynolds  shear  stress.  The 
factor  a  is  a  scaling  factor,  which  determines  the  vortical  strength  of  the 
initial  structure  relative  to  the  vorticity  of  the  mean  flow.  The  factor  p  is 
the  asymmetry  parameter;  p  =  0  corresponds  to  a  symmetric  event  and 
results  in  an  initial  symmetric  hairpin.  For  a  representative  Q2  event,  the 
stochastic  estimation  process  guarantees  that  the  initial  field  possessed  the 
correct  length  scales,  shape,  and  vorticity  distribution  of  a  typical  Q2 
structure.  Thus  we  believe  that  the  initial  hairpin  structure  is  more 
representative  of  the  hairpin  vortices  observed  in  real  turbulence. 

Further,  the  background  flow  in  which  the  hairpin  vortex  is 
embedded  is  chosen  to  be  a  unidirectional  flow  obtained  from  the  mean 
streamwise  velocity  profile  of  Rer  =180  channel  flow  direct  numerical 

simulation  [  1 8],  rather  than  a  Poiseuille  flow.  This  difference  at  first  glance 
might  seem  not  so  important;  however,  in  the  case  of  the  turbulent  mean 
flow  profile  the  mean  shear  is  predominantly  contained  close  to  the  channel 

walls  within  approximately  25%  of  the  channel  half  height  (  y+  <  45  ), 
whereas  in  the  case  of  a  plane  Poiseuille  flow  the  mean  shear  extends  over 
the  entire  channel.  As  a  result  the  peak  shear  in  the  case  of  the  mean 
turbulent  profile  is  about  factor  four  greater  than  that  of  the  Poiseuille 
flow.  A  delicate  balance  between  the  self-induced  velocity  that  tends  to  curl 
up  the  vortex  and  the  influence  of  the  mean  shear,  which  tends  to  stretch 
the  hairpin  vortex,  governs  the  evolution  of  the  hairpin  vortex.  Thus 
differences  in  the  mean  background  flow  will  have  a  strong  influence  on 
the  dynamics  of  the  initial  hairpin  vortex  and  the  formation  of  the  hairpin 
packet.  In  particular,  the  impact  on  the  spatial  and  temporal  scales  of  the 
resulting  structure  is  likely  to  be  strong. 

In  a  real  turbulent  boundary  layer  the  formation  and  evolution  of  the 
hairpin  packet  occurs  in  the  presence  of  other  hairpin  packets,  vortical 
debris,  outer  layer  perturbations  and  so  on.  These  disturbances  are  in  deed 
collectively  responsible  for  the  mean  turbulent  profile,  but  of  course  in  a 
time-averaged  sense.  The  rational  for  using  the  unidirectional  mean 
turbulent  profile  as  the  background  flow  is  to  account  for  the  influence  of 
the  other  turbulent  structures  at  least  in  a  statistical  sense,  and  at  the  same 
time  maintain  the  hairpin  evolution  simple  and  controlled  so  as  to  be  able 
to  follow  it  in  dose  detail  without  any  clutter  from  other  vortical  structures. 

The  simulations  were  performed  at  a  Reynolds  number  of 
Rer  =  180  in  a  box  of  streamwise  (jc)  wall  normal  (y)  and  spanwise  (z) 

size  4/r,  2  and  4/z/3  respectively.  The  iso-surface  of  the  imaginary  part  of 
the  eigenvalue  of  the  velocity  gradient  tensor  [16]  is  used  to  visualize 
vortices  in  the  present  study. 

Time  evolution  of  both  symmetric  and  asymmetric  initial  structures 
were  followed  in  detail  with  a  direct  numerical  simulation.  In  both  cases 
the  quasi-streamwise  vortices  quickly  lift  away  from  the  boundary  due  to 
mutual  induction  and  the  lift-up  is  the  strongest  at  the  downstream  end. 
Simultaneously  a  shear  layer  forms  where  the  Q2  velocity  encounters  the 
mean  flow.  Spanwise  vorticity  associated  with  this  shear  layer  quickly 
rolls-up  and  forms  a  compact  spanwise  vortex  located  just  above  the 

downstream  end  of  the  quasi-streamwise  vortices.  By  t+  ~  25  the  rolled- 
up  spanwise  vortex  viscously  connects  with  the  lifted  quasi-streamwise 
vortices  to  form  a  hairpin  structure.  The  geometry  of  this  vortex  resembles 
in  appearance  the  hairpin  vortices  observed  in  many  experiments.  Figure 

4a  shows  the  hairpin-like  vortex  at  t+  -  27  that  resulted  from  an 
asymmetric  initial  structure  with  ym+=30,  <x=2  and  p= 0.5.  Apart  from  the 
hairpin  vortex,  marked  by  the  head  and  an  asymmetric  pair  of  quasi- 
streamwise  vortices  on  the  upstream  side  of  the  hairpin  head,  a  pair  of 
vortical  tongues  can  be  seen  on  the  downstream  side  of  the  head.  These 


34 


vortical  tongues  will  later  develop  into  new  downstream  hairpin  vortices 
that  will  form  part  of  the  hairpin  packet. 

The  head  of  the  primary  hairpin  vortex  continues  to  lift  up  into  a  near 
vertical  orientation  and  also  grows  wider  evolving  into  the  characteristic 
ft-shape.  Simultaneously  the  quasi-streamwise  legs  stretch  and  form  a  kink 
as  a  result  of  mutual  induction  and  interaction  with  the  head.  A  shear  layer 
forms  above  the  kink  and  quickly  intensifies.  Subsequently  the  upstream 
portion  of  the  quasi-streamwise  legs  detach  from  the  primary  hairpin  at  the 
kink  and  merge  with  the  rolled  up  shear  layer  to  form  a  secondary  hairpin 
which  remains  distinct  from  the  primary  hairpin. 

This  process  of  new  hairpin  generation  continues  along  similar  lines 
both  upstream  and  downstream  of  the  primary  hairpin  resulting  in  a  hairpin 

packet,  which  is  shown  in  Figure  4b  and  4c  at  /+  =  144  .  The  envelope  of 
the  packet  of  hairpin  vortices  has  a  tent  like  appearance  with  an 
approximate  angle  of  10°  upstream  and  7°  downstream  of  the  primary 
vortex.  The  velocity  signature  of  the  computed  hairpin  packet  qualitatively 
compares  with  the  PIV  measurements  similar  to  those  shown  in  figure  3. 
However  discrepancies  exist  since  the  computed  hairpins  are  separated 
along  the  streamwise  direction  about  200450  viscous  wall  units,  while  in 
the  experiments  the  distance  between  hairpins  is  observed  to  be  around 
100-150  viscous  units. 

The  effect  of  asymmetry  on  the  evolution  of  hairpin  vortices  is  also 
investigated  by  systematically  increasing  the  ft  parameter  from  0.  It  is 
observed  that  the  process  by  which  new  hairpins  are  autogenerated  remains 
qualitatively  the  same  as  in  the  symmetric  case.  Thus  the  formation  of  a 
coherent  hairpin  packet  is  a  robust  mechanism  active  under  a  wide  range  of 
conditions.  However,  the  asymmetric  hairpins  are  one-sided  and  the  packet 
consists  of  a  streamwise  train  of  alternating  left  and  right  handed  one-sided 
hairpins  that  are  staggered  along  the  span.  Both  the  symmetric  and 
asymmetric  cases  display  a  threshold  behavior;  hairpins  only  above  a 
certain  threshold  initial  amplitude  result  in  the  autogeneration  of  new 
hairpins  and  formation  of  a  hairpin  packet.  The  threshold  amplitude  is 
observed  to  decrease  with  the  degree  of  asymmetry  suggesting  that 
asymmetric  hairpins  are  more  likely  to  autogenerate  and  form  hairpin 
packets  than  the  idealized  symmetric  ones.  This  result  is  in  total  agreement 
with  the  experimental  and  computational  observation  of  predominantly 
one-sided  haiipins. 

IV.  SINGLE  HAIRPIN  PARADIGM 

Here  we  will  consider  significant  experimental  and  computational 
observations  that  are  consistent  with  the  picture  of  the  turbulent  boundary 
layer  populated  with  a  forest  of  symmetric  and  cane-type  hairpins. 

1)  The  often  observed  quasi-streamwise  vortices,  hairpin  shape  and 
horseshoe  (omega)  shaped  vortices,  one-sided  cane  type  vortices  are  all 
part  of  the  same  entity  at  various  stages  of  their  evolution  and  with 
different  degree  of  asymmetry. 

2)  The  range  of  hairpin  vortex  angle  from  15°-75°  (with  45°  being  more 
typical)  is  consistent  with  the  range  of  angles  observed  from  the  quasi- 
streamwise  vortices  to  the  hairpin  head.  Furthermore,  the  tilt  or  angle  of 
the  hairpin  head  is  a  strong  function  of  its  location;  the  head  takes  a  near 
vertical  orientation  in  the  outer  regions  of  the  boundary  layer,  while  near 
the  wall  it  takes  a  more  conventional  45°  angle. 

3)  The  experimentally  observed  inclined  internal  shear  layers  can  be 
explained  on  the  basis  of  the  Q2  fluid  pumped  by  the  haiipin 
encountering  the  free  stream  flow. 

IV.  HAIRPIN  PACKET  PARADIGM 

One  must  appeal  to  a  coherent  packet  of  streamwise  aligned  hairpin 
vortices  in  order  to  consistently  explanation  other  experimental  and 
computational  observations  of  the  past.  Below  we  list  all  the  important 
features  that  can  be  explained  on  the  basis  that  the  boundary  layer  is  made 
up  of  hairpin  packets. 

•  Low-Speed  Streaks 

1)  The  cooperative  Q2  pumping  of  the  near- wall  fluid  by  the 
streamwise  aligned  hairpin  vortices  explain  the  very  long  (more  than 
1000  wall  units)  low-speed  streaks. 

2)  The  spanwise  staggering  of  the  one-sided  hairpins  in  the  asymmetric 
case  explain  the  often  observed  spanwise  jogging  of  the  low-speed 
steaks. 

3)  Recent  measurements  by  Meinhart  &  Adrian  [5]  indicate  that  the 
low-speed  streaks  are  not  limited  to  the  buffer-layer,  but  extend  into  the 
log-layer  as  well.  Streamwise  aligned  hairpin  vortices  that  extend  into 


the  log-layer,  through  their  combined  induced  velocity  can  explain  the 
long  log-layer  low-speed  streaks. 

4)  The  packet  paradigm  also  explains  the  long  tail  observed  in  the  w- 
correlation  [20,21]. 

•  Burst  Process 

1)  There  is  similarity  to  the  POD  results  of  Sirovich  [22],  in  which  the 
most  important  modes  are  the  streamwise  independent  modes  that  hug 
close  to  the  walls.  These  modes  correspond  to  the  streamwise  aligned 
quasi-streamwise  legs  of  the  hairpins  and  the  resulting  long  low-speed 
streaks.  We  interpret  the  propagating  modes  that  trigger  the  onset  of 
burst-like  activity  to  be  the  projections  of  the  hairpin  heads. 

2)  The  streamwise  arrangement  of  the  hairpin  vortices  is  in  agreement 
with  the  measurements  of  [23-25],  where  the  near-wall  burst  process 
was  observed  to  be  typically  made  up  of  multiple  Q2  events.  In  this 
sense  the  hairpin  packet  constitutes  a  burst. 

3)  The  adjacency  of  hairpins  within  the  packet  results  in  strong  internal 
shear  layers  where  the  induced  downflow  (Q4)  from  the  upstream  vortex 
head  meets  the  low-speed  upflow  (Q2)  induced  by  the  downstream 
vortex.  This  Q2/Q4  stagnation  point  flow  provides  convincing  evidence 
for  the  VITA  signature,  often  used  to  identify  burst  process. 

4)  The  conventional  view  of  the  burst  process  as  wavy  oscillation  of  the 
low-speed  streaks  and  Q2  eruption  t  the  end  also  fits  into  the  framework 
of  hairpin  packet.  While  the  low-speed  (Q2)  pumping  of  the  downstream 
hairpins  are  somewhat  mitigated  by  the  corresponding  Q4  induced 
velocity  of  their  upstream  neighbors,  the  low-speed  pumping  of  the 
chronologically  last  upstream-most  hairpin  remains  unopposed  and  in 
fact  is  reinforced  by  its  downstream  neighbors. 

•  Structure  and  Symmetry 

1)  Preference  for  cane-shaped  one-sided  hairpins  in  the  experimental 
[2]  and  computational  results  [3]  can  be  explained  on  the  basis  that  the 
autogeneration  of  new  hairpins  is  much  more  robust  and  readily 
occurring  when  they  are  asymmetric. 

2)  Often  observed  inline  alignment  of  the  streamwise  vortices  is  due  to 
the  quasi-streamwise  legs  of  the  streamwise  aligned  hairpins  within  the 
packet. 

3)  In  the  event  of  strong  asymmetry,  only  the  alternative  quasi- 
streamwise  legs  are  significant  -  the  packet  is  made  up  of  alternating 
sequence  of  right  and  left  handed  canes.  If  one  confines  attention  to  only 

the  near  wall  region  ( y+  <  60 )  the  behavior  of  the  packet  is  very  similar 
to  that  proposed  by  [26]. 

•  Hierarchy  of  Packets 

1)  Recent  PIV  measurements  [7]  over  a  range  of  Reynolds  numbers 
show  velocity  signature  that  is  consistent  with  a  picture  of  the  turbulent 
boundary  layer  made  up  of  hierarchy  of  hairpin  packets  that  travel 
downstream  coherently. 

2)  We  believe  that  the  hydrogen  bubble  measurements  of  [1 1]  and  the 
smoke  visualizations  of  Head  &  Badyopadhyay  [9]  extract  the  near- wall 
and  outermost  groups  of  hairpins,  respectively.  This  suggests  the 
presence  of  hairpin  packets  right  from  the  near-wall  region  to  the 
outermost  reaches  of  the  boundary  layer. 

3)  The  outer  scale  structures  such  as  the  backs  and  bulges  are  consistent 
with  a  large-scale  hairpin  packet  that  extends  into  the  outer  layer. 

4)  The  scaling  of  different  quantities  on  inner,  outer  and  mixed  scales  is 
compatible  with  the  notion  of  a  hierarchy  of  hairpin  packets. 

5)  The  smallest  near-wall  haiipin  packet  provides  adequate  explanation 
for  the  buffer-layer  behavior.  The  nesting  of  smaller  packets  within 
larger  ones,  which  are  within  even  larger  ones,  and  so  on  may  explain 
the  log-layer. 

6)  The  hierarchy  of  packets  can  explain  Robinson’s  observation  that  the 
buffer-region  contains  predominantly  quasi-streamwise  vortices,  the 
log-region  contains  both  quasi-streamwise  vortices  and  hairpin  heads 
and  the  wake-region  contains  mostly  hairpin  heads. 

VI.  IMPLICATIONS  OF  PACKET  PARADIGM 

Implications  of  the  hairpin  packet  paradigm  for  prediction,  control 
and  modeling  of  turbulent  boundary  layer  are  very  many.  The 


35 


superposition  of  the  induced  fields  of  the  streamwise-aligned  hairpins  result 
in  a  strong  Q2  velocity  due  to  the  “solenoid  effect”.  This  cooperative  action 
leads  to  a  potentially  very  large  increase  in  momentum  and  heat  transport 
from  the  wall.  For  example,  the  total  Reynolds  stress  of  N  incoherently 
distributed  (spatially  uncorrelated)  hairpin  vortices  is  simply  N  times  the 
individual  contribution  arising  from  the  Q2  pumping  of  each  of  the  hairpin. 
On  the  other  extreme,  if  the  N  hairpins  are  perfectly  overlaid  (perfect 

correlation)  the  resulting  total  Reynolds  stress  is  N2  times  the  individual 
contribution.  The  Reynolds  stress  contribution  of  a  real  hairpin  packet  is 
likely  to  scale  somewhere  in  between  and  depend  critically  on  the  strength 
and  spatial  scales  of  the  hairpin  packet. 

The  above  observation  suggests  that  boundary  layer  models  that  are 
based  on  a  hierarchy  of  random  distribution  of  hairpins  as  in  Perry  et  al. 

[4]  have  many  of  the  ingredients  necessary  for  an  accurate  description  of 
the  turbulent  boundary  layer,  except  for  the  coherence  of  hairpins  within  a 
packet.  In  a  similar  manner  the  phenomenological  semi-Markov  model  of 
the  turbulent  boundary  layer  [27]  does  not  fully  account  for  the  spatial 
coherence  within  the  hairpin  packet.  By  incorporating  this  important 
feature  the  predictive  capability  of  these  models  can  be  significantly 
advanced. 

Hairpin  packets  also  provide  exciting  possibilities  for  the  control  of 
boundary  layer  turbulence  and  hence  drag  management.  One  simple 
conceptual  approach  to  drag  reduction  is  to  delay  the  formation  of 
secondary  and  subsequent  vortices  and  thereby  increase  the  streamwise 
spacing  between  the  hairpins  within  the  packet.  The  resulting  reduced 
cooperation  among  the  hairpins  will  significantly  cut  down  the  Reynolds 
shear  stress  and  the  momentum  transfer.  Recent  results  by  Sirovich  and 
coworkers  [22]  indicate  that  reasonable  drag  reduction  can  be  achieved  by 
random  distribution  of  roughness  elements.  They  hypothesized  that  the 
roughness  elements  disturb  the  propagating  modes  and  thereby  control  the 
bursting  process.  An  alternative,  but  certainly  related,  viewpoint  will  be 
that  the  roughness  elements  adversely  affect  the  hairpin  generation  process 
and  mitigate  the  internal  coherence  within  packets. 

Experimental  and  computational  evidence  [12-17]  suggests  that 
many  types  of  low  momentum  events  at  the  wall  can  create  a  succession  of 
hairpins.  This  along  with  [22]  can  be  taken  to  suggest  that  by  appropriate 
surface  excitation,  for  example  by  momentum  addition  to  overcome  a  local 
low  momentum  event  the  hairpin  formation  process  can  be  controlled  to 
reduce  drag.  Such  exciting  possibilities  must  be  pursued  in  the  future. 

Vn.  REFERENCES 

[1]  Smith,  C.  R.,  Walker,  J.  D.  A.,  Haidari,  A.  H.,  &  Sobrun,  U.  "On  the 
dynamics  of  near-wall  turbulence",  Phil.  Trans,  of  Roy.  Soc.  London  A, 
336, 131-175,  1991. 

[2]  Guezennec,  Y.  G.  &  Choi,  W.  C.  "Stochastic  Estimation  of  coherent 
structures  in  turbulent  boundary  layers".  In  Proc.  Zoran  P.  Zaric 
Memorial  International  Seminar  on  Near  Wall  Turbulence ,  May  1988 
(ed.  S.  J.  Kline,  N.  H.  Afgan),  pp.  420-436.  New  York:  Hemisphere, 
1989. 

[3]  Robinson,  S.  K.  "Coherent  motions  in  the  turbulent  boundary  layer", 
Ann.  Rev.  Fluid  Mech.  23,601-639,  1991. 

[4]  Perry,  A.  E.,  Henbest,  S.  &  Chong,  M.  S.  "A  theoretical  and 
experimental  study  of  wall  turbulence",  J.  Fluid  Mech.  165,  163-199, 
1986. 

[5]  Meinhart,  C.  D.  &  Adrian,  R.  J.  "On  the  existence  of  uniform 
momentum  zones  in  a  turbulent  boundary  layer",  Phys.  Fluids  7,  694-696, 
1996. 

[6]  Meinhart,  C.  D.  &  Adrian,  R.  J.  "The  coherent  structure  of  the  overlap 
region  in  the  turbulent  boundary  layer",  (manuscript  in  preparation),  1998. 

[7]  Tomkins,  C.  D.  "A  particle  image  velocimetry  of  coherent  structures 
in  a  turbulent  boundary  layer",  M.S.  Thesis,  University  of  Illinois,  Urbana, 
Illinois,  1998. 

[8]  Theodorsen,  T.  "Mechanism  of  turbulence".  In  Proc.  Second 
Midwestern  Conf.  of  Fluid  Mechanics,  pp.  1-19.  Ohio  State  University, 
Columbus,  Ohio,  1952. 

[9]  Head,  M.  R.  &  Bandyopadhyay,  P.  "New  aspects  of  turbulent 
boundary  layer  structure",  J.  Fluid  Mech.  107,297-338,  1981. 

[10]  Bandyopadhyay,  P.  "Large  structure  with  a  characteristic  upstream 
interface  in  turbulent  boundary  layers",  Phys.  Fluids  23,  2326-2327, 
1980. 

[11]  Smith,  C.  R.  "A  synthesized  model  of  the  near-wall  behavior  in 
turbulent  boundary  layers".  In  Proc.  Eighth  Symp.  on  Turbulence  (ed.  G. 
K.  Patterson  &  J.  K.  Zakin).  University  of  Missouri-Rolla.  Dept,  of  Chem. 
Engng.,  Rolla,  Missouri,  1984. 


[12]  Acarlar,  M.  S.  &  Smith,  C.  R.  "A  study  of  hairpin  vortices  in  a 
laminar  boundary  layer.  Part  1.  Hairpin  vortices  generated  by  a  hemisphere 
protuberance",  /  Fluid  Mech.  175, 1-41,  1987a. 

[13]  Acarlar,  M.  S.  &  Smith,  C.  R.  "A  study  of  hairpin  vortices  in  a 
laminar  boundary  layer.  Part  2.  Hairpin  vortices  generated  by  fluid 
injection",/.  Fluid  Mech.  175,43-83, 1987b. 

[14]  Haidari,  A.  H.  &  Smith,  C.  R.  "The  generation  and  regeneration  of 
single  hairpin  vortices",  /.  Fluid  Mech.  277 , 135-162,  1994. 

[15]  Zhou,  J.,  Adrian,  R.  J.  &  Balachandar,  S.,  "Autogeneration  of  near 
wall  vortical  structure  in  channel  flow”,  Phys.  Fluids,  8, 288-291, 1996. 

[16]  Zhou,  J.,  Adrian,  R.  J.,  Balachandar,  S.,  &  Kendall,  T.  M. 
"Mechanisms  for  generating  coherent  packets  of  hairpin  vortices  in  channel 
flow"  submitted  to  /.  Fluid  Mech.,  1998. 

[17]  Singer,  B.  A.  &  Joslin,  R.  D.  "Metamorphosis  of  a  hairpin  vortex  into 
a  young  turbulent  spot",  Phys.  Fluids  6,  3724-3736,  1994. 

[18]  Kim,  J.,  Moin,  P.,  &  Moser,  R.  D.  "Turbulent  statistics  in  fully 
developed  channel  flow  at  low  Reynolds  number",  /.  Fluid  Mech.  177, 
133-166,1987. 

[19]  Adrian,  R.  J.  "Stochastic  Estimation  of  the  Structure  of  Turbulent 
Fields".  In  Eddy  Structure  Identification  (ed.  J.  P.  Bonnet),  pp.  145-196. 
Berlin:  Springer,  1996. 

[20]  Townsend,  A.A  "The  structure  of  turbulent  shear  flow",  Cambridge 
University  Press,  1976. 

[21]  Grant,  H.  L.  "The  large  eddies  of  turbulent  motion",  /.  Fluid  Mech., 
4,  149-190,  1958. 

[22]  Sirovich,  L.  "Dynamics  of  coherent  structures  in  wall  turbulence".  In 
Self  Sustaining  Mechanisms  of  Wall  Turbulence,  (ed.  R.L.  Panton),  pp. 
333-364,  Computational  Mechanics  Publications,  Southampton,  UK. 

[23]  Bogard,  D.  G.  &  Tiederman,  W.  G.  "Burst  detection  with  single-point 
velocity  measurements",  /.  Fluid  Mech,  162,  389-413,  1986. 

[24]  Luchik,  T.  S.  &.  Tiederman,  W.  G.  Timescale  and  structure  of 
ejections  and  bursts  in  turbulent  channel  flows",  /.  Fluid  Mech.  174,  529- 
552, 1987. 

[25]  Tardu,  F.  "Characteristics  of  single  and  clusters  of  bursting  events  in 
the  inner  layer.  Part  1:  Vita  events",  Exp.  Fluids ,  19,  112-124,  1995. 

[26]  Jeong,  J.  &  Hussain,  F.  "On  the  identification  of  a  vortex",  J.  Fluid 
Mech.  285,69-94,  1995. 

[27]  Meng,  J.  C.  S.  "Wall  layer  microturbulence  Phenomenological  model 
and  a  semi-Markov  probability  predictive  model  for  active  control  of 
turbulent  boundary  layer".  In  Self  Sustaining  Mechanisms  of  Wall 
Turbulence,  (ed.  R.L.  Panton),  pp.  201-252,  Computational  Mechanics 
Publications,  Southampton,  UK. 


Figure  1 .  Schematic  of  a  hairpin  vortex  and  associated  flow  field 
properties  that  form  the  signature  of  a  hairpin  on  the  x-y  plane. 


36 


Streamwise  Vortex  Stretching 


Figure  3.  PIV  measurements  of  instantaneous  velocity  fields  in  the  x-y  plane  of  a  turbulent  boundary  layer,  (a)  Ree=10 15;  (b)  Re^7705. 


VORTEX  DEVELOPMENT  AND  INTERACTIONS  IN  TURBULENT  BOUNDARY  LAYERS: 
IMPLICATIONS  FOR  SURFACE  DRAG  REDUCTION 


Dr.  Charles  R.  Smith 

Department  of  Mechanical  Engineering  and  Mechanics 
19  Memorial  Drive  West 
Lehigh  University 
Bethlehem,  PA  18015 
crsl@lehigh.edu 

Abstract  -  Ultimately,  control  of  turbulent  boundary  layers  must  center  around  the  selected  modification  of  the  flow  structure  of  the 
turbulence,  or  the  conditions  which  give  rise  to  the  flow  structure.  The  present  paper  examines  the  particular  importance  of  vortices,  and  their 
role  in  generating  and  maintaining  turbulence  production  in  a  turbulent  boundary  layer.  A  conceptual  model  is  outlined  illustrating  how  vortex 
interactions  with  both  other  vortices  and  the  bounding  surface  control  the  processes  of  fluid,  momentum,  and  energy  transport,  and  ultimately 
surface  drag.  The  implications  of  these  vortical  processes  on  approaches  to  drag  reduction/control  are  discussed. 


I.  INTRODUCTION 

A  variety  of  flow  structures  have  been  suggested  as  important  in  the 
development  and  regeneration  of  turbulent  boundary  layers.  We  now 
know,  through  a  number  of  detailed  experimental,  computational,  and 
analytical  studies,  that  vortex  deformation  and  evolution  play  a  dominant 
role  in  creating  and  sustaining  "turbulence,"  and  that  these  vortical 
processes  give  rise  to  the  deterministic  "structure"  of  irregular,  but 
repetitive,  spatial-temporal  flow  patterns  such  as  low-speed  wall  "streaks," 
wall  region  "bursts,"  "ejections,"  and  "sweeps"  which  characterize  near¬ 
wall  turbulence.  These  characteristic  patterns  are  what  have  been 
perceived  as  the  "coherent  structure"  of  a  turbulent  boundary  layer.  The 
majority  of  these  flow  patterns  are  now  understood  to  be  associated  with 
some  form  of  vortex  structure,  from  streamwise  and  transverse  vortices  to 
multiple  hairpin-like  vortices.  Excellent  experimental  and  computational 
studies1'26  have  provided  detailed  correlation,  assessment,  and 
categorization  of  the  myriad  three-dimensional  patterns,  or  flow  structure 
of  turbulent  boundary  layers,  and  the  relation  of  such  flow  structure  to  the 
presence  and  interaction  of  vortices. 

The  present  paper  provides  an  overview  of  the  hypothesized 
behavior  of  vortices  in  sustaining  and  developing  a  turbulent  boundary 
layer,  focussing  on  how  vortices  and  vortex  interactions  control  the 
process  of  momentum  exchange,  energy  extraction  from  the  mean  flow, 
and  maintenance  of  the  turbulence  process.  The  characteristic  patterns  of 
behavior  that  have  been  observed  and  detected  in  turbulent  boundary 
layers  are  discussed  first,  leading  to  a  discussion  of  the  role  of  vortices  in 
the  physical  processes  giving  rise  to  those  patterns.  The  manifold 
importance  of  vortices,  and  their  role  in  generating  and  maintaining 
turbulence  are  examined.  Finally,  a  conceptual  model  of  wall  turbulence 
based  on  vortex  interactions  and  development  is  presented,  and  the 
implications  of  this  model  in  developing  rational  methods  for  surface  drag 
reduction  and/or  control  of  a  turbulent  boundary  layer  is  discussed. 

D.  PATTERNS  OF  BEHAVIOR 

Prior  to  the  late  1950s,  turbulent  boundary  layers  were  studied  as  if 
they  were  random  velocity  fluctuations  riding  on  an  otherwise  time- 
averaged  flow.  However,  numerous  studies5’3,5,6,9  over  the  past  forty 
years  have  revealed  that  turbulent  boundary  layers  display  irregular,  but 
repeatable,  patterns  of  behavior  in  time  and  space  which  are  reflective  of 
the  processes  of  turbulence  generation  and  regeneration.  These  repetitive 
patterns  were  originally  detected  by  the  use  of  various  flow  visualization 
techniques,  such  as  dye  and  hydrogen  bubbles,  but  similar  patterns  have 
been  subsequently  detected  using  direct  velocity  measurement  and 
computation  techniques  as  well.  The  most  organized  of  these  patterns  are 
found  nearest  the  solid  boundary,  or  wall,  and  have  been  characterized  by 
such  terms  as  low-speed  wall  "streaks,"  and  fluid  "ejections,"  "sweeps," 
and  "bursts.”  These  patterns  are  intermingled  with  patterns  which  relate  to 
apparent  vortices  of  manifold  descriptions.  These  patterns  reflect  the 
presence  of  vortices  that  appear  generally  more  coherent  in  proximity  to 
the  wall,  and  appear  to  evolve  into  increasingly  more  complex 
amalgamations  of  vortices  with  increasing  distance  above  the  surface. 


Well  removed  from  the  wall,  large  patterns  of  somewhat  organized 
vortical  fluid  described  as  “bulges”10,1*  appear  to  be  the  dominate  flow 
pattern  near  the  edge  of  the  boundary  layer. 

Low-speed  wall  streaks9,12,13  are  the  most  pervasive  turbulent  flow 
pattern  adjacent  to  a  bounding  surface.  Figure  1  shows  the  appearance  of 
these  low-speed  streaks  in  a  water  flow  visualized  by  lines  of  hydrogen 
bubble  markers  created  using  a  pulsed  electrolysis  process.  These  flow 

patterns  develop  very  close  to  the  surface  (about  y +  »  yu^.  Iv  <25  , 

where  y  is  distance  above  the  surface  and  wT  -  Jr/ p  is  the  shear 

velocity),  appearing  as  narrow,  closely-spaced  regions  of  low-speed  fluid, 
interspersed  between  regions  of  higher-speed  flow.  The  consensus  is  that 
this  pattern  of  alternating  high-speed/low-speed  flow  reflects  low-speed 
fluid,  originally  very  close  to  the  surface,  which  is  moving  away  from  the 
surface  in  narrow,  low-speed  bands,  and  being  replaced  by  high-speed 
fluid  inflows  in  regions  flanking  the  low-speed  bands. 


Bubble  Schematic  Actual  Image 

Wire 


Figure  1.  Visualization  of  low-speed  streak  pattern  beneath  a  turbulent 
boundary  layer 

When  one  considers  that  the  processes  of  turbulence  create 
significant  fluid  and  momentum  exchange,  resulting  in  elevated  shear 
stress  at  the  wall,  it  is  clear  that  the  streak  pattern  is  reflective  of  Nature’s 
mechanism  for  effecting  this  momentum  exchange  process.  The  fluid 
flowing  closest  to  a  surface  is  of  course  the  most  strongly  affected  by 
viscous  shear,  which  redistributes  momentum,  dissipates  energy,  and 
causes  the  continued  development  of  the  boundary  layer.  Nature’s 
problem  is  how  to  reenergize  this  viscously-retarded  boundary  layer  and 
keep  it  moving.  This  is  accomplished  in  a  laminar  flow  through  viscous 
diffusion,  until  the  boundary  layer  develops  to  a  thickness  where  this 
process  of  viscous  diffusion  of  momentum  becomes  unstable,  and  a  more 
effective  method  of  momentum  transport  becomes  necessary.  It  is  the 
generation  of  turbulence,  following  this  boundary  layer  destabilization, 
that  is  Nature’s  vehicle  for  infusing  momentum  and  energy  back  toward 
the  wall.  The  alternating  high/low  speed  streak  surface  pattern  reveals  the 
grand  plan  of  turbulence  for  implementing  this  momentum/energy  infusion: 
via  lateral,  extended  regions  of  surface  fluid/momentum  exchange. 


39 


This  surface  fluid  exchange  process  is  not  a  steady  process,  but 
occurs  in  an  intermittent,  somewhat  chaotic  manner,  with  low-speed  fluid 
from  the  wall  streaks  suddenly  rising  away  from  the  surface  and 
“ejecting”  into  the  passing  flow3.  The  reason  for  intermittent 
energy/momentum  transport  via  these  ejection  events,  rather  than  a  smooth 
transport  process,  is  generally  a  result  of  the  repetitive  breakdown  of  the 
low-speed  streaks.  Since  these  streaks  are  local  momentum  deficit  regions 
surrounded  by  higher- speed  flows,  local  inflectional  velocity  profiles 
develop  at  the  interface  between  the  outward  growing,  low-velocity 
streaks  and  the  higher-velocity  surrounding  flow,  as  shown  in  Figure  2 
from  a  study  of  Kim  et  al.3.  These  local  inflectional  regions  are  inherently 
unstable,  resulting  in  the  subsequent  breakdown  of  the  streak,  and  the 


Figure  2. 


The  original  streak  ejection  process  of  Kim  et  al.3 


side-view  schematic  of  this  process,  shown  in  Figure  2,  illustrates  how  this 
ejection  was  originally  observed.  To  balance  this  ejection  of  low-speed 
fluid,  continuity  considerations  require  that  a  portion  of  the  high-speed 
outer  fluid  replace  the  ejected  fluid,  which  appears  as  a  “sweep”  of 
higher-speed  fluid  moving  inward  toward  the  surface,  as  shown  in  Figure 
3.  Physically,  this  sweep  process  brings  new,  higher-momentum  fluid  into 
close  proximity  of  the  surface,  re-energizing  the  flow  near  the  surface. 

These  intermittent  ejections  and  sweeps  of  fluid  are  cumulatively  the 


Flow 


“Sweep 


Low-Speed 
Wall  Streaks" 


High-Speej 

Regions- 


High-Speed 
”  Inflows 


Low-Speed 
Streak  “Ejections” 


Figure  3.  Surface  fluid/momentum  exchange  via  low-speed  streak 
ejections  and  consequent  high-speed  inflows 


agents  of  a  more  encompassing  process  termed  “bursting.”  Originally,  the 
term  bursting  came  from  the  visual  appearance  of  localized  regions  of 
fluid  appearing  to  “burst”  rapidly  upward  from  near  the  boundary3. 
However,  over  the  years  turbulent  bursting  has  also  become  associated 
with  measured  “bursts”  of  fluid  momentum  (and  the  commensurate 
generation  of  Reynolds  stresses),  which  consist  of  the  transport  of  both  low 
momentum  fluid  away  from  the  surface  through  the  streak  ejections,  and 
high  momentum  fluid  toward  the  surface  by  the  inward  sweeps  of  fluid,  as 
illustrated  in  Figure  3. 

Remarkably,  the  streak  pattern  reflecting  this  surface  momentum 
exchange  is  extremely  repetitive  and  persistent,  demonstrating  a 
consistency  in  pattern  over  a  broad  range  of  Reynolds  numbers9,  1 


Figure  4  is  a  graph  from  Klewicki,  which  demonstrates  that  the  average 
nondimensional  spacing  between  the  low-speed  streaks  is  astoundingly 

consistent  at  A+  «  AwT  /  v  *  100  (where  A  is  the  average  spacing  between 
the  streaks)  over  Reynolds  numbers  ranging  from  low-speed  water  flows13 
to  atmospheric-scale  boundary  layers12.  However,  it  is  to  be  emphasized 
that  these  fluid/momentum  exchange  processes,  while  somewhat 
organized  immediately  adjacent  to  the  surface,  become  quite  irregular 


160- 
140- 
120- 
100- 
^  80- 
6  0- 
40- 
20- 


•  V*  i 


3 

•  Smith  &  Metzler 
□  Present  Study 


mj - r  t -mTTrf  >  i  i  >  rrrr| - r-r-rrrrrrj- 

4  5  6  7 

10  R  10  10  10 


Figure  4.  Average  low-speed  streak  spacing  in  turbulent  boundary 
layers.  Dark  symbols,  water  channel  flow;  open  symbol, 
atmospheric  flow.  (Klewicki  et  al.12) 

within  a  very  narrow  distance  from  the  surface,  with  the  spanwise 
regularity  of  the  process  degenerating  rapidly. 

The  presence  of  vortices  in  a  turbulent  boundary  layer  was 
hypothesized,  among  others,  by  Theodorsen8  and  Townsend  from 
theoretical  arguments,  and  Kim  et  al.3,  Head  and  Bandy opadhyay2,  and 
Smith6  from  visualization  studies.  However,  the  evaluation  by  Robinson 
of  an  early  Navier-Stokes  spatial-temporal  numerical  simulation  of  a  low 
Reynolds  number  turbulent  boundary  layer10,  clearly  began  to  illustrate  the 
manifold  presence  of  vortices  in  boundary  layers,  and  their 
interrelationships  with  other  turbulence  patterns.  Using  isosurfaces  of  low 
pressure  to  indicate  the  presence  of  rotational  vortices,  Robinson  was  able 
to  demonstrate  through  both  dynamic  simulations  and  statistical 
assessments,  that  there  appeared  to  be  two  predominant  types  of  vortex 
structures  populating  a  turbulent  boundary  layer:  horseshoe-shaped 
vortices  (often  termed  “heads”)  that  tend  to  be  oriented  transverse  to  the 
flow,  and  quasi-streamwise  vortices  (often  referred  to  as  “tilted 
streamwise  vortices”),  that  extend  in  a  predominantly  streamwise 
direction.  Figure  5  is  a  summary  schematic  of  the  type  of  the  generic 
three-dimensional  vortex  patterns  Robinson  detected  near  the  surface 
within  a  turbulent  boundary  layer.  Often  there  seemed  to  be  a  connection 
between  the  two  types  of  vortices,  with  the  streamwise  vortices  appearing 
to  be  a  streamwise  extension  (termed  a  “leg”)  of  a  horseshoe  head.  When 


Figure  5.  Summary  of  generic  vortex  topologies  and  juxtaposed 
behavior  established  for  a  low  Re  turbulent  boundary 
layer  computational  simulation  (after  Robinson  ). 


combined,  a  head  and  two  legs  are  often  termed  a  “hairpin”  vortex;  the 
more  predominant  pattern  of  a  head  plus  a  single  leg  is  often  termed  a 
one-legged  “hairpin.” 

Robinson  observed  that  vortices  appear  in  myriad  sizes,  but  it  is  the 
ones  nearest  the  surface  that  seemed  to  be  associated  with  the 
characteristic  turbulence  patterns  (i.e.  low-speed  streaks,  ejections. 


40 


Sweeps)  and  statistical  processes  (generation  of  Reynolds  stress). 
Interestingly,  the  horseshoe-type  vortices  seem  to  predominate  in  the 
region  away  from  the  surface,  and  the  quasi-streamwise  vortices  are 

dominate  in  the  near- wall  region  (about  y+  «  yUj.  /  v  -  100  ).  And  while 

both  types  of  vortices  seem  to  be  associated  with  the  generation  of  local 
Reynolds  stresses  (i.e.  local  momentum  exchange),  it  is  the  quasi- 
streamwise  vortices  that  are  most  associated  with  the  low-speed  streaks, 
and  generation  of  “new”  vortices. 

Well  removed  from  the  bounding  surface,  the  flow  becomes  quite 
complex,  with  the  flow  well  above  the  surface  dominated  by  highly- 
contorted  collections  of  vortical  fluid  extending  to  the  outer  edges  of  the 
boundary  layer.  These  patterns  are  generally  referred  to  as  turbulent 
“bulges”;  a  smoke  visualization  illustrating  these  bulges10  is  shown  in 
Figure  6.  It  has  been  demonstrated  that  these  bulges  are  somehow 
centrally  involved  in  the  accretion  or  engulfment  of  higher-velocity  fluid 
at  the  edge  of  the  boundary  layer11,  which  helps  facilitate  the  momentum 
exchange  process  in  turbulent  boundary  layers.  And  while  at  low 


Figure  6.  Smoke  visualization  of  turbulent  boundary  layer  bulges  (Falco1  °) 

Reynolds  numbers  these  bulges  appear  to  consist  of  essentially  the 
horseshoe  vortex  elements  observed  by  Robinson,  these  bulges  can  grow 
to  substantial  scale,  and  apparently  unfathomable  complexity,  such  that 
they  dominate  almost  all  of  the  boundary  layer  for  the  high  Reynolds 
number  boundary  layers  encountered  in  practical  aerodynamic  and 
hydrodynamic  flows. 

III.  PROCESSES 

In  a  recent  article  on  the  sustaining  mechanisms  of  turbulent 
boundary  layers,  turbulence  pioneer  Steve  Kline16  pointed  out  that,  “two 
central  questions  must  be  answered:  (i)  what  are  the  [flow]  structures  that 
extract  energy  from  the  mean  flow  and  convert  it  into  turbulent 
fluctuations?  (ii)  how  are  these  turbulence-producing  structures  created 
and  maintained?”  He  hypothesizes  that  the  tilted  streamwise  vortices  near 
the  wall,  and  the  head  vortices  in  the  outer  flow,  as  described  by 
Robinson5,  provide  the  mechanistic  answers  to  these  questions.  However, 
while  generally  agreeing  with  this  hypothesis,  if  one  is  to  make  use  of  flow 
structure  information  for  turbulence  drag  reduction/control  it  is  important 
to  understand  the  dynamics  of  vortices  that  support  Kline’s  hypothesis,  and 
to  examine  how  these  vortex  dynamics  both  relate  to  the  patterns  discussed 
in  the  first  section  of  this  paper,  and  are  intimately  involved  in  the 
sustaining  nature  of  turbulence.  This  section  briefly  examines  the 
processes  of  vortex  deformation,  vortex-vortex  interaction,  vortex-surface 
interactions,  and  vortex  regeneration,  pointing  out  how  these  processes 
relate  to  the  development  and  maintenance  of  turbulent  boundaiy  layers. 
For  a  more  detailed  discussion  and  review  of  these  concepts,  the  reader  is 
referred  to  Smith  et  al. 7  and  Doligalski  et  al. 1 . 

Evolution  of  Vortices  in  a  Shear  Flow:  Clearly,  the  boundary  layer 
of  a  turbulent  flow  is  an  environment  of  relatively  high  streamwise  shear. 
This  raises  the  question  of  how  vortices  evolve  in  the  presence  of  this  high 
shear.  To  address  this  question,  Hon  and  Walker17  considered  the 
evolution  of  a  three-dimensional  distortion  in  an  otherwise  two- 
dimensional  inviscid  line  vortex  located  in  a  shear  layer  near  a  bounding 
surface,  or  wall.  They  noted  that  when  the  fluid  above  the  wall  moves 
with  a  uniform  speed,  any  distortion  in  a  straight  vortex  appears  to 
gradually  spread  along  the  length  of  the  vortex,  but  does  not  amplify. 
However,  when  the  vortex  is  located  within  a  shear  flow ,  a  distortion  in  the 
line  vortex  immediately  starts  to  amplify  and  grow  as  a  result  of  Biot- 
Savart  effects,  displaying  the  temporal  development  shown  schematically 
in  Figure  7.  From  the  initial  distortion  (the  form  of  distortion  is  not  critical, 
if  it  is  small),  a  vortex  head  quickly  develops  and  rises  from  the  surface,  as 
shown,  bending  backward  in  the  shear  flow.  Concurrently,  vortex  legs 
evolve  and  move  progressively  toward  the  surface.  As  time  advances,  the 
vortex  head  moves  farther  from  the  wall,  while  the  legs  continue  to 
approach  the  wall.  As  a  result,  the  streamwise  extent  of  the  distortion 


continually  increases.  As  shown,  the  original  disturbance  also  spreads 
laterally ,  producing  vortex  structures  termed  “subsidiary  vortices”.  These 
subsidiary  vortices  are  produced  through  the  interaction  with  the 
background  shear  flow,  which  induces  a  spreading  of  the  disturbance  in 
both  the  streamwise  and  spanwise  directions,  yielding  a  characteristic 


trailing 
uniform  *e8 


primary 

bea(^f  subsidiary 
head 


shear 

flow 


Time 


Figure  7.  Generic  deformation  in  a  uniform 

shear  flow  of  an  inviscid  line  vortex  with  a 
small  initial  deformation 

“hairpin”  shape.  Note  that  the  characteristic  spacing  of  the  spanwise  legs 
is  dependent  on  the  vortex  strength  and  background  shear. 

Because  most  distortions  in  the  vorticity  field  of  a  turbulent  boundary 
layer  are  expected  to  be  asymmetric,  results  have  been  obtained  by  Smith 
et  al.7  for  a  variety  of  such  situations,  with  the  generic  behavior  illustrated 
in  Figure  8.  Here  the  initial  configuration  is  an  inviscid  line  vortex  strongly 
displaced  near  the  center.  As  shown,  in  this  case  a  "one-legged”  or 
asymmetric  hairpin  vortex  evolves  from  the  distortion  in  the  vortex,  with  a 
single  leg  developing  and  moving  toward  the  surface.  With  advancing 
time,  the  disturbance  expands  in  both  the  streamwise  and  spanwise 
directions  as  subsidiary  hairpin-shaped  structures  form  (although  not  as 
definitively  as  for  the  symmetric,  small-deformation  case).  Again,  the 


Figure  8.  Generic  distortion  in  a  uniform 
shear  flow  of  an  inviscid  line  vortex 
with  a  large  initial  deformation 

lateral  spacing  of  the  subsidiary  hairpins  is  found  to  be  highly  dependent 
on  the  level  of  background  shear. 

In  a  turbulent  boundary  layer,  the  background  shear  is  the  largest  at 
the  wall,  but  then  rapidly  diminishes  outside  of  the  near-wall  layer. 
Consequently,  as  a  hairpin-shaped  vortex  develops  in  this  environment,  the 
legs  of  the  vortex  squeeze  together  as  they  penetrate  toward  the  wall, 
whereas  the  head  expands  as  it  moves  away  from  the  wall7.  This  process 
is  similar  to  that  noted  by  Robinson5,  where  vortex  heads  were  observed  to 
(1)  send  legs  down  toward  the  surface,  and  (2)  have  a  greater  spanwise 
extent  with  distance  from  the  surface. 

If  one  considers  that  a  turbulent  boundary  layer  contains  myriad 
advected,  3-D  vortices  in  continual  asymmetric  distortion,  the  behavior  of 
the  inviscid  line-vortex  simulations  are  quite  instructive  as  to  how  vortices 
in  turbulence  behave.  Near  the  wall,  boundary  layer  vortices  are 
expected  to  be  of  relatively  small  spanwise  extent  and  varying  strengths, 
and  strongly  influenced  by  their  immediate  neighbors.  As  they  deform, 
each  of  the  vortices  produces  leg-like  extensions  which  propagate  toward 
the  wall.  In  the  complex  mutual  interactions  near  the  wall,  the  legs  of 
relatively  weak  vortices  will  either  intertwine  with  their  stronger  neighbors 


41 


or  dissipate  as  they  penetrate  the  viscous  flow  close  to  the  surface.  On  the 
other  hand,  strong  vortices  will  successfully  approach  the  surface  and 
undergo  a  process  of  vortex  surface  interaction  (which  is  discussed  later). 

In  contrast,  the  natural  tendency  for  the  vortex  heads  is  to  rise  and 
expand  laterally  in  the  shear  flow  as  they  migrate  away  from  the  tangle  of 
vorticity  near  the  surface  and  into  zones  of  decreased  shear.  In  addition 
to  lateral  expansion,  the  heads  of  the  vortices  are  hypothesized  to  undergo 
a  process  of  vortex  coalescence  and  reinforcement  as  the  upward- 
migrating  vortices  closely  approach  one  another.  This  coalescence  of 
multiple  hairpin-type  vortices  in  a  shear  flow  into  larger  flow  structures 
has  been  has  been  simulated7  and  is  depicted  schematically  in  Figure  9.  As 
suggested  by  the  schematic,  a  group  of  distorted  vortices  soon  start  to 
intertwine  and  amalgamate,  producing  an  asymmetric  hairpin  vortex 
structure  of  larger  spanwise  scale.  Note  that  only  a  slight  degree  of 


moving  zone  of  separation  within  the  boundary  layer  which  grows  rapidly 
normal  to  the  wall.  If  the  vortex  is  sufficiently  strong  and  close  to  the 
surface,  the  boundary-layer  fluid  beneath  the  vortex  will  rapidly  focus  into 
a  narrow  band  and  appear  to  leave  the  wall  as  a  sharply-focused  fluid 
spike19,  as  shown  in  Figure  10(c).  This  process  is  generically  known  as  an 
"unsteady  separation,”  which  implies  a  process  in  which  an  initially  thin 
boundary  layer  grows  rapidly  outward  and  interacts  strongly  with  the 
external  flow.  In  physical  terms,  the  fluid  particles  just  above  the  wall  are 
significantly  compressed  by  the  opposing  inertia  and  pressure-gradient 


Figure  9.  Generic  schematic  of  the 

amalgamation  of  a  sequence  of  initially 
distorted  line  vortices  in  a  shear  flow 

asymmetry  in  the  initial  vortices  leads  to  the  evolution  of  a  strongly 
asymmetric  vortex  entanglement. 

However,  inviscid  simulations  employing  the  Biot-Savart  law  must  be 
viewed  cautiously  in  extension  to  real,  viscous  situations,  since  such 
simulations  must  generally  be  terminated  when  two  vortex  cores  move  into 
close  proximity.  A  number  of  studies  have  shown  (e.g.  Zhou  et  al.18)  that 
when  vortices  come  into  close  approach,  the  vortex  cores  can  and  will 
break  and  reconnect,  which  cannot  be  described  by  a  Biot-Savart 
simulation.  The  probability  is  that  the  processes  of  vortex  reconnection, 
coalescence,  and  annihilation  (cross-cancellation  of  vorticity  (or  vorticies) 
of  opposite  sign)  will  all  lead  to  migration  of  vortices  away  from  the 
surface  and  their  growth  into  larger  vortex  structures.  In  fact,  recent  PIV 
results  obtained  by  Adrian20  at  high  Reynolds  numbers  suggest  that  the 
large  outer-region  structures  may  indeed  be  composed  of  a  more  or  less 
organized  coalescence  of  smaller  vortical  flow  structures  (a  process 
suggested  by  Falco10;  c.f.  Figure  6) 

Vortex-Surface  Interaction  and  Vortex  Regeneration:  The 
development  of  the  previously  discussed  low-speed  streaks,  and  their 
subsequent  breakdown  and  eruption  from  the  wall  can  be  explained  by  the 
viscous  response  of  the  fluid  near  a  wall  to  the  passage  of  wall-region 
vortices.  This  type  of  generic  response  is  demonstrated  in  a  number  of 
fundamental  experimental  and  theoretical  "kernel"  studies,  including  ^the 
motion  induced  by  a  two-dimensional  vortex  translating  above  a  wall’  *  . 
These  studies  illustrate  that  when  a  vortex  is  brought  into  close  proximity 
of  a  surface,  a  sequence  of  events  is  initiated  which  results  in  a  discrete 
eruption  of  wall-layer  fluid,  which  can  culminate  in  the  generation  and 
ejection  of  a  new  vortex.  The  following  summarizes  the  sequence  of 
events  that  occurs  due  to  strong  vortex  interaction  with  a  wall. 

Figure  10  illustrates  the  basic  surface-eruption  processes  created  b^ 
a  two-dimensional  vortex  advecting  in  a  uniform  flow  above  a  wall  . 
When  viewed  by  an  observer  moving  with  the  vortex,  the  instantaneous 
streamlines  associated  with  the  inviscid  flow  near  the  wall  will  appear 
generically  as  sketched  in  Figure  10(a);  note  that  the  details  of  the  vortex 
core  geometry  and  the  motion  inside  the  core  are  not  important.  As  the 
vortex  moves,  a  thin  unsteady  boundary  layer  must  develop  in  order  to 
satisfy  the  no-slip  condition  at  the  wall.  Characteristic  velocity  and 
pressure  distributions  (as  viewed  advecting  with  the  vortex)  are  impressed 
on  the  viscous  fluid  layer  [Figure  10(b)],  It  is  the  imposition  of  the  adverse 
portion  (on  the  trailing,  or  upflow  side  of  the  vortex)  of  this  translating 
pressure  gradient  that  stimulates  the  subsequent  interaction  process.  The 
presence  of  the  local  adverse  pressure  gradient  causes  the  formation  of  a 


Figure  10.  Schematic  of  the  generic  interaction 
of  a  vortex  in  close  proximity  to  a  surface 
with  the  viscous  wall  layer. 

forces,  causing  a  rapid  vertical  extension  of  the  fluid.  Thus,  the  presence 
of  the  leg  vortices  moving  wallward  in  a  turbulent  boundary  layer  provide 
the  stimulus  for  these  types  of  surface  interactions,  which  are  essentially 
the  low- speed  streaks  and  surface  ejections  discussed  in  section  II. 

An  important  effect  of  this  compression  process  is  a  local 
concentration  of  the  local  boundary  layer  vorticity  into  a  relatively  narrow 
band.  Under  normal  circumstances,  vorticity  diffuses  slowly  outward 
from  the  wall  in  response  to  a  pressure  distribution  imposed  at  the  outer 
edge  of  the  boundary  layer,  such  that  at  any  instant  the  vorticity  field  is 
relatively  smooth.  However,  once  an  event  of  the  type  illustrated  in  Figure 
10  occurs,  the  vorticity  field  is  concentrated  locally  into  a  double-sided 
shear  layer  which  moves  rapidly  away  from  the  wall.  Note  that  the 
generation  of  the  truly  eruptive  events  requires  a  strong  interaction 
process  that  will  generally  occur  only  when  a  strong  vortex  is  brought  into 
close  proximity  of  a  wall.  Relatively  weak  vortices,  or  vortices  which  are 
farther  removed  from  the  wall,  may  cause  boundary-layer  growth,  but 
such  growth  will  be  much  more  gradual  and  no  eruptive  response 
occurs1,19. 

The  three-dimensional  response  of  a  viscous  wall  layer  due  to  an 
advecting  three-dimensional  vortex,  such  as  the  vortices  depicted  in 
Figures  7  and  8,  is  rather  more  complicated  than  two-dimensional 
situations1.  An  eruption  stimulated  by  a  three-dimensional  vortex  tends  to 
develop  as  a  ridge  in  the  surface  fluid,  the  shape  of  which  depends  on  the 
portion  of  the  vortex  in  proximity  to  the  wall.  A  rapid  outward  penetration 
of  fluid  will  initiate  from  such  a  ridge,  with  die  furthest  penetration 
occurring  at  the  point  of  closest  approach  by  the  vortex.  These  eruptive 
tongues  of  fluid  have  been  illustrated  to  roll  rapidly  over  into  vortices  ’  , 
starting  from  the  point  of  highest  penetration  and  rolling  progressively 
outboard. 

This  process  of  vortex  regeneration  is  illustrated  using  an  asymmetric 
hairpin  vortex,  since  we  assume  that  most  wall-region  vortices  are 
asymmetric  with  one  dominant  trailing  leg,  as  Robinson  observed.  As 
sketched  in  Figure  11,  an  asymmetric  hairpin  vortex  can  potentially 
generate  surface-layer  separations  both  behind  the  head  and  immediately 
inboard  of  the  leg.  Note  that  in  the  region  immediately  behind  the  vortex 
head,  a  streamwise  region  of  adverse  pressure  gradient  develops,  which  is 
very  similar  to  that  produced  by  the  two-dimensional  vortex  shown  in 
Figure  10.  In  addition,  a  local  spanwise  adverse  pressure  gradient  also 
develops  on  the  upflow  side  of  the  dominant  vortex  leg.  In  general,  the 
adverse  pressure  gradient  associated  with  the  vortex  head  is  often  weak, 
and  may  not  stimulate  an  interaction,  since  the  head  moves  away  from  the 
wall  and  outward  in  the  shear  flow.  In  contrast,  the  vortex  leg  moves 
progressively  closer  to  the  wall,  which  intensifies  the  spanwise  adverse 
pressure  gradient  generated  by  the  leg. 


42 


As  indicated  in  Figure  11(a),  separation  initiates  along  U-shaped 
fronts,  with  the  tip  of  the  ejected  tongue  originating  somewhere  near  the 
base  of  the  U  and  moving  outward.  As  this  ejected  tongue  penetrates 
regions  of  increased  streamwise  velocity,  the  tongue  rolls  up  into  a  new 


Surface  Proximity 
Vortex 


Figure  11.  Generation  of  secondary  vortices  by  vortex-surface 
interaction  for  an  asymmetric  wall-region  vortex. 

hairpin-like  vortex  as  shown  in  Figure  1 1(b)  and  11(c).  In  the  final  stage 
of  this  viscous-inviscid  interaction,  the  erupting  ridge  completely  detaches 
from  the  surface  layer  and  a  new  secondary  hairpin  vortex  is  formed. 
The  displacement  of  fluid  outward  by  this  eruption/vortex  formation 
process  is  countered  by  an  inflow  of  faster-moving  fluid  from  immediately 
upstream  due  to  continuity  considerations.  As  discussed  in  section  II,  this 
inward  movement  of  fluid  appears  as  a  “sweep”  of  fluid  bringing  higher- 
momentum  fluid  to  the  wall. 

Note  that  the  events  shown  in  Figure  1 1  occur  intermittently,  over 
very  short  time  scales  (relative  to  that  of  the  overall  motion  of  the  vortex), 


(Top  View) 


(b)  One-Sided  Regeneration 

Figure  12.  Schematic  of  regeneration  of  hairpin-like 

vortices  in  the  near- wall  region  (modified  from 
Robinson5) 

and  that  the  eruptive  events  will  (generally)  not  occur  simultaneously  near 
the  head  and  leg.  Note  also,  that  for  the  less  common  case  of  a  symmetric 
hairpin-type  vortex,  the  process  shown  in  Figure  11  is  essentially  the  same 
except  that  the  eruptive  activity  associated  with  the  vortex  head  is 
expected  to  be  much  more  significant. 


The  process  outlined  here  is  consistent  with  the  description  of 
Robinson5  of  the  evolution  of  "new  vortical  arches"  (i.e.  new  hairpin 
vortices)  near  “quasi-streamwise”  vortices  (c.f.  Figure  5),  as  illustrated  in 
Figure  12.  Similar  to  Figure  11,  Robinson  identifies  two  types  of 
regeneration,  that  he  refers  to  as  (1)  symmetric  and  (2)  one-sided 
regeneration,  depending  on  whether  the  process  occurs  respectively 
behind  the  vortex  head  or  adjacent  to  the  leg,  with  the  one-sided 
regeneration  by  far  the  more  common  process. 

The  regenerative  process  outlined  in  Figure  1 1  was  clearly  observed 
by  Haidari  and  Smith21,  who  observed  that  the  production  of  new  hairpin- 
type  vortices  quickly  leads  to  the  streamwise  and  spanwise  spread  of 
turbulent-like  disturbances  in  an  otherwise  laminar  boundary  layer.  This 
spreading  is  the  result  of  an  ever-expanding  sequence  of  wall-layer 
eruption/hairpin  generation  cycles,  which  promote  continued  streamwise 
and  spanwise  growth.  Eventually,  a  lar|e^ structure  similar  to  a  turbulent 
spot  evolves  from  a  single  hairpin  vortex2  ’  . 

In  a  turbulent  boundary  layer,  newly -created  vortices  may  intertwine 
with  the  parent  vortex  or  neighboring  vortices  as  discussed  in  section  II. 
Alternatively,  new  vortices  can  act  to  induce  further  eruptions 
downstream,  thereby  perpetuating  the  generation  of  additional  hairpin-like 
vortices.  Note  that  only  those  vortices  strongest  and  closest  to  the  wall  will 
induce  eruptions.  Robinson5  detected  that  only  a  fraction  (perhaps  less 
than  fifty  percent)  of  lifted  streaks  roll  up  to  form  a  new  vortex,  with  the 
rest  appearing  to  dissipate  and  disappear. 

In  end-view  visualization  studies  of  the  turbulent  near- wall" 2  , 
visualization  material  introduced  immediately  upstream  has  been  shown  to 
concentrate  into  intermittent  spanwise  regions,  which  sporadically  erupt  in 
thin  spires  of  fluid  which  often  penetrate  outward  on  the  order  of  y+  *100. 
These  spires  are  believed  to  be  the  eruptive  regions  shown  in  Figure  11, 
and  are  coincident  with  the  ubiquitous  low-speed  streaks.  Consequently, 
these  eruptive  plumes  are  the  fundamental  way  in  which  fluid  and 
momentum  from  the  wall  region  is  exchanged  with  the  outer  part  of  the 
flow  and  turbulence  is  sustained. 

IV.  A  CONCEPTUAL  MODEL 

Based  the  vortex  processes  discussed  in  section  III,  a  conceptual 
model  is  hypothesized,  illustrating  how  vortex  development  and 
interactions  sustain  and  maintain  a  turbulent  boundary  layer.  The  key 
element  in  this  model  is  the  understanding  of  the  behavior  of  three- 
dimensional,  hairpin- type  vortices  in  proximity  to  a  surface. 

From  the  previous  discussion,  it  is  clear  that  once  vortex  deformation 
develops,  most  likely  due  to  transition  of  a  laminar  boundary  layer,  or 
from  external  vorticity  contamination,  hairpin-like  vortices  will  develop  in 
the  shear  layer  near  a  surface.  Once  these  three-dimensional  vortices  are 
present,  they  are  able  to  (1)  regenerate  new  vortices  through  an 
interaction  with  the  viscous  wall  layer,  (2)  interact  with  other  three- 
dimensional  vortices  to  yield  larger-scale  flow  structures,  and  (3) 
facilitate  the  transfer  of  energy  and  momentum  within  the  turbulent 
boundary  layer.  The  following  description,  in  conjunction  with  Figures  13 
and  14,  summarizes  the  key  aspects  of  a  vortex-based  conceptual  model 
both  for  the  transport  processes  in  the  near-wall  region,  and  for  the 
development  of  outer-region  flow  structures. 

•  Low- speed  streaks  are  generated  by  the  interaction  of  a  passing 
streamwise  or  hairpin-like  vortex  with  wall-region  fluid,  and  comprise  a 
narrow  spire  of  low-speed  fluid  lifted  from  the  wall.  If  the  original  vortex 
is  strong,  this  can  precipitate  a  burst  event  wherein,  a  streak  in  proximity  to 
the  vortex  penetrates  the  outer  flow  (i.e.  erupts),  destabilizes,  and  rolls 
over  into  a  secondary  hairpin-like  vortex  via  a  viscous/inviscid  interaction, 
resulting  in  the  ejection  of  a  portion  of  the  streak  into  the  outer  region.  If 
the  vortex  is  weak,  a  streak  may  form,  but  the  vortex  action  may  be 
insufficient  to  create  a  local  breakdown  and  subsequent  formation  of  a 
secondary  hairpin  vortex.  In  this  latter  case,  a  streak  will  either  diffuse  or 
be  acted  upon  by  subsequent  streamwise  or  hairpin-like  vortices 
(generated  independently  upstream),  which  can  cause  a  refocusing  of  the 
original  streak.  Vortex  interaction  with  an  existing  streak  can  cause  the 
original  streak  to  develop  further  (possibly  through  combination  or 
amalgamation  with  other  adjacent  streaks)  until  a  subsequent  eruption 
occurs. 

•  A  "burst"  is  conceptualized  as  the  local  breakdown  and  ejection 
into  the  outer  region  of  wall-layer  fluid  essentially  comprising  a  low-speed 
streak;  this  breakdown  is  a  form  of  localized  unsteady  separation, 
precipitated  by  a  local  adverse  pressure  gradient  created  by  an  advecting 
wall-region  vortex.  The  ejection  associated  with  this  burst  can  result  in  the 
formation  of  one  or  more  secondary  hairpin-like  structures  in  the 
immediate  wake  of  the  initial  vortex  via  a  viscous/inviscid  interaction;  a 


Original 
'  Vortex. 


New 

Vortex 


(Top  View) 

(a)  Symmetric  Regeneration 


43 


burst  may  also  occur  well  behind  the  initial  vortex  due  to  the  stimulation  of 
a  breakdown  by  the  passage  of  a  subsequent  vortex21 .  In  either  case,  the 
result  is  the  rapid  ejection  of  fluid  from  a  streak  into  the  outer  flow, 
regenerating  other  hairpin-type  flow  structures. 

•  A  "sweep"  is  the  three-dimensional  inflow  of  high-speed  fluid  from 
the  outer  region  due  to  both  the  formation  and  presence  of  hairpin-like 
vortices.  This  process  takes  conceptually  two  forms:  1)  During  the 
formation  stage,  when  low-speed  fluid  is  ejected  outward  from  a  streak, 
an  inflow  of  higher-speed  fluid  will  occur  near  the  plane  of  symmetry  of 
the  streak,  resulting  in  the  local  recovery  of  the  mean  velocity  profile23, 
which  will  appear  and  be  detected  as  a  local  acceleration  of  the  flow;  2) 
Alternatively,  higher-speed  fluid  will  be  induced  toward  the  wall  on  the 


Wall 
Vortices  - 


Vortex-Surface 

Interactions 


Ejections 


Viscous/Inviscid  \ 

Interactions  ' '  1  *  V ' 

V  N  > 


Energy  Input  via 
Stretching  in  Wall 
Gradient 

Y+-100 


High-Speed  “Sweep” 


Flow 


Low-Speed  Streak 
Generation 


Figure  13.  Generalized  processes  of  near- wall 
turbulence  generation. 

wallward-rotating  portion  of  either  a  quasi-streamwise  vortex  or  a  leg  of 
a  hairpin-like  vortex;  this  can  result  in  the  observation  (visual  studies)  or 
detection  (fixed  probe  studies)  of  what  appears  as  an  accelerated  "sweep" 
type  behavior5. 

•  As  illustrated  in  Figure  13,  the  processes  occurring  in  the  near-wall 
are  cyclical,  although  not  periodic.  Wall-region  vortices  interact  with  and 
precipitate  ejections  of  wall-region  fluid,  which  subsequently  roll  up  to 
form  new  vortices  through  viscous/inviscid  interactions  with  the  higher- 
speed,  outer-region  fluid.  This  process  defines  a  continuing  cycle  which 
perpetuates  both  the  elements  which  sustain  turbulence  (i.e.  three- 
dimensional  vortices),  and  the  process  for  their  generation  (i.e. 
viscous/inviscid  interactions). 

•  The  engine  that  powers  the  turbulence  regeneration  process  and  is 
necessary  to  sustain  the  energy  transfer  from  the  free-stream  to  the  near¬ 
wall  is  three-dimensional  vortex  stretching  in  the  local  velocity  gradient. 
As  suggested  originally  by  Theodorsen8,  the  formation  of  hairpin-like 
vortices  provides  the  logical  mechanism  for  achieving  this  energy  transfer 
process  in  the  near-wall  region,  with  the  energy  input  to  the  hairpin 
vortices  supplied  by  the  free-stream  work  done  during  vortex  stretching  in 
the  local  velocity  gradient.  Note  that  during  rapid  stretching  in  the  local 
velocity  gradient,  the  angular  momentum  (proportional  to  cor2)  in  a  tilted 
streamwise  vortex  or  leg  of  a  hairpin-like  vortex  will  be  roughly 
conserved,  while  the  energy  (proportional  to  co2r2)  will  increase 
significantly  as  the  vortex  tube  narrows.  Note  also  that  this  narrowing  of  a 
vortex  tube  sharply  increases  the  radial  velocity  gradients  within  the 
vortex  tube,  which  strongly  elevates  viscous  dissipation  (proportional  to  the 
square  of  the  velocity  gradient  in  the  tube);  as  is  characteristic  of 
turbulence,  this  dissipation  will  thus  be  highest  in  regions  of  high  shear, 
such  as  in  the  vicinity  of  the  wall. 

•  As  Figure  14  shows,  the  process  of  growth  to  a  fully- turbulent 
boundary  layer  can  be  explained  by  the  proximity  of  multiple  hairpin-like 
vortices  in  different  phases  of  development,  which  creates  a  condition 
conducive  to  three-dimensional  vortex  amalgamation  and  coalescence. 
This  process  of  amalgamation,  demonstrated  in  both  simulations7  (c.f. 
Figure  9)  and  experiments24,  suggests  that  local  collections  of  hairpin-like 
vortices  can  intertwine  and  interact  to  yield  essentially  a  hairpin-like 
structure  of  somewhat  larger  scale.  Recent  studies21,25  have  observed  the 
development  of  just  such  an  amalgamation  process,  tracking  the  controlled 
evolution  of  a  single  hairpin  vortex  into  a  multi-hairpin,  turbulent  spot-like 
structure.  This  suggests  that  the  outer  region  of  a  turbulent  boundary  layer 
can  evolve  from  hairpin-like  vortex  structures,  and  that  the  large,  arch¬ 
type  vortices5  observed  in  the  outer  region  of  turbulent  boundary  layers 


are  essentially  amalgams  of  initially  smaller,  deformed  vortices;  recent 

Boundary  of 

__  Turbulent  Behavior 

Outer  Flow  ,  . .  » 


—  Flow 

^^^^Entrainment 


Amalgamation  Growth 


Viscous/inviscid 

Interactions 


Wall  Vortices 


High-Speed“Sweep” 


Low-Speed  Streak 
Generation 


Figure  14.  Conceptual  model  of  turbulence 
regeneration,  amalgamation,  and  evolution  of  outer- 
region  structures 

PIV  results  by  Adrian20  strongly  support  this  interpretation  (note  also  the 
discrete-appearing  vortices  in  Figure  6). 

•  Since  the  larger  outer-region  structures  directly  interface  with  the 
free-stream  flow,  they  play  an  instrumental  part  in  inducing  the  flow  of 
higher-speed  fluid  toward  the  wall  (i.e.  intermittent  engulfment)  along  a 
tortuous  gauntlet  of  vortex- induced  motions,  terminating  in  a  “sweep” 
motion  at  the  wall,  as  shown  in  Figure  14.  However,  despite  the  overall 
size  and  strength  of  these  outer  structures,  the  stretching  mechanism  for 
energy  transfer  to  these  larger-scale  vortical  structures  is  strongly 
diminished  because  of  the  weak  mean-velocity  gradient  in  the  outer 
region.  Following  an  initially  strong  energy  input  to  the  initial  vortex  scales 
near  the  wall,  these  outer  structures  will  basically  “evolve”  to  larger  and 
larger  scales,  but  with  no  significant  additional  energy  input,  eventually 
succumbing  to  slow,  viscous  dissipation.  The  outer  part  of  the  boundary 
layer  may  thus  be  regarded  as  a  "graveyard"  for  vorticity,  where  the 
cumulative  remnants  of  deformed  wall-region  vortices  pass  through  a 
complicated  process  of  dissipation,  diffusion  and  mutual  cancellation, 
similar  to  the  hierarchy  model  of  Perry  and  Chong4 

As  a  cautionary  note,  one  should  recognize  that  the  above 
hypotheses  on  the  mechanisms  of  energy  exchange  and  growth  of  a 
turbulent  boundary  layer  are  based  on  studies  which  have  been  done 
primarily  at  low  Reynolds  number  and  on  smooth  walls.  Thus,  although 
one  presumes  that  the  basic  processes  outlined  above  should  maintain  in 
general,  caution  needs  to  be  exercised  when  extrapolating  these  processes 
to  the  very  high  Reynolds  number  behavior  encountered  for  flows  over 
aircraft  or  large  ships,  or  in  environmental  circumstances  where 
roughness  is  particularly  important,  such  as  flows  in  rivers  or  in  the 
atmospheric  boundary  layer.  Indeed,  the  earlier  cited  work  of  Klewicki 
et  al.  in  the  near  wall  of  a  true  atmospheric  boundary  layer,  indicates 
that  the  non-dimensional  spacing  of  streaks  measured  at  high  Reynolds 
numbers  is  consistent  with  the  spacing  originally  established  for  low 
Reynolds  number  flows.  However,  Klewicki  also  notes  several  variations 
in  local  turbulence  statistics  from  accepted  low  Reynolds  number  flows, 
such  as  reduced  levels  of  local  velocity  fluctuation.  It  is  unclear  whether 
such  differences  indicate  that  a  growth  in  boundary  layer  scale  results  in  a 
small  modification  of  the  energy  exchange  process  outlined  above,  or  a 
substantive  change  in  the  physical  processes  hypothesized  from  the  low 
Reynolds  number  studies. 

One  must  remember  that  at  high  Reynolds  numbers  the  outer  region 
turbulent  bulges  will  dominate  almost  the  entire  boundary  layer,  and 
contain  almost  all  the  momentum  and  energy.  It  thus  stands  to  reason  that 
the  outer  region  must  play  a  role  in  the  turbulence  regeneration  process. 
If  the  near-wall  structure,  as  Klewicki  shows  us,  is  essentially  canonical 
even  at  very  high  Reynolds  numbers,  the  best  guess  is  that  the  outer  region 
structure  acts  as  a  modulator  of  the  near-wall  response.  As  Meinhart  and 
Adrian26  have  shown,  the  outer  region  of  a  turbulent  boundary  layer  often 
displays  large  areas  of  almost  constant  velocity,  separated  by  irregular 
interfaces.  If  such  is  the  case,  the  possible  effect  on  the  turbulence 
regeneration  process  may  be  through  a  modulation  of  the  wall  processes 
by  the  application  of  a  lower-frequency  pressure  variation  on  the  near¬ 
wall  by  the  outer  flow  variations.  However,  it  is  expected  that  the 
character  of  the  physical  regeneration  process  at  the  wall  will  remain 
unchanged.  The  implications  of  these  variations,  and  whether  they 


44 


indicate  significant  changes  in  the  turbulent  energy  exchanges  process  at 
high  Reynolds  number  is  a  particularly  important  area  for  future  research. 

IV.  IMPLICATIONS  FOR  DRAG  REDUCTION/CONTROL 

The  reduction  of  turbulent  surface  drag  requires  a  reduction  in  the 
level  of  momentum  exchange  at  the  wall,  which  in  turn  requires  a 
reduction  of  the  bursting  activity  near  the  wall.  In  principle  this  may  be 
accomplished  either  by  reducing  the  number  of  low-speed  streaks  (i.e. 
"burst”  sites)  adjacent  to  the  wall  or  by  increasing  the  cycle  time  for  the 
momentum  exchange  bursting  process.  Considering  the  vortex  dynamics 
described  above,  it  is  clear  that  to  accomplish  this,  one  must  generally 
inhibit  the  interaction  of  the  near- wall  vortices  with  the  retarded  near-wall 
flow.  Since  these  vortices  generate  the  low-momentum  streaks  and 
eventually  provoke  an  eruption  to  produce  new  hairpin-like  vortices,  this 
cyclical  momentum  exchange  process  might  be  interrupted  in  at  least  two 
ways.  The  first  is  to  provide  mechanisms  which  inhibit  the  viscous-inviscid 
interaction  by  interfering  with  the  capability  of  the  vortices  to  focus  low- 
momentum  fluid  at  the  wall  and  generate  eruptions.  The  second  is  to 
maintain  the  streaks  in  a  stable  state  for  a  longer  period.  The  first  of  these 
approaches  is  clearly  the  mechanism  implemented  by  streamwise  surface 
riblets,  which  have  been  shown  to  be  effective  in  reducing  surface  drag 
by  up  to  10%27.  The  riblets  inhibit  lateral  flow  near  the  surface,  reduce 
the  capacity  of  wall-region  vortices  to  generate  low-momentum  streaks, 
and  thus  retard  the  wall  vortex  regeneration  process;  this  is  evidenced  by 
an  increase  in  streak  spacing2  ,  which  suggests  reduced  momentum 
exchange.  Passive  modification  of  surface  topography  to  interfere  with 
the  vortex  interaction  process  is  therefore  a  viable  approach  for  reducing 
the  local  momentum  exchange  process,  and  thus  surface  drag.  The  recent 
success  with  streamwise  fences  and  shark  scale-like  surface  modifications 
are  other  examples  of  this  approach27. 

The  maintenance  of  streak  stability  is  a  more  tenuous  approach, 
since  this  entails  a  delicate  balance  between  the  inherent  stability  of  the 
low-speed  streak  and  the  amplitude  of  the  destabilizing  pressure 
perturbations  in  the  outer  flow.  The  injection  of  a  polymer  into  the  near¬ 
wall  of  the  boundary  layer  is  an  example  where  streak  stability  is 
increased  by  addition  of  an  external  additive,  as  evidenced  by  wider 
streak  spacing  and  reduced  bursting  activity.  It  is  speculated  that  polymer 
addition  may  either  affect  the  streak  stability  directly,  by  inhibiting  lateral 
concentration  of  fluid  by  the  hairpin  vortices,  or  indirectly,  by  providing  a 
region  which  is  locally  more  viscous,  which  (1)  more  effectively  damps 
external  perturbations  (thus  retarding  streak  breakdown)  and  (2)  dissipates 
the  energy  in  the  hairpin  vortices  generated  by  the  breakdowns,  thus 
weakening  the  vortex  strength  of  the  hairpin  vortices  and  inhibiting  their 
effectiveness  in  perpetuating  the  vortex  regeneration  cycle. 

With  regard  to  active  control,  one  must  again  somehow  modify  the 
streak  development  process,  force  the  wall  flow  toward  uniformity,  and 
thus  reduce  the  development  of  the  eruptive  wall-region  momentum 
exchange.  Distributed  wall  suction  is  successful,  since  it  essentially 
removes  the  inner  layer  of  low-momentum  fluid.  Magnetic  effects  apply  a 
body  force  that  inhibits  movement  normal  to  the  surface,  and  thus  restricts 
the  development  of  low-momentum  streaks.  The  concept  of  generation  of 
opposite  sign  vortices  near  the  surface  by  surface  actuators,  with  the  intent 
of  effecting  vorticity  “cancellation”  of  the  strength  (and  thus  the 
regenerative  capabilities)  of  the  wall-region  vortices,  is  somewhat 
dubious.  It  is  unclear  that  such  actuators  are  capable  of  generating 
Sufficiently  “clean”  streamwise  vortices  to  effect  a  cancellation  process. 
And  if  such  vortices  can  be  effectively  generated  juxtaposed  to  the 
existing  wall  vortices,  it  is  not  clear  that  a  cancellation  process  will  occur, 
as  opposed  to  some  other  form  of  induced  motion.  Of  course,  one  must 
also  account  for  the  momentum  lost  during  the  generation  process  due  to 
the  form  drag  of  the  actuator,  which  raises  questions  of  net  drag  reduction. 

The  possibility  for  drag  reduction/control  by  manipulation  of  the 
outer  region,  either  passively  or  actively,  does  not  seem  to  hold  much 
promise,  since  this  region  is  effectively  an  inactive  participant  in  the 
turbulence  generation  process.  While  outer-region  splitter  plates  and 
airfoils  have  shown  that  they  can  have  a  temporary  effect  on  modifying 
surface  drag,  this  is  probably  due  to  a  modulation  of  the  local  surface 
pressure,  which  only  affect  the  near-wall  turbulence  regeneration  process 
adjacent  to  the  control  device.  And  as  has  been  shown,  when  device  drag 
effects  are  accounted  for,  the  net  system  drag  will  always  increase. 

ACKNOWLEDGEMENTS 

I  would  like  to  thank  the  AFOSR  for  their  extended  support.  I  would 
also  like  to  thank  Dr.  J.D.A.  Walker  for  his  long-standing  collaboration 
and  insight.  And  finally,  I  would  like  to  express  my  life-long  admiration 


and  thanks  to  Dr.  Steve  Kline  for  his  insight,  inspiration,  encouragement, 

mentorship,  and  guidance.  He  will  be  greatly  missed. 

REFERENCES 

1.  Doligalski,  T.L.,  Smith,  CJL,  and  Walker,  J.D.A.  “Vortex  interactions 
with  walls,”  Am .  Rev.  Fluid Mech.,  26,  573-616, 1994. 

2.  Head,  M.R.  and  Bandyopadhyay,  P.  “New  aspects  of  turbulent 
boundary  layer  structure,  J.  Fluid  Mech.,  107,  297-338, 1981. 

3.  Kim,  H.T.,  Kline,  S.J.,  and  Reynolds,  W.C.  “The  production  of 
turbulence  near  a  smooth  wall,”  J.  Fluid  Mech.,  50, 133-160, 1971. 

4.  Perry,  A.E.  and  Chong,  M.S.  “On  the  mechanisms  of  wall 
turbulence,”  J.  Fluid  Mech.,  119, 173-217, 1982 

5.  Robinson,  S.K.  “Coherent  motions  in  the  turbulent  boundary  layer,” 

Am.  Rev.  Fluid  Mech.,  23,601-639,  1991. 

6.  Smith,  C.R.  “A  synthesized  model  of  the  near-wall  behavior  in 
turbulent  boundary  layers,”  In  Proc.  8th  Biennial  Symp.  on  Turb ., 

Zakin,  J.L.  &  Patterson,  G.  (Ed),  U.  of  Missouri-Rolla,  299-327, 1984. 

7.  Smith,  C.R.,  Walker,  J.D.A.,  Haidari,  A.H.  and  Sobrun,  U.  “  On  the 
dynamics  of  near- wall  turbulence,”  Phil  Trans.  Roy.  Soc.  Lond.  A., 

336, 131-175, 1991. 

8.  Theodorsen,  T.  “Mechanism  of  turbulence,”  In  Proceedings  Second 
Midwestern  Conference  on  Fluid  Mechanics ,  Bull.  No.  149,  Ohio  State 
University,  Columbus,  Ohio,  1952. 

9.  Kline,  S.J.,  Reynolds,  W.C.,  Schraub,  F.A.  &  Runstadler,  P.W.  “The 
structure  of  turbulent  boundary  layers,”  J.  Fluid  Mech.,  95,  741-773, 

1967. 

10.  Falco,  R.E.  “Coherent  motions  in  the  outer  region  of  turbulent 
boundary  layers,”  Phys.  Fluids ,  20,  S124, 1977. 

11.  Kovasznay,  L.S.G.,  Kibens,  V.,  and  Blackwelder,  R.F.  “Large-scale 
motion  in  the  intermittent  region  of  a  turbulent  boundary  layer,”  J. 

Fluid  Mech.,  41, 283-325, 1970. 

12.  Klewicki,  J.C.,  Metzger,  M.M.,  Kelner,  E.,  and  Thurlow,  E.M. 

“Viscous  sublayer  flow  visualization  at  Ree**l  ,500,000,”  Phys.  Fluids , 

7,  857-865,  1995 

13.  Smith,  C.R  and  Metzler,  S.P.  “The  characteristics  of  low-speed  streaks 
in  the  near- wall  region  of  a  turbulent  boundary  layer,”  J.  Fluid  Mech., 
129,27-54,1983.. 

14/  Townsend,  A.A.  The  structure  of  turbulent  shear  flow.  Second  Edition, 
Cambridge  University  Press, 150-158, 1976. 

15.  Spalart,  P.R.  “Direct  simulation  of  a  turbulent  boundary  layer  up  to 
Ree«1410,”  J.  Fluid  Mech.,  187,61-98,  1988, 

16.  Kline,  S.J.  &  Portela,  L.M.  “A  view  of  the  structure  of  turbulent 
boundary  layers,”  in  Self-Sustaining  Mech.  of  Wall  Turb,.  R.L. 

Panton,  ed..  Comp.  Mech.  Pubs.,  Boston,  165-180,  1997 

17.  Hon,  T.L.  and  Walker,  J.D.A.  “Evolution  of  hairpin  vortices  in  a  shear 
flow,”  Computers  and  Fluids,  20,343-358,1991. 

18.  Zhou,  J,  Meinhart,  C.D.,  Balanchandra,  S.,  Adrian,  R.J.  “Formation 
of  coherent  hairpin  packets  in  wall  turbulence”  in  Self-Sustaining 
Mech.  of  Wall  Turb..  R.L.  Panton,  ed.,  Comp.  Mech.  Pubs.,  Boston, 

109-134, 1997. 

19.  Peridier,  V.J.,  Smith,  F.T.  &  Walker,  J.D.A.  “Vortex-induced 
boundary-layer  separation.  Part  2.  Unsteady  interacting  boundary- 
layer  theory,”  J.  Fluid  Mech.,  232,  133-165, 1991. 

20.  Adrian,  R.J.  Private  communication,  1998. 

21.  Haidari,  A.H.  and  Smith,  C.R.  “  The  generation  and  regeneration  of 
single  hairpin  vortices,”  J.  Fluid  Mech.,  277, 135-162, 1994. 

22.  Wallace,  J.M.  and  Balint,  J.L.  “  Flow  visualization  study  of  the  effects 
of  trip  type  on  the  structure  of  the  turbulent  boundary  layer,”  Video 
Tape,  Turbulence  Laboratory,  University  of  Maryland,  1990. 

23.  Lu,  L.J.  and  Smith,  C.R.  “Use  of  flow  visualization  data  to  examine 
spatial-temporal  velocity  and  burst-type  characteristics  in  a  turbulent 
boundary  layer,”  J.  Fluid  Mech.,  232,  303-340,  1991. 

24.  Gretta,  W.J.  and  Smith,  C.R.  “The  flow  structure  and  statistics  of  a 
passive  mixing  tab,”  ASMEJ.  Fluid  Engng.,  115,  225-263, 1993. 

25.  Singer,  B.A.  and  Joslin,  R.D.  “Metamorphosis  of  a  hairpin  vortex  into 
a  young  turbulent  spot,”  Phys.  Fluids .,  6,  3724-3730, 1994. 

26.  Meinhart,  C.D.  &  Adrian,  R.J.  “On  the  existence  of  uniform 
momentum  zones  in  a  turbulent  boundary  layer,”  Phys.  Fluids,  7,  694- 
696, 1995. 

27.  Bechert,  D.W.,  Bruse,  M.,  Hage,  W.,  &  Van  Der  Hoeven,  J.G.T.,  “Experiments 
on  drag-reducing  surfaces  and  their  optimization  with  an  adjustable  geometry,” 
J.  Fluid  Meek,  338,  59-87,  1997. 

28.  Bacher,  E.V.  &  Smith,  C.R.  "Turbulent  Boundary-Layer  Modification  by  Surfac< 
Riblets' UJAA  J.,  24,  8,  1382-1385,  1986. 


45 


COHERENT  STRUCTURES,  SELF-SUSTAINING  PROCESS 
AND  BIFURCATIONS  IN  SHEAR  FLOWS 


Fabian  Waleffe 

Departments  of  Mathematics  and  Engineering  Physics 
Center  for  Mathematical  Sciences 
University  of  Wisconsin-Madison 
Madison  WI  53706-1388 
waleffe@math.wisc.edu 

Abstract:  Experiments  and  simulations  have  revealed  the  existence  of  Coherent  Structures  in  the  near¬ 
wall  region  of  turbulent  shear  flows.  A  complete  self-sustaining  process  responsible  for  the  origin  of  those 
structures  is  briefly  reviewed.  The  process  consists  of  streamwise  rolls  that  create  streaks  whose  instability 
directly  feeds  back  onto  the  rolls.  The  understanding  of  that  process  is  used  to  calculate  exact  hidden 
steady  states  of  the  Navier-Stokes  equations  that  are  strikingly  similar  to  the  observed  coherent  structures. 
The  self-sustaining  process  thus  appears  to  be  fundamental  to  the  physics  of  near-wall  turbulence.  Its 
elucidation  and  characterization  should  provide  a  solid  basis  for  the  development  of  turbulence  models  and 
control  strategies. 


I.  INTRODUCTION 

This  work  presently  focuses  on  fundamentals  of  wall  tur¬ 
bulence  physics  and  in  particular  on  the  physical  origin  of  the 
observed  coherent  structures  (CS).  The  objective  is  to  estab¬ 
lish  the  complete  dynamical  and  mathematical  characterization 
of  a  nonlinear,  three-dimensional,  self-sustaining  process  (SSP) 
suggested  by  many  experimental  observations.  Instead  of  di¬ 
rectly  trying  to  model  the  observations,  the  strategy  has  been 
to  take  clues  from  those  observations  to  extract  a  fundamen¬ 
tal  nonlinear  process  from  the  Navier-Stokes  equations.  One 
of  the  most  surprising  results  of  this  approach  is  the  calcula¬ 
tion  of  hidden  ordered  solutions  that  are  intimately  linked  to 
the  coherent  structures.  The  calculation  of  these  steady  and 
other  periodic  or  nearly-periodic  solutions  provide  a  solid  foun¬ 
dation  for  the  notion  of  “active  motions”  in  the  near-wall  layer 
that  can  be  completely  and  rigorously  separated  from  the  “in¬ 
active  motions”.  A  fundamental  understanding  of  the  physics 
of  near-wall  turbulence  is  essential  to  the  development  of  robust 
turbulence  models  and  optimum  control  strategies.  Turbulence 
models  of  the  “K-Epsilon”  type,  for  instance,  require  a  variety 
of  drastic  and  ad  hoc  adjustments  ( e.g .  wall  functions)  in  order 
to  recover  adequate  near- wall  behavior,  that  are  symptomatic 
of  an  incomplete  understanding  of  the  wall  layer  dynamics.  The 
elucidation  of  the  SSP  should  remedy  that  unsatisfactory  aspect 
of  turbulence  models. 

With  respect  to  drag  reduction,  this  work  and  observations 
suggest  that  much  of  the  “turbulent”  drag  actually  results  from 
the  coherent  motions.  Indeed,  the  disorder  characteristic  of  tur¬ 
bulence  may  actually  reduce  the  drag  that  would  result  from  the 
the  3D  ordered  steady  solutions  such  as  those  discussed  below. 
The  characterization  of  the  SSP,  and  low-order  models  of  that 
process  in  particular,  should  thus  be  critical  to  the  development 
of  active  control  strategies. 

II.  COHERENT  STRUCTURES 

Coherent  structures  in  the  near-wall  region  of  turbulent 
shear  flows  were  first  revealed  by  visualization  experiments 
about  three  decades  ago  [1].  Many  analyses  of  experiments 
and  computer  simulations  have  educed  the  typical  structures 
and  shown  their  relationship  not  only  with  the  increased  drag 


on  the  wall,  but  also  with  the  maintenance  of  turbulence  it¬ 
self.  A  sketch  of  the  typical  coherent  structure  is  shown  in 
Fig'.  1  [4,5].  This  sketch  summarizes  a  series  of  analyses  of  a 
well-known  database  of  computer  generated  turbulent  channel 
flows  [6],  Experimental  visualizations  {e.g.  [2,3])  often  empha¬ 
size  symmetric  structures  known  as  hairpin  vortices ,  as  opposed 
to  the  staggered  vortices  of  Fig.  1.  Although  the  numerical  and 
theoretical  evidence  tend  to  favor  the  asymmetric  structure  of 
Fig.  1,  and  there  has  been  much  debate  over  which  structure 
predominates,  the  underlying  physical  processes  are  in  fact  es¬ 
sentially  identical.  The  existence  of  two  types  of  structures  is 
closely  related  to  the  existence  of  two  modes  of  instability  of 
wakes:  sinusoidal  and  varicose  [9,11,12].  The  beautiful  sketches 
of  the  generation  and  regeneration  of  hairpin  vortices  in  Acarlar 
&  Smith  [2]  were  in  fact  most  inspiring  to  this  author,  as  was  the 
theoretical  work  of  Benney  [16]  on  a  “mean  flow-first  harmonic 
theory”. 


data,  from  Ref.  [4],  see  also  [5]. 

III.  SELF-SUSTAINING  PROCESS 

A  complete,  three-dimensional,  self-sustaining  process 
(SSP)  responsible  for  the  coherent  structures  has  been  stud- 


47 


ied  [7-12].  For  the  case  of  plane  parallel  shear  flow  in  the  X 
direction  between  two  walls  located  at  y  =  il,  the  process 
can  be  seen  as  consisting  of  the  interaction  between  three  ele¬ 
ments:  streamwise  rolls,  streaks  and  a  streak  instability.  The 
streamwise  rolls  [0,  V (y,  z),  W(y,  z)\  redistribute  the  mean 
momentum  [U(y):  0,  0]  to  create  a  spanwise  modulation  of  the 
streamwise  velocity  known  as  streaks  [U(y,z)  —  £/(y),  0,0] 
(these  fields  maybe  time-dependent  but  t  is  kept  implicit).  The 
resulting  spanwise  inflections  drive  a  three-dimensional  instabil¬ 
ity  leading  to  the  development  of  a  sinusoidal  modulation  in  the 
streamwise  direction  of  the  form  eiaxv(y,  Z )  4*  C.C..  The  non¬ 
linear  quadratic  interaction  of  the  latter  with  its  conjugate,  i.e. 
v(y,  z)v*(y,  z)  feeds  back  on  the  X-averaged  flow.  This  feed¬ 
back  is  the  direct  and  primary  effect  of  nonlinearity  (together 
with  the  generatiqn  of  an  e2zax  harmonic). 


advection  of  y 
mean  shear  i 


Streamwise 

Rolls 


nonlinear 
self -inter action 

FIG.  2.  The  self-sustaining  process. 


The  full  equations  for  the  X-averaged  flow  consist  of  one 
equation  for  the  streaky  flow  Ux  —  U(y^z)  and  one  equation 
for  the  streamwise  rolls  which  can  be  represented  in  terms  of  a 
streamfunction  \I/(y,z)  with  vx  —  V(y,z)  =  dz^ ,  wx  = 
W(y,z )  =  -dy$.  These  equations  read  respectively 


F(y)- 


du'v,x 

dy 


d  u'w'x 

Fz 


(i) 


4- v2$  +  J(V2tf , ¥)  -  4v4*  = 
Ot  -ti 


where  the  primed  variables  are  the  ^-dependent  fluctuations 
with  u,X  —  V1  =  U)'  =0.  It  has  been  demon¬ 

strated  elsewhere  [8,9,11]  that  the  nonlinear  interaction  of  the 
streaky  flow  eigenmode  etaxv(y ,  z)  with  its  complex  conjugate 
e"za2;v*  (y,  z)  leads  to  Reynolds  stresses  u'v '  ,  u'w*  whose 
net  effect  is  to  extract  energy  from  the  streaks  while  the  net  ef¬ 
fect  of  the  stresses  VlV*  ,VfWr  and  wfWf  is  to  regenerate  the 
streamwise  rolls.  It  is  noteworthy  that  the  stresses  Ufvl  ,  U [w 1 
put  energy  back  into  the  mean  shear  U (y).  Energy  and  momen¬ 
tum  are  extracted  from  the  mean  shear  by  the  X-independent 


components:  [C/(y,z)  —  U(y)]V(y,z)  averaged  over  z.  The 
overbar  denotes  an  average  over  both  X  and  Z. 

The  term  F(y)  in  the  U(y,z)  equation  represents  a  steady 
deterministic  forcing  that  maintains  the  shear  flow  ( e.g .  F(y)  = 
constant  for  plane  Poiseuille  flow).  In  this  paper,  F(y)  =  0 
and  the  shear  flow  is  maintained  by  the  boundary  conditions 
(namely  imposed  stress  at  the  walls)  but  other  F(y)  have  also 
been  considered  such  as  F(y)  OC  sin  7H//2  with  free-slip  bound¬ 
ary  conditions  (i.e.  du/dy  =  dw/dy  =  v  =  0  at  y  =  ±1). 
Imposed  stress  can  be  seen  as  a  limit  case  of  the  body  force 
situation  in  which  the  forcing  consists  of  Dirac  delta  functions 
localized  at  the  plates:  F(y)  =  2 R~*\5(y  —  1)  —  5(y  +  1)]. 
For  imposed  stress,  one  steady  solution  of  the  Navier-Stokes 
equations  has  the  plane  Couette  flow  form,  U(y)  =  2/,  and  is 
linearly  stable  for  all  Reynolds  numbers.  Many  other  linearly 
stable  plane  parallel  shear  flows  U (y)  can  be  constructed  by 
proper  choices  of  F(y)  [13]. 


IV.  HIDDEN  STEADY  STATES 

Numerical  simulations  [7,8],  a  stability  analysis  [9,11]  and 
a  low-order  model  [10,11]  have  been  used  to  study  the  SSP. 
Here,  the  existence  of  steady  states  that  are  remarkably  simi¬ 
lar  to  the  coherent  structure  of  Fig.  1  is  shown  for  the  case  of 
plane  Couette  flow  with  imposed  stress  at  the  wall,  correspond¬ 
ing  to  the  boundary  conditions  du/dy  =  1,  dw/dy  =  V  =  0 
at  y  =  ±1.  The  steady  states  are  exact  solutions  of  the 
Navier-Stokes  equations  for  incompressible  flow  with  no  turbu¬ 
lence  model  and  no  approximations,  except  for  negligible  error 
from  numerical  truncation  of  the  modal  expansions.  Similar 
steady  solutions  exist  for  no-slip  (imposed  velocity)  boundary 
conditions.  The  imposed  stress  boundary  condition  is  instruc¬ 
tive  because  it  eliminates  several  potential  mechanisms  for  the 
origin  of  the  coherent  structures.  Viscous  instabilities  leading 
to  growing  Tollmien-Schlichting  waves  cannot  occur  [13]  for  in¬ 
stance,  and  the  viscous  rebound  mechanism  [14]  cannot  operate 
either. 

The  velocity  field  is  expanded  into  Fourier  modes  in  all  3 
directions.  The  expansion  is  truncated  to  keep  only  the  Fourier 
modes  with  indices  (/,m,n)  in  directions  X,y,Z  respectively, 
that  satisfy 


VLT  +  r  'Mr- 


with  p  =  1,2,00.  Resolutions  that  provide  converged  results 
on  the  scale  of  the  plots  (errors  of  less  than  1%)  are,  for  in¬ 
stance,  [Lr,  Mr,  Nt]  =  [11,  25,  11]  for  p  =  1  (1256  degrees 
of  freedom),  and  [8,20,8]  for  p  =  2  (1764  degrees  of  free¬ 
dom)  (Fig.  4  results).  The  Fourier  expansion  in  the  wall-normal 
direction  is  not  asymptotically  satisfactory  as  it  lead  only  to 
algebraic  scaling  (error  0(m"4)  as  m  ->  (X)).  However,  for 
the  low  truncations  to  which  we  are  limited  for  the  continuation 
procedure,  the  Fourier  expansion  may  actually  be  superior  to 
an  asymptotically  exponential  expansion  in  Chebyshev  modes. 
The  better  accuracy  of  the  Fourier  expansion  for  low  truncations 
(i.e.  Mt  <  25)  was  verified  for  the  linearized  vertical  vorticity 
equation  (the  “Squire  equation”). 

The  procedure  to  compute  steady  states  consists  in  cal¬ 
culating  a  solution  of  the  steady  Navier-Stokes  equations  by 


48 


Newton’s  method.  The  key  issue  is  to  generate  a  suitable 
initial  guess.  A  good  initial  guess  is  provided  by  a  “mean 
field”  approach  [9,11]  based  on  the  self-sustaining  process,  where 
the  mean  field  consist  of  a  steady  ^-averaged  streaky  flow 
and  streamwise  rolls  [C/(y,  z),  V{y,  z),  W(y,  z)].  The  mean 
field  is  constructed  by  picking  the  weakest  streamwise  rolls 
[0,  V(y,  z),  W(y,  z)]  that  create  the  largest  streaks,  holding 
the  rolls  steady  and  computing  the  corresponding  steady  streaky 
flow  [U (yy  z),  0,  0]  which  is  the  solution  of  the  linear  advection- 
diffusion  equation  V dU / dy  +  W8U / dz  =  R~X V2t/.  A  lin¬ 
ear  eigenvalue  analysis  of  the  streaky  flow  [9,11]  is  then  employed 
to  locate  the  streamwise  wavenumber'  a  at  which  the  streaky 
flow  is  marginally  stable  and  to  compute  the  corresponding  neu¬ 
tral  eigenmode  etaxv(y,  z)  +  C.C..  The  nonlinear  interaction 
of  that  mode  with  its  conjugate  has  been  shown  to  properly 
feed  back  on  the  streamwise  rolls.  The  amplitude  of  that  eigen¬ 
mode  can  then  be  chosen  so  as  to  exactly  balance  the  viscous 
dissipation  of  the  streamwise  rolls  (Eqn.  (6)  in  [11]).  This  pro¬ 
cedure  provides  an  initial  guess  good  enough  for  the  calculation 
of  an  exact  steady  solution  of  the  incompressible  Navier-Stokes 
equations  by  Newton’s  method. 

The  steady  solutions  come  in  pairs.  They  arise  “out  of 
nowhere”  through  a  saddle-node  bifurcation  as  for  the  simple 
ODE  y  =  (R  —  Rc)  —y2  which  has  no  fixed  point  for  R  <  Rc 
but  two  fixed  points  for  R  >  Rc.  The  solutions  are  referred 
to  as  “upper”  and  “lower  branch  solutions”  based  on  the  am¬ 
plitude  of  the  modulation  in  X  (Fig.  3).  Both  solutions  look 
alike  as  they  result  from  the  same  self-sustaining  process.  The 
upper  branch  has  a  more  pronounced  waviness  in  X  but  weaker 
streaks  than  the  lower  branch.  For  Oi  =  0.48  and  spanwise 
wavenumber  7  =  1.50,  the  3D  steady  states  do  not  exist  be¬ 
low  R  144.  This  is  not  the  smallest  Reynolds  number  at 
which  such  steady  states  exist.  The  absolute  smallest  R  has 
not  been  fully  calculated  yet  but  appear  to  be  around  110  for 
the  optimum  a  and  7.  Figure  4  shows  the  upper  branch  steady 
state  at  R  =  150  for  O'  =  0.48  and  spanwise  wavenumber 
7  =  1.5.  The  maximum  velocity  components  at  the  mid¬ 
plane  y  —  0  (xz  cut)  are  max(u)  =  0.29,  max(v)  —  0.07, 
max(u>)  =  0.11,  and  at  the  mid-section  X  =  7 r/a  ( yz  cut) 
they  are  0.75,  0.06  and  0.12,  respectively.  The  similarity  with 
the  sketch  of  the  coherent  structures  in  Fig.  1  is  striking.  The 
wavy  low-speed  streak  and  the  staggered  vortices  are  clearly 
recognizable.  It  is  remarkable  that  such  strong  similarity  occurs 
in  spite  of  the  facts  that  Fig.  1  is  a  sketch  of  an  ensemble  av¬ 
erage  of  snapshots  of  a  turbulent  channel  flow  with  no-slip  at 
the  walls  at  J?*  =  180  while  the  steady  solution  of  Fig.  4  is 
an  exact  steady  state  occupying  the  full  channel  with  imposed 
stress  at  the  walls  at  R*  ~  \/150  «  12.25.  The  friction 
Reynolds  number  R *  =  u*hjv  is  based  on  the  friction  veloc¬ 
ity  u 2  ’=  udU / dy\ waii  and  the  half-channel  width  h.  The 
mean  flow  for  the  steady  state  of  Fig.  4  is  shown  in  Fig.  5.  The 
maximum  velocity  is  less  than  half  the  maximum  velocity  in  the 
basic  laminar  flow  plane  Couette  flow  U(y)  =  y. 


Bifurcation  diagram 


FIG.  3.  Bifurcation  diagram  for  3D,  nonlinear  steady  states 
at  a  =  0.48  and  spanwise  wavenumber  7  =  1.5. 


U  contours  at  y=0 


x 

U-W  velocities  at  y=0 


U  contours,  V-W  velocities  at  x=  n/a 


FIG.  4.  Cuts  through  exact  upper  branch  steady  solution  at 
R  —  150,  a  =  0.48,  7  =  1.5.  Compare  xz  cuts  to  ‘Plan  View’ 
in  Fig.  1  and  yz  cut  to  ‘Section  XX’  in  Fig.  1. 


49 


Mean  flow 


FIG.  5.  Mean  flow  U(y)  for  upper  branch  steady  state 
(solid)  and  basic  steady  state  U(y)  =  y  (dashed). 

Such  steady  solutions  appear  to  exist  for  forcings  F(y)  in 
(1)  that  are  sufficiently  localized  near  the  walls  in  which  case  the 
mean  shear  dU / dy  of  the  steady  streaky  flow  U(y,z)  is  wiped 
out  in  the  center  of  the  channel  (Fig.  5).  For  the  sinusoidal 
forcing  F(y)  =  7T2/(4i?)  sin7n//2,  there  are  apparently  no 
steady  states.  Spurious  steady  states  can  be  found  that  do  not 
converge  as  the  truncation  is  increased.  For  that  sine  forcing  the 
mean  shear  of  the  streaky  flow  remains  close  to  sinusoidal  and 
is  thus  maximum  at  the  center  of  the  channel.  The  bifurcation 
from  purely  streamwise  flow  then  occurs  through  a  subcritical 
Hopf  bifurcation,  hence  we  expect  that  a  saddle-node  bifurca¬ 
tion  of  cycles  takes  place  with  sine  forcing  ( i.e .  wall-bounded 
Kolmogorov  flow).  The  low-order  model  developed  earlier  [9,11] 
is  still  expected  to  apply  but  the  variable  “W”  should  be  rein¬ 
terpreted  as  the  amplitude  of  the  cycle  in  such  cases. 

Similar  steady  state  solutions  exist  for  the  regular  plane 
Couette  flow  with  no-slip  boundary  conditions.  Such  solutions 
have  been  calculated  by  other  authors  recently,  either  by  contin¬ 
uation  of  wavy  Taylor- Couette  vortices  in  rotating  plane  Cou¬ 
ette  flow  [17,18]  or  of  wavy  convection  rolls  in  sheared  convection 
[19].  The  exact  nature  of  the  boundary  conditions,  imposed  ve¬ 
locity  or  imposed  stress,  thus  does  not  have  much  effect  on  the 
steady  states.  This  is  probably  because  the  self-sustaining  pro¬ 
cess  responsible  for  those  solutions  is  essentially  nonlinear  and 
inertial.  In  fact,  the  present  evidence  is  that  even  the  critical 
Reynolds  numbers  for  existence  of  the  3D  steady  states  are  very 
close,  within  10%  of  each  other,  for  both  types  of  boundary  con¬ 
ditions.  In  contrast,  the  critical  Rayleigh  number  in  Rayleigh- 
Benard  convection  with  free-slip  boundary  conditions  is  about 
657  and  thus  significantly  different  from  the  critical  value  of  1708 
with  no-slip  boundary  conditions. 

V.  BRIEF  DISCUSSION 

The  3D  steady  solutions  have  been  dubbed  “hidden”  be¬ 
cause  they  are  unstable.  Hence  they  cannot  be  observed  in 
physical  experiments  or  through  numerical  simulations  of  the 
time-dependent  Navier-Stokes  equations.  Preliminary  analyses 


indicate  that  the  lower  branch  of  solutions  is  a  “saddle  point” 
(i.e.  a  linear  stability  analysis  of  that  solution  always  yields  one 
positive  real  eigenvalue)  as  expected  from  a  saddle-node  bifur¬ 
cation.  The  upper  branch,  however,  is  not  the  expected  stable 
node.  Instead,  it  would  appear  as  an  unstable  node  (two  positive 
real  eigenvalues)  near  onset  and  quickly  turn  into  an  unstable 
spiral  as  the  Reynolds  number  is  increased.  This  behavior  is  in 
agreement  with  that  seen  in  a  related  low-order  model  [11].  The 
strong  similarity  with  the  observed  coherent  structures  suggests 
however,  that  the  steady  solutions  may  be  central  to  our  under¬ 
standing  of  turbulence  in  shear  flows  in  spite  of  their  instability, 
or  perhaps  because  of  it.  These  solutions  may  for  instance  pro¬ 
vide  the  “backbone”  for  strange  attractors.  This  would  mean 
that  although  the  flow  does  not  settle  onto  a  steady  state,  it 
fluctuates  around  or  between  them.  This  is  also  suggested  by 
the  numerical  simulations  analyzed  in  Ref.  [8].  Although  the 
solutions  herein  have  been  calculated  at  low  Reynolds  numbers, 
there  is  no  evidence  that  these  solutions  cease  to  exist  for  larger 
Reynolds  number.  In  fact,  a  simple  asymptotic  argument  sug¬ 
gests  that  the  solutions  exist  for  all  Reynolds  numbers  above 
their  (finite)  critical  value.  Figure  5  shows  that  these  ordered 
steady  states  have  strongly  decreased  flow  velocity  for  imposed 
drag  (or  increased  drag  for  imposed  velocity)  as  compared  to  the 
basic  laminar  shear  flow.  Thus,  in  agreement  with  research  on 
coherent  structures,  the  “turbulent”  drag  probably  results  from 
the  hidden  ordered  solutions  (the  “active  motions”)  while  the 
disorder  itself  results  from  the  transient  instabilities  (the  “in¬ 
active  motions”)  of  those  sustained  ordered  states  and  in  fact 
probably  reduce  the  maximum  drag  achievable  by  the  coherent 
motions. 

The  existence  of  these  hidden  steady  states  is  remarkable 
and  should  have  fundamental  implications  for  the  nature  of  tur¬ 
bulence  and  its  onset  in  shear,  flows.  The  calculation  of  these 
steady  states  provide  an  excellent  objective  verification  of  the 
validity  of  the  Self-Sustaining  Process.  From  an  applications 
point  of  view,  the  derivation  of  simplified  njodels,  such  as  the 
low-order  model  or  the  mean  field  approach  [10,11]  sufficiently 
sophisticated  to  faithfully  capture  the  self-sustaining  process 
promises  to  lead  to  robust  turbulence  models.  Simplified  models 
could  also  be  incorporated  into  prediction  and  control  strategies 
in  order  to  reduce  drag.  As  discussed  above,  controlling  the  co¬ 
herent  motions  allowed  by  the  SSP  appear  to  be  the  key  to  drag 
reduction. 

ACKNOWLEDGEMENTS 

The  author  is  grateful  to  the  MIT  Research  Support  Com¬ 
mittee  for  financial  support  from  the  MIT  Sloan  fund  and  to 
Derek  Stretch  for  providing  Fig.  1. 

REFERENCES 

1.  S.J.  Kline,  W.C.  Reynolds,  F.A.  Schraub  &  P.W.  Run- 
stadler  “The  structure  of  turbulent  boundary  layers,”  J. 
Fluid  Mech.  30,  741-773  (1967). 

2.  Acarlar,  M.S.  and  Smith,  C.R.,  “A  study  of  hairpin  vortices 
in  a  laminar  boundary  layer,”  J.  Fluid  Mech.  1T5,  pp.  1- 
41  and  43-83  (1987). 


50 


3.  Head,  M.R.  and  Bandyopadhyay,  P.  “New  aspects  of  tur¬ 
bulent  boundary  layer  structure,”  J.  Fluid  Mech.  107, 
297-338  (1981). 

4.  D.D.  Stretch,  “Automated  pattern  eduction  from  turbulent 
flow  diagnostics,”  Annual  Research  Briefs- 1990,  Center 
for  Turbulence  Research,  Stanford  U. 

5.  J.  Jeong,  F.  Hussain,  W.  Schoppa  &;  J.  Kim  “Coherent 
structures  near  the  wall  in  a  turbulent  channel  flow,”  J. 
Fluid  Mech.  332,  185-214  (1997). 

6.  J.  Kim,  P.  Moin  &  R.  Moser,  “Turbulence  statistics  in  fully 
developed  channel  flow  at  low  Reynolds  number,”  J.  Fluid 
Mech.  177,  133-166  (1987). 

7.  F.  Waleffe,  J.  Kim  and  J.  Hamilton,  “On  the  origin  of 
streaks  in  turbulent  shear  flows”,  in  Turbulent  Shear 
Flows  8:  selected  papers  from  the  Eighth  International 
Symposium  on  Turbulent  Shear  Flows ,  Munich,  Ger¬ 
many,  Sept.  9-11,  1991,  F.  Durst,  R.  Friedrich,  B.E. 
Launder,  F.W.  Schmidt,  U.  Schumann,  J.H.  Whitelaw, 
Eds.,  pp.  37-49,  Springer-Verlag,  Berlin,  1993. 

8.  J.  Hamilton,  J.  Kim  and  F.  Waleffe,  “Regeneration  mecha¬ 
nisms  of  near- wall  turbulence  structures,”  J.  Fluid  Mech. 
287,  317-348  (1995). 

9.  F.  Waleffe,  “Hydrodynamic  stability  and  turbulence:  be¬ 
yond  transients  to  a  self-sustaining  process,”  Studies  in 
Appl.  Math.,  95,  319-343  (1995). 

10.  F.  Waleffe,  “Transition  in  shear  flows.  Nonlinear  normality 
versus  non-normal  linearity,”  Phys.  Fluids,  7,  3060-3066 
(1995). 

11.  F.  Waleffe,  “On  a  self-sustaining  process  in  shear  flows,” 
Phys.  Fluids ,  9,  883-900  (1997). 

12.  F.  Waleffe  and  J.  Kim,  “How  streamwise  rolls  and  streaks 
self-sustain  in  a  shear  flow,”  in  Self-Sustaining  Mecha¬ 
nisms  of  Wall  Turbulence,  R.L.  Panton,  Ed.,  pp.  309-332, 
Computational  Mechanics  Publications,  Southampton  UK 
and  Boston  USA,  August  1997. 

13.  Lou  Howard  has  proven  stability  under  no-stress  boundary 
conditions  for  U(y)  =  y,  1  —  y2  and  sin7ry/2  (September 
1997,  private  communication). 

14.  J.  Jimenez  &  P.  Orlandi  “The  rollup  of  a  vortex  layer  near 
a  wall,”  J.  Fluid  Mech.  248,  297  (1993). 

15.  D.  Meksyn  &  J.T.  Stuart,  “Stability  of  viscous  motion  be¬ 
tween  parallel  planes  for  finite  disturbances,”  Proc .  Roy. 
Soc.  London  A,  208,  517-526  (1951). 

16.  D.J.  Benney,  “The  evolution  of  disturbances  in  shear  flows 
at  high  Reynolds  numbers,”  Stud.  Appl.  Math.  70,  1-19 
(1984). 

17.  M.  Nagata  “Three-dimensional  finite-amplitude  solutions 
in  plane  Couette  flow:  bifurcation  from  infinity,”  J.  Fluid 
Mech.  217,  519-527  (1990). 

18.  A.  Conley,  “New  plane  shear  flows,”  Ph.D.  Thesis,  Cal¬ 
ifornia  Institute  of  Technology,  H.  B.  Keller,  advisor 
(1994). 

19.  Clever,  R.M.  and  Busse,  F.H.  “Three-dimensional  convec¬ 


tion  in  a  horizontal  layer  subjected  to  constant  shear,”  J. 
Fluid  Mech.  234,  511-527  (1992). 


51 


DETECTION  OF  TRANSITION  AND  FLOW  BIFURCATION  REGIONS  ON  A  HYDROFOIL  USING 

HOT-FILM 

CONSTANT  VOLTAGE  ANEMOMETRY 


S.M.  Mangalam,  G.R.  Sarma 
R.A.  Pfouts,  and  T.S.  Kwa 
tao@taosystem.com 
Tao  Systems,  Inc. 

47 1  McLaws  Circle,  Ste.  A 
Williamsburg,  VA  23185 


J.H.  Casper  casperjh@nns.com 
M.A.  Wallace  wallace_ma@nns.com 
H.E.  Moghadam 
Newport  News  Shipbuilding 
Bldg.  600  4101  Washington  Ave. 
Newport  News,  VA  23607 


R.  Nigon  nigon@oasys.dy.navy.mil 
NSWC,  Carderock  Division 
9500  MacArthur  Blvd. 

Code  5600 

West  Bethesda,  MD  20817 


Abstract  -  The  potential  for  global  measurement  of  surface  shear  stress  characteristics  with  a  large  number  of  water-proofed,  micro-thin,  multi¬ 
element  hot-film  sensor  arrays  operated  by  a  Constant  Voltage  Anemometer  (CVA)  instrumentation  system  was  successfully  demonstrated  in 
tests  carried  out  on  a  6”-chord  NACA  0012  hydrofoil  model  in  the  NSWC’s  24”  water  tunnel  up  to  speeds  of  7  knots  at  0°,  5°,  and  10°  angles- 
of-attack.  The  hydrofoil  model  was  instrumented  with  an  80-element  hot-film  sensor  array  extending  from  about  30%  chord  on  the  lower  surface 
to  the  trailing-edge  on  the  upper  surface.  Pressure  distribution  on  the  hydrofoil  model  was  obtained  with  differential  pressure  gages.  Boundary- 
layer  characteristics  measured  with  hot-film  sensors  were  in  good  agreement  with  numerical  simulations  obtained  with  Reynolds-Averaged 
Navier-Stokes  (RANS)  equations  and  boundary-layer  integral  methods.  The  experimental  approach  described  in  this  paper  will  be  useful  for  the 
development  and  evaluation  of  various  sea-water  drag  reduction  methods. 

The  classical  sequence  of  phenomena  associated  with  the  Iaminar-to-turbulent  transition  was  very  clearly  demonstrated  in  these 
experiments.  The  laminar  region  was  characterized  by  very  low  amplitude  signals  followed  by  the  birth  of  turbulent  bursts,  their  growth,  rapid 
multiplication,  and  final  break-down  in  the  transition  region.  These  classical  features  were  clearly  observed  in  raw,  unprocessed  signals 
themselves  which  were  displayed  in  real  time  on  the  computer  screen.  The  transition  region  was  demarcated  by  the  unmistakable  presence  of 
large  amplitude  fluctuations  which  were  orders  of  magnitude  higher  than  the  laminar  signal.  One  of  the  interesting  observations  in  these 
experiments  was  the  consistent  presence  of  ‘laminar  bursts’  in  the  turbulent  region  mirroring  the  ‘turbulent  bursts’  in  the  laminar  region.  It  is 
conjectured  that  they  arise  as  a  result  of  laminar  separation,  transition  in  the  separated  shear  layer,  and  subsequent  turbulent  reattachment  which 
may  bring  a  few  ‘laminar  bursts’  from  the  outer  layer  to  the  solid  boundary  of  the  model.  The  leading-edge  stagnation,  flow  separation,  and 
reattachment  points  were  characterized  by  the  presence  of  a  local  minimum  (cusp)  in  the  mean  voltage  distribution  of  signals  from  sensors 
located  in  these  bifurcation  regions.  The  bifurcation  regions  were  also  identified  by  the  presence  of  phase  reversal  signatures  in  signals  from 
sensors  located  across  the  critical  region. 


I.  INTRODUCTION 

Identification  and  characterization  of  hydrodynamic  flow  features 
such  as  transition,  separation,  and  turbulence  around  model  hulls  and 
control  surfaces  are  critical  in  the  evaluation  of  the  performance  of  new 
designs  incorporating  sea-water  drag  reduction  technology  and  in 
validating  computational  fluid  dynamic  (CFD)  codes.  Flush-mounted 
array  of  micro-thin  hot-film  sensors  have  been  used  extensively  in  aero- 
and  hydrodynamic  measurements  [1-8]  to  characterize  viscous 
phenomena.  The  formation  of  bubbles  at  high  currents,  corrosion  and 
degradation  of  sensors  due  to  electro-chemical  reactions,  and  electrical 
conductivity  of  the  fluid  medium  are  some  of  the  problems  associated 
with  the  operation  of  sensors  in  water.  These  problems  have  resulted  in 
less  extensive  use  of  hot-film  sensors  in  hydrodynamic  measurements. 
The  need  to  obtain  high  sensitivity  (without  losing  bandwidth)  at  low 
currents  (to  prevent  bubble  formation)  and  the  high  power  requirements 
resulting  from  high  thermal  conductivity  of  water  are  some  of  the 
problems  associated  with  the  operation  of  the  anemometer.  In  addition 
to  these  problems,  the  experimenter  also  faces  the  possibility  of  losing 
sensors  due  to  burn-out  and  damage  from  particles  present  in  the  flow. 
There  is  a  need  to  develop  effective  water-proofed  shear-stress  sensors 
and  a  suitable  instrumentation  system  to  operate  them  over  long  periods 
of  testing.  The  following  discussions  are  based  on  work  recently 
conducted  to  demonstrate  the  use  of  advanced  techniques  (developed  in 
aerodynamic  measurements)  in  hydrodynamic  test  environment.  Tests 
were  carried  out  at  the  Naval  Surface  Warfare  Center’s  Carderock 
facility  on  a  NACA  0012  hydrofoil  model  instrumented  with  an  array  of 
water-proofed  hot-film  sensors  and  differential  pressure  gages.  NASA 
Langley  Research  Center  provided  the  technical  know-how  and 
assistance  in  water-proofing  the  sensors  for  long-duration  applications. 


II.  TEST  OBJECTIVE 

The  objective  of  the  experiment  was  threefold: 

•  Assess  the  effectiveness  of  chemical  coating  on  hot-film  sensors  to 
insure  extended  sensor  life  in  under-water  applications, 

•  demonstrate  the  use  of  CVA  to  operate  hot-film  sensors  in  water  to 
obtain  high  sensitivity  at  low  sensor  currents  (to  avoid  bubble 
formation  and  erosion  through  electrolysis),  and 

•  detect  critical  hydrodynamic  viscous  phenomena  such  as  the 
boundary-layer  transition,  flow  separation,  and  flow  reattachment 
regions  and  compare  results  with  computational  predictions. 

III.  TEST  SET-UP  AND  TEST  CONDITIONS 

The  test  model  was  a  6”-chord,  14”-span  hydrofoil  with  NACA 
0012  airfoil  section  equipped  with  ten  pressure  taps  that  were  evenly 
spaced  along  the  chord  of  the  model  to  make  pressure  measurements 
using  the  Micro  Switch  pressure  gages.  The  pressure  tubes  were  1/16- 
inch  stainless  steel  tubes  having  an  inside  diameter  of  1/32  inches.  An 
array  of  80-element  micro-thin  hot-film  sensors  was  glued  on  to  the 
hydrofoil.  The  sensor  elements  were  aligned  along  the  centerline  of  the 
hydrofoil  and  extended  from  about  30%  chord  location  on  the  lower 
surface  to  the  trailing  edge  of  the  upper  surface.  The  sensor  elements 
were  spaced  0.1  inch  apart  in  the  chordwise  direction  (1.66%  chord). 
Holes  were  punched  in  the  substrate  material  to  expose  the  pressure 
orifices  to  the  flow.  A  special  breakout  box  was  used  to  connect  all  the 
80  sensors  from  the  hydrofoil  and  connect  them  to  16-channel  CVA 
instrumentation  system  in  groups  of  16  sensors.  The  output  from  each  of 
the  16-channel  CVA  was  taken  to  an  auto-zero  unit  which  was  used  to 
create  a  level  reference  voltage  (zero  volt)  for  all  the  sensors. 


53 


A  schematic  of  the  instrumentation  system  is  shown  in  Fig.  (1). 
Tests  were  conducted  in  the  24”  water  tunnel  facility  at  the  Carderock 
Division  of  Naval  Surface  Warfare  Center.  The  hydrofoil  was  tested  at 
0°,  5°,  and  10°  angles -of-attack.  The  free-stream  velocity  was  varied 
from  1  to  a  maximum  of  7  knots  for  the  lower  two  angles  but  restricted 
to  6  knots  for  the  highest  angle  because  of  concern  for  the  structural 
integrity  of  the  hydrofoil  model.  Test  data  was  acquired  with  a  16- 
channel  tape  recorder  as  well  as  with  a  16-channel  analog-to-digital 
converter  operated  by  a  laptop  personal  computer.  Data  was  sampled  at 
50  Hz  with  a  minimum  of  512  and  a  maximum  of  4096  samples  for 
each  realization.  Over  150  test  runs  were  made  at  the  above  test 
conditions  and  the  experiment  was  completed  in  less  than  two  days.  On¬ 
line  display  of  the  test  data  was  accomplished  with  Tao  Systems’  data 
acquisition  and  analysis  software. 

Hot-Film  Sensors 

The  hot-film  sensors  were  designed  and  fabricated  by  Tao 
Systems,  Inc.  The  nickel  sensor  elements  were  typically  about  0.25 
microns  thick  with  a  nominal  cold  resistance  of  about  6  Ohms.  The  hot- 
film  sensors  and  copper  leads  on  a  polyimide  substrate  were  coated  with 
chemicals  to  provide  electrical  insulation  for  under-water  applications. 
The  water-proofing  with  chemicals  was  carried  out  with  the  support  of 
technical  know-how  from  NASA  Langley  Research  Center.  The  coated 
sensor  was  submerged  in  water  and  operated  by  CVA  for  many  weeks 
before  tests  were  conducted  in  the  water  tunnel.  Simultaneously,  tests 
were  also  conducted  on  uncoated  sensors  to  evaluate  the  impact  of  water 
on  the  performance  and  life  of  sensors.  Preliminary  studies  also  showed 
that  CVA  was  able  to  provide  high  sensitivity  without  causing  problems 
such  as  bubble  formation.  Various  combinations  of  hot-film  sensors,  in 
batches  of  16,  were  connected  to  the  16-channel  CVA  system  and  data 
recorded  at  different  test  conditions.  In  spite  of  the  chemical  coating,  the 
signal  levels  obtained  on  CVA  were  large,  even  with  a  unity  gain,  and 
the  maximum  sensitivity  was  in  excess  of  one  (1)  volt/knot  at  one  knot. 
Not  a  single  sensor  was  burnt  or  damaged  in  these  tests. 

Constant  Voltage  Anemometer 

The  Constant  Voltage  Anemometer  system  has  been  described  in  a 
number  of  recent  publications  [9-13].  Constant  Current  and  Constant 
Temperature  Anemometers  (CCA  and  CTA)  are  the  other  two  types  of 
anemometers  used  extensively  in  dynamic  measurements.  As  the  name 
implies,  the  sensor  is  maintained  at  a  constant  voltage  (Fig.  2).  The 
voltage  level  maintained  across  the  sensor  determines  the  current 
through  the  sensor  and  is  used  for  ohmic  heating  of  the  sensor.  The 
thermal  gradient  between  the  sensor  and  the  fluid  medium  results  in  heat 
transfer  by  convection.  'The  changes  in  sensor  temperature  due  to 
convection  results  in  changes  in  sensor  resistance  and  corresponding 
changes  in  sensor  current  is  measured  across  a  large  resistor  R2. 

The  output  voltage  from  the  CVA  is  a  measure  of  the  convective 
heat  transfer  (and  conduction  losses  to  the  substrate)  from  the  surface 
hot-films  which  can  be  directly  related  to  surface  shear  stress.  Hence  the 
output  voltage  is  expected  to  be  small  in  laminar  boundary  layers  and 
high  in  turbulent  boundary  layers.  The  output  voltage  will  also  be  small 
when  the  convective  heat  transfer  and  the  corresponding  shear  stress  is 
small  as  in  flow  bifurcation  regions  (leading-edge  stagnation  point,  flow 
separation  and  flow  reversal  regions).  In  order  to  effectively  detect 
various  critical  flow  features,  the  CVA  system  is  equipped  with  an  auto¬ 
zero  unit  which  creates  a  level  initial,  (reference)  voltage  for  all  the 
sensors.  Subsequently,  the  output  voltage  at  any  test  condition  is  an 
indication  of  relative  change  in  shear  stress  from  the  reference 
condition.  The  CVA  instrumentation  system,  since  it  operates  on  a 
constant  voltage  basis,  does  not  suffer  from  the  adverse  impact  of  EMI 
and  RFI,  cable  length  (capacitance)  does  not  pose  any  operational 
problems  (such  as  instability  or  oscillations),  has  high  sensitivity  and 
large  bandwidth  even  at  low  currents.  It  is  fully  automated  and  requires 
no  critical  adjustments. 


IV.  TEST  TECHNIQUES  &  NUMERICAL  SIMULATIONS 

Detection  of  Boundary  Laver  Transition 

Heated  element  sensors  have  been  used  extensively  since  their 
introduction  by  Ludwig  [14]  and  subsequent  pioneering  work  by 
Liepmann  and  Skinner  [15]  who  established  mathematical  expressions 
relating  convective  heat  transfer  and  surface  shear  stress  to  the  measured 
electrical  output  from  anemometers.  In  addition  to  their  use  in 
measuring  surface  shear  stress  distribution,  heated  element  sensors  have 
also  been  used  extensively  in  flow  diagnostics.  Typically  the  heated 
elements  are  operated  at  elevated  temperatures  to  enable  heat  transfer  to 
take  place  from  the  sensor  to  the  fluid.  The  convective  heat  loss 
experienced  by  the  sensor  results  in  change  in  the  sensor  temperature 
and  hence  its  electrical  resistance.  This  change  in  electrical  properties  is 
used  as  a  measure  of  the  state  of  the  boundary  layer.  The  changes  are 
minimal  in  a  laminar  boundary  layer.  Transition  is  characterized  by  the 
generation  of  large  disturbances  that  result  in  large  convective  heat 
transfer  and  when  these  large  eddies  breakdown  to  smaller  eddies 
(turbulent  flow),  the  heat  transfer  is  relatively  less  compared  to  the  peak 
transition  but  significantly  higher  in  the  turbulent  region  than  in  the 
laminar  boundary  layer. 

The  most  commonly  used  quantifiable  criteria  to  identify  laminar- 
to-turbulent  transition  region  are: 

•  A  significant  increase  in  signal  amplitude  (dc+ac)  and  RMS 
voltages  compared  to  the  output  voltage  in  the  laminar  region. 

•  A  sharp  increase  in  intermittence  factor  (a  self-normalized 
measure  of  the  turbulence  level  of  the  signal,  [16-17])  from  close 
to  zero  in  the  laminar  region  to  nearly  one  in  the  fully  turbulent 
flow. 

In  addition  to  these  methods,  one  could  also  identify  boundary- 
layer  transition  from  power  spectra  of  signals.  In  the  interest  of  brevity, 
the  present  paper  describes  transition  process  by  observing  the  raw 
signals  and  their  RMS  distribution. 

Detection  of  Flow  Bifurcation  Regions 

Flow  bifurcates  at  a  number  of  points  along  the  surface  of  a  body 
in  motion.  For  a  two-dimensional  body,  the  streamlines  bifurcate  first  at 
the  leading-edge  where  the  surface  streamlines  diverge  in  two  opposite 
directions  across  the  stagnation  point  Fig.  (3).  At  flow  separation,  the 
surface  streamlines  converge  towards  each  other  from  two  opposite 
directions.  The  situation  at  the  flow  reattachment  point  is  similar  to  the 
leading-edge  stagnation  point,  with  the  surface  streamlines  diverging 
away  from  each  other.  One  common  feature  for  flow  bifurcation  regions 
is  that  the  flow  stagnates  at  these  critical  points  where  the  convective 
heat  transfer  and  surface  shear  stress  reach  a  local  minimum  and 
increase  monotonically  both  upstream  and  downstream  of  these 
locations.  In  terms  of  hot-film  measurements,  the  sensors  located  at 
these  points  can  be  looked  at  as  local  ‘hot-spots’  because  the  fluid 
convects  less  heat  away  from  them  than  from  their  neighboring  sensors 
which  are  ‘cooler’.  In  electrical  terms,  the  sensors  located  at  the  ‘hot¬ 
spots’  have  higher  resistance  and  hence  the  CVA  voltage  output  from 
them  will  exhibit  a  local  minimum.  Another  property  exhibited  by  the 
signals  from  sensors  across  the  bifurcation  point  is  the  presence  of  a 
phase  reversal  signature  (PRS)  caused  by  the  characteristic  unsteadiness 
associated  with  the  flow  at  these  locations  [18]. 

Analvtical/Computational  Predictions  for  NACA  0012 

Since  this  experiment  was  the  first  attempt  to  demonstrate  the  use 
of  water-proofed  multi-element  hot-film  sensors  to  simultaneously 
detect  transition  as  well  as  all  the  bifurcation  points  on  a  hydrofoil 
model,  boundary-layer  theory  and  computational  simulations  were 
chosen  to  serve  for  the  validation  of  the  test  results.  These  numerical 
simulations  were  used  to  predict  the  locations  of  separation  and 
transition  as  a  function  of  chord  length.  No  attempt  was  made  to  predict 
reattachment  point.  The  test  cases  discussed  in  this  section  are:  a  =  0°, 


54 


Uoo  =7  knots;  :  a  =  5°,  U„  =  7  knots;  and  a  =  10°,  U«  =  6  knots.  These 
cases  represent  the  highest  free-stream  speeds  obtained  in  experiments. 

These  NACA  0012  [19]  test  cases  have  been  analyzed  in  two 
ways:  by  boundary-layer  integral  methods  accompanied  with  empirical 
formulations,  and  by  numerical  solutions  of  the  Reynolds-Averaged 
Navier-Stokes  (RANS)  equations.  Two-dimensional,  steady-state  flow 
conditions  were  assumed  in  these  computations.  The  flow  separation 
points  were  deduced  from  an  inspection  of  the  velocity  distribution 
within  the  boundary  layer  of  a  RANS  solution  since  a  2D  separation 
must  be  accompanied  by  flow  reversal.  Boundary-layer  integral  methods 
[20]  were  applied  for  the  prediction  of  laminar  separation  and  transition 
to  turbulence. 

V.  TEST  RESULTS 

Test  Conditions:  a  =  0°.  U-,  =  7  knots  (Re  =  5.41  x  105) 

Inspection  of  the  tangential  velocity  distribution  from  the  RANS 
solution  at  one  point  off  the  surface  (y+  =  1)  revealed  no  flow  reversal 
occurring  before  the  trailing  edge,  at  approximately  x/c  =  0.99.  This 
value  is  consistent  with  the  prediction  of  the  boundary-layer  integral 
method  which  determines  the  location  of  the  turbulent  separation  at  x/c 
=  0.998.  However,  the  experimental  measurements  did  not  extend  to  the 
trailing  edge  of  the  hydrofoil.  The  momentum  thickness  0  and  velocity 
at  the  edge  of  the  boundary  layer  Ue,  from  the  boundary-layer  integral 
method  were  used  to  determine  Iaminar-to-turbulent  transition  with  the 
Michel  criterion  [21].  For  incompressible  flows  about  airfoil  shapes, 
transition  is  predicted  when 

Ree  >  1.174  (1  +  22,400  /  Rex)  Rex046 

where  Ree  =  Ue,  0  /  v  and  Rex  =  Ue,  x  /  v.  For  the  7-knot  case  the  chord- 
Reynolds  number  is  5.46  X  105,  and  the  Michel  criterion  predicts 
transition  at  x/c  =  0.567. 

Figures  (4)  and  (5a)  show  time  series  signals  (output  voltage) 
obtained  from  sensors  at  various  chord  locations  at  a  free-stream 
velocity  of  7  knots  and  a  =  0°.  The  first  indication  of  the  presence  of  a 
turbulent  ‘burst’  is  observed  at  about  13.4%  chord.  The  number  of  such 
bursts  and  their  amplitude  begins  to  increase  gradually  in  the  beginning, 
up  to  about  46%  chord,  and  explosively  beyond  50%  chord,  reaching  a 
peak  at  about  56%  chord.  The  flow  is  practically  fully  turbulent  beyond 
this  point. 

The  RMS  distribution  is  shown  in  Fig.  (5b)  for  the  same  test 
conditions.  The  different  symbols  indicate  different  batches-  of  sensors 
used  to  acquire  data  over  the  test  region.  The  laminar  region  appears  to 
extend  from  the  leading  edge  to  about  10%  chord  beyond  which  the 
RMS  value  begins  to  increase  gradually  from  the  low  laminar  values. 
The  rate  of  increase  is  dramatic  beyond  about  40%  chord,  reaching  a 
peak  at  about  55%  chord.  As  observed  in  the  raw  signals,  the  peak  RMS 
(peak  transition)  occurs  at  about  56%  chord.  Computational  results 
using  boundary-layer  integral  methods  predicted  transition  location  at 
56.7%  chord  for  the  given  test  conditions,  showing  that  the  measured 
data  are  in  excellent  agreement  with  CFD. 

We  can  observe  an  interesting  feature  in  the  raw  signals  in  the  pre- 
transitional  and  post-transitional  regions:  the  ‘turbulent’  bursts  in  the 
laminar  region  appear  as  mirror  images  of  the  ‘laminar’  bursts  in  the 
turbulent  region.  For  greater  clarity,  the  data  have  been  plotted  in  Fig. 
(4)  for  individual  sensors  in  order  to  clearly  show  the  disturbances  levels 
relative  to  the  mean  voltage.  In  the  predominantly  laminar  region,  the 
sensors  experience  intermittent  turbulent  eddies  observed  as  ‘bursts’ 
which  ‘ride’  on  top  of  the  flat  laminar  signal.  In  the  transition  region 
(approximately,  0.45  <  x/c  <  0.58),  the  disturbances  are  evenly 
distributed  about  the  mean  voltage  level.  In  the  immediate  post- 
transitional  region,  the  mean  voltage  level  itself  is  relatively  higher  than 
the  laminar  region  and  the  disturbances  are  primarily  below  the  flat 
peak,  indicating  that  the  flow  is  primarily  turbulent  with  relatively  high 
rate  of  heat  transfer  by  convection  but  occasionally  interrupted  by  the 


lower  heat  transfer  rates  caused  by  vertical  convection  of  relatively 
smoother  (laminar)  flow  from  the  outer  edge  of  the  boundary  layer.  Such 
a  behavior  could  also  exist  immediately  downstream  of  the  reattachment 
region  of  a  laminar  separation  bubble.  This  phenomenon  needs  to  be 
studied  more  systematically. 

Figure  (5c)  shows  the  CVA  output  voltage  distribution  in  the 
leading-edge  region  for  the  above  test  conditions.  The  sensor  located 
exactly  at  the  leading  edge  was  destroyed  during  the  installation  of 
sensors  on  the  model.  The  voltage  distribution  exhibits  a  cusp  at  x/c  = 
0.0365  indicating  that  the  model  was  initially  at  a  negative  angle-of- 
attack  to  the  flow. 

Test  Conditions:  a  =  5°«  Uoo  =  7  knots 

The  boundary-layer  integral  method  predicts  separation  for  this 
test  case  to  occur  at  x/c  =  0.109.  Transition  is  predicted  with  the  Michel 
criterion  to  occur  at  x/c  =  0. 17 1 . 

Raw  signals  and  RMS  distributions  at  a  =  5°  are  shown  in  Fig. 

(6) .  The  transition  region  between  the  laminar  and  turbulent  boundary 
layers  is  clearly  observed  between  16%-20%  chord.  This  chord  location 
for  transition  again  agrees  veiy  well  with  the  theoretical  predictions. 
Compared  to  the  zero-degree  angle-of-attack  case,  where  the  transition 
was  located  at  56%  chord,  the  transition  region  at  a  =  5°,  U  =  7  knots 
moved  upstream,  as  expected. 

Figure  (6c)  shows  the  mean  voltage  distribution  in  the  leading- 
edge  region  at  this  test  condition.  Figure  (6b)  shows  the  corresponding 
RMS  distribution.  A  significant  drop  in  mean  voltage  at  about  10% 
chord  indicates  flow  separation  at  this  location.  Numerical  simulations 
also  predicted  laminar  flow  separation  to  occur  at  about  10.9%  chord. 
At  this  location  we  observe  a  sharp  rise  in  the  RMS  distribution.  Thus, 
we  can  conclude  that  boundary-layer  transition  takes  place  rapidly 
downstream  of  the  separation  point,  with  the  peak  occurring  at  about 
20%  chord.  The  next  minimum  in  the  mean  output  voltage  occurs  at 
about  28%  chord,  indicating  a  turbulent  reattachment  region  of  the 
separation  bubble.  The  RMS  distribution  also  indicates  the  completion 
of  the  transition  process  and  the  beginning  of  a  fully  turbulent  boundary 
layer  downstream  of  this  chord  location.  Thus,  the  laminar  separation 
bubble  extended  from  10%  chord  to  about  28%  chord  at  the  above  test 
conditions. 

Phase  Reversal  Signatures 

The  disturbance  amplitude  of  signals  from  the  hot-film  sensors 
located  in  the  bifurcation  region  was  extremely  low  compared  to  other 
regions.  The  extremely  low  noise  levels  of  the  CVA  system  made  it 
possible  to  measure  even  a  couple  of  millivolts  but,  unfortunately,  the 
data  acquisition  system  had  only  about  4  millivolts  resolution.  On  the 
other  hand,  the  disturbance  amplitude  in  the  transition  region  sometimes 
exceeded  2.5  volts.  Hence,  in  order  to  adequately  cover  such  a  large 
change  in  voltage  levels  the  test  set  up  will  require  modifications  for 
future  experiments.  Incidentally,  this  is  not  a  problem  but  a  luxury  we 
have  to  deal  with  because  of  the  very  low  noise  and  high  sensitivity  of 
the  CVA  instrumentation  system. 

Since  the  data  acquisition  system  was  unable  to  resolve  the  very 
low  level  of  fluctuations  in  the  signals  near  bifurcation  regions,  it  was 
not  possible  to  clearly  obtain  phase  reversal  signatures  in  all  the  cases. 
However,  at  low  speeds,  the  unsteadiness  in  the  water  tunnel  free-stream 
was  sufficient  to  create  large-scale,  low-frequency  fluctuations  in  the 
flow  at  these  critical  points.  For  example,  (Fig.  7)  shows  the  mean 
voltage  distribution  from  sensors  located  between  25%  and  36%  chord, 
indicating  that  the  local  minimum  in  the  mean  output  voltage  occurs 
near  31.72%  chord.  Raw  signals  from  sensors  located  in  this  region  Fig. 

(7)  are  clearly  out  of  phase  with  each  other  indicating  the  presence  of  a 
bifurcation  point  between  them.  The  RMS  voltage  levels  at  these 
locations  (not  shown  here)  are  low  and  indicate  a  laminar  separation 
between  these  two  sensor  locations.  Figure  (8)  shows  similar  plots  for 
the  reattachment  region  with  a  clear  PRS  observed  in  signals  from 
neighboring  sensors.  It  is  worth  noting  that  while  the  signals  from 


55 


sensors  across  the  separation  point  are  both  indicative  of  a  laminar  flow, 
the  sensor  signals  at  reattachment  indicate  turbulent  flow. 

Test  Conditions:  a  =  10°,  U~  =  6  knof" 

The  chord-Reynolds  number  for  this  test  case  is  4.69  X  105.  The 
boundary-layer  integral  method  predicts  separation  for  this  test  case  to 
occur  at  x/c  =  0.008.  However,  this  method  is  not  capable  of  predicting 
reattachment.  Figure  (9)  depicts  the  tangential  velocity  distribution  from 
the  RANS  solution  at  one  point  off  the  surface.  The  flow  reversal  in  the 
2-6%  chord  region  is  indicative  of  a  separation  region.  Transition  is 
predicted  to  occur  at  x/c  =  0.06. 

The  mean  voltage  distribution  shown  in  Fig.  (10c)  shows  that  the 
leading-edge  stagnation  point  is  at  about  6%  chord  on  the  lower  surface. 
Laminar  flow  separation  occurred  practically  at  the  leading-edge  of  the 
hydrofoil  followed  by  rapid  transition  to  turbulence  near  5%  chord. 
Flow  reattachment  appears  to  take  place  near  9%  chord.  As  in  the 
previous  test  case,  the  flow  separation  and  reattachment  points  also 
coincide  with  the  beginning  and  end  of  transition  to  turbulence  as 
shown  by  the  raw  signals  and  RMS  distribution  Figs.  (10a, b).  Again,  the 
agreement  with  theoretical  predictions  is  excellent. 

VI.  CONCLUSIONS 

•  Water-proofed,  micro-thin,  multi-element  hot-film  sensors  were 
successfully  used  in  water-tunnel  tests  on  a  hydrofoil  model.  Not  a 
single  sensor  was  burnt  or  damaged  in  the  experiment. 

•  Tao  Systems’  Constant  Voltage  Anemometry  system  was 
successfully  used  to  operate  these  sensors  in  water  to  obtain  high 
sensitivity  at  low  sensor  currents  without  bubble  formation  and 
erosion  through  electrolysis. 

•  Advanced  flow  diagnostics  techniques  were  successfully  used  for 
the  detection  of  critical  boundary-layer  characteristics  such  as 
transition,  flow  separation,  and  flow  reattachment  regions. 

•  Computational  results  showed  very  good  agreement  with  test 
results. 

•  The  low  noise  feature  of  the  CVA  made  it  possible  to  measure  the 
very  low  fluctuating  signal  levels  (of  the  order  of  2  mV)  present  in 
the  bifurcation  region  and  the  high  sensitivity  provided  extremely 
large  signals  in  the  transition  region.  Additional  work  is  required 
to  properly  accommodate  this  wide  range  of  signal  levels  in  future 
experiments. 

VII.  ACKNOWLEDGMENT 

A  number  of  new  techniques  were  tried  in  this  experiment  which 
could  not  have  been  made  possible  without  the  participation  and  help 
received  from  many  individuals.  We  sincerely  acknowledge  the  help 
received  from  Dave  Bochinski  and  Dave  Fishpaw  of  NSWC,  Jim 
Bartlett  of  NASA  Langley  Research  Center,  and  Bob  Lankes  of  Tao 
Systems,  Inc.,  for  their  assistance  at  various  stages  of  this  experiment. 


VIII.  REFERENCES 

1.  W.  Bechteler,  H.  B.  Kleeberg,  H.  Teichmann,  and  H.  J.  Vollmers 
“Application  of  Hot-Film  Probes  for  Measurement  of  Wall  Shear  Stress 
in  Water”,  Institutfur  Wasserwesen,  Germany  1992. 

2.  B.  J.  Bellhouse  and  D.  L.  Schultz  “Determination  of  Mean  and 
Dynamic  Skin  Fricion,  Separation,  and  Transition  in  Low  Speed  Flow 
With  a  Thin-film  Heated  Element”,  Journal  of  Fluid  Mechanics,  Vol. 
24,  pt.  2,  1966. 

3.  H.  H.  Braun  “Hot  Wire  Anemometry,  Principles  and  Signal 
Analysis”,  Oxford  University  Press,  1995. 

4.  R.  Houdeville  and  J.  C.  Juillen  “Skin  Friction  Measurement  With 
Hot  Elements”,  in  VKI  Lecture  Series  1989-05,  Measurement 
Techniques  in  Aerodynamics,  April  1989. 

5.  S.  M.  Mangalam,  J.  P.  Stack,  and  W.  G.  Sewall  “Simultaneous 
Detection  of  Separation  and  Transition  in  Surface  Shear  Layers.  Fluid 
Dynamics  of  Three-Dimensional  Turbulent  Shear  Flows”,  AGARD  CP- 
438,  1988. 

6.  S.  M.  Mangalam,  G.  R.  Sarma,  and  S.  Kuppa  “Quantitative  Flow 
Diagnostics  Techniques  for  Unsteady  Aerodynamics”,  P1CAST2-AAC6 
International  Conference,  Australia,  1995. 

7.  S.  M.  Mangalam,  G.  R.  Sarma  and  T.  R.  Moes  “In  Flight  Shock 
Detection  Using  Hot-Film  Sensors  and  Constant  Voltage  Anemometer 
System”,  To  be  presented  at  the  21st  Congress  of  I CAS,  Melbourne, 
Australia,  Sep.  1998. 

8.  V.  A.  Sanborn  “Resistance  Temperature  Transducers”,  Metrology 
Press,  1972. 

9.  G.  Comte-Bellot  “Hot  Wire  Anemometry”,  Handbook  of  Fluid 
Dynamics,  ed.  R.  W.  Johnson,  CRC  Press,  1998. 

10.  M.  S.  Kegerise  and  E.  F.  Spina  “A  Comparative  Study  of  Constant 
Voltage  and  Constant  Temperature  Hot-Wire  Anemometer  in 
Supersonic  Flows”,  3rd  International  Symposium  on  Thermal 
Anemometry,  San  Diego,  CA.,  July  1996. 

11.  M.  A.  Kegerise  “A  Study  of  the  Constant  Voltage  Hot-Wire 
Anemometer”,  M.  S.  Thesis,  Syracuse  University,  1997. 

12.  G.  R.  Sarma  “Analysis  of  a  Constant  Voltage  Anemometer 
Circuit”,  IEEFJ1MTC  Conference,  May  1993. 

1 3.  G.  R.  Sarma  “Transfer  Function  Analysis  of  the  Constant  Voltage 
Anemometer”,  Review  of  Scientific  Instruments,  to  be  published  June, 
1998. 

14.  H.  Ludwig  “Instrument  for  Measuring  the  Wall  Shearing  Stress  of 
Turbulent  Boundary  Layers”,  NACA  TM-1284,  1950. 

15.  H.  W.  Liepmann  and  G.  T.  Skinner  “Shearing  Stress 
Measurements  by  Use  of  a  Heated  Element”,  NACA  TN-3268,  1954. 

16.  S.  Dhawan  and  R.  Narasimha  “Some  Properties  of  Boundary 
Layer  Flow  During  the  Transition  from  Laminar  to  Turbulent  Motion”, 
Journal  of  Fluid  Mechanics,  Vol.  3,  pt.  4,  pp.418-436,  January  1958. 

17.  S.  P.  Schneider  “Improved  Methods  for  Measuring  Laminar- 
Turbulent  Intermittency  in  Boundary  Layers”,  Experiments  in  Fluids  18, 
pp.  370-375,  1995. 

18.  S.  M.  Mangalam  “Instrumentation  System  for  Determining  Flow 
Stagnation  Points”,  US  Patent  No.  5,218,863.  June  1993. 

19.  I.  H.  Abbott  and  A.  E.  Von  Doenhoff  “Theory  of  Wing  Section” 
Dover  Publications,  Inc.  1959 

20.  J.  Moran  “Theoretical  and  Computational  Aerodynamics”,  New 
York :  John  Willey  and  Sons,  1984. 

21.  R.  Michel  “Etude  de  la  Transition  sur  les  Profiles  d’Aile”,  ONERA 
Report  1-1578A,  1951. 


56 


¥:**** 

iiO«  * 

e  •  6  *; 

I* 


(c)  Mean  Voltage  (b)  RMS  Voltage 


MEASURED  WALL  PRESSURE  SIGNATURES  OF  TURBULENCE  PRODUCING  STRUCTURES 


Steven  J.  Russell 
Naval  Surface  Warfare  Center 
Carderock  Division,  Code  725 
9500  MacArthur  Blvd 
West  Bethesda,  MD  20817-5700 
srusseIl@oasys.dt.navy.mil 


Abstract  -  An  extensive  database  of  simultaneously  obtained  wall  pressure  and  velocity  measurements  was  acquired  for  a  high  Reynolds 
number,  equilibrium  turbulent  flow.  These  data  were  obtained  in  both  streamwise  and  spanwise  measurement  planes  using  an  array  of  wall 
pressure  transducers.  Analyses  of  these  data  were  performed  to  examine  the  spatial  extent  and  convective  features  of  turbulence  producing 
structures. 

Several  signal  processing  techniques  were  shown  to  extract  detailed  structural  features  of  the  turbulent  motions.  These  techniques  included 
digital  band-pass  filtering  to  discriminate  between  turbulent  scales  and  a  localized  variance  method  for  the  detection  of  clusters  of  high 
frequency  turbulent  activity. 

Cross-spectral,  cross-correlation,  and  conditional  sampling  methods  applied  to  these  data  clearly  show  the  dynamic  relationships  between 
coherent  turbulent  motions  as  well  as  their  induced  wall  pressure  signatures.  Both  pressure -velocity  correlation  results  and  conditionally 
averaged  maps  of  the  flow  field  sampled  on  peak  wall  pressure  events,  reveal  a  consistent  correlation  between  large  scale  motions  and  near¬ 
wall,  small  scale  turbulent  production  activity.  The  large  scale  vortical  motions  (or  shear  layers)  extend  across  the  turbulent  boundary  layer 
and  exhibit  Reynolds  stress  (turbulent  production)  characteristics.  These  findings  are  consistent  with  many  of  the  proposed  conceptual  models 
of  organized  motions. 


L  INTRODUCTION 

Active  turbulence  control  schemes,  whether  for  drag  reduction, 
noise/vibration  reduction,  or  other  purposes,  must  tackle  the  turbulence 
production  process.  Since  turbulence  is  inherently  self-sustaining,  to 
disrupt  its  effect  on  a  body,  an  active  control  method  must  be 
developed  which  affects  the  production  chain.  The  purpose  of  this 
investigation  is  to  examine  the  dynamic  relationships  between  coherent 
motions  related  to  turbulent  production  in  a  boundary  layer.  This  is 
achieved  by  measuring  the  spatial  and  temporal  characteristics  of  these 
structures  as  seen  in  their  velocity  and  wall  pressure  statistics.  If  a 
model  for  the  wall  pressure  signature  of  these  motions  could  be 
defined,  turbulent  production  events  could  then  be  identified  using 
pressure  sensors  as  part  of  the  detection  loop  of  a  control  system. 

An  explicit  criterion  for  turbulent  production  or  “active”  motions 
can  be  established  by  examining  the  equation  for  the  turbulence  kinetic 
energy: 

DKt  — dUi  duidui  d  \— —  puj  dKr~\  m 

Dt  ox j  oxjdxj  oxj\_  p  ox} 

where  D/Dt  is  the  substantial  derivative,  p  is  the  density,  and  p  is  the 
fluctuating  pressure.  Overbars  represent  time  averages.  The  focus  of 
this  investigation  is  the  first  term,  turbulence  production,  characterized 
by  the  interaction  of  the  Reynolds  stress  -UiUj  with  the  mean  shear 
gradient.  In  the  flow  field  studied  in  this  investigation,  positive 
production  occurs  when  u  <  0,  and  v  >  0  or  u  >  0,  v  <  0,  which 
correspond  to  the  second  and  fourth  quadrants  of  the  u-v  plane.  These 
motions  are  commonly  referred  to  as  Q2  and  Q4  motions,  or  ejections 
and  sweeps  of  fluid.  The  wall  pressure  signatures  of  these  active 
motions  are  the  focus  of  this  investigation  and  are  measured  using  an 
array  of  flush-mounted  pressure  transducers. 

II.  BACKGROUND 

Recent  research  in  the  field  of  turbulent  boundary  layers, 
numerical  and  experimental,  has  yielded  a  multitude  of  descriptions  or 
models  of  the  turbulence  production  process  and  the  structures 
involved.  Robinson1  compiled  a  summary  of  turbulent  structures 
identified  by  the  turbulence  community  in  the  last  40  years  and  divided 
them  into  eight  categories: 

•  Low  speed  streaks  in  the  viscous  sublayer. 

•  Lifting  and  ejection  of  these  streaks. 

•  Subsequent  sweep  of  high  speed  fluid  inward. 

•  Vortical  structures  of  varying  form. 

•  Sloped  near-wall  shear  layers  with  high  spanwise  vorticity. 

•  Near  wall  pockets  swept  clean  of  marker  fluid  (splats). 

•  8-scale  motions  capped  by  the  inner/outer  interface. 

•  Shear  layer  backs  of  these  motions. 


Two  fundamental  questions  that  have  challenged  researchers  are: 
which  of  these  inner  and  outer  layer  structures  play  the  dominant  role 
in  the  physical  mechanism  governing  turbulence,  and  to  what  extent  do 
these  structures  interact  during  these  production  and  maintenance 
processes?  Since  nearly  80  percent  of  turbulence  energy  is  produced 
during  the  quasi-periodic  burst/sweep  events,2  disrupting  this  process  is 
the  key  to  active  control.  If  a  link  could  be  established  between  the 
near  wall,  turbulent  production  events  and  other  larger  scale  structures 
in  the  outer  flow  (shear  layers,  backs,  etc.)  then  detection  of  the  large 
scale  structures  could  be  used  to  predict  or  pinpoint  turbulent 
production  events. 

Many  researchers  have  proposed  models  which  describe  the 
kinematic  and  dynamic  processes  of  turbulence  production. 
Theodorsen3  first  proposed  a  horse  shoe  or  hairpin-like  vortex  model 
based  on  the  vorticity  transport  form  of  the  Navier-Stokes  equations. 
Willmarth  and  Tu4  proposed  a  model  for  the  average  near  wall  eddy 
structure  based  on  space  time  correlations  between  wall  pressure  and 
velocity.  Again,  the  hairpin  vortex  was  the  dominant  theme;  however, 
they  extended  the  influence  of  the  vortex  to  the  outer  edge  of  the 
boundary  layer.  Offen  and  Kline5,  Hinze6,  and  many  others  suggested 
similar  models  based  on  the  lift  up  and  ejection  of  horseshoe-like 
vortical  structures  in  the  near  wall  region  of  the  turbulent  boundary 
layer.  A  relationship  between  coherent  outer  motions  and  near  wall 
turbulence  production  was  presented  by  Praturi  and  Brodkey7  where 
near  wall  ejections  were  induced  by  the  passage  of  8-scale  shear 
layers.  Falco8  also  suggested  that  large  scale  outer  structures  affect  but 
do  not  govern  near-wall  production.  Thomas  and  Bull9  demonstrated 
that  near  wall,  high  frequency  activities  were  associated  with  the 
passage  of  large-scale  organized  flow  structures  by  correlating  filtered 
pressure  and  velocity  data. 

Kline10  reviewed  the  results  of  several  DNS  studies  and  found  that 
two  types  of  vortices  are  found  to  be  “central  structures” 

•  inner  layer:  tilted  streamwise  vortices  (legs) 

•  outer  layer:  transverse  vortices  (heads) 

The  two  forms  overlap  in  the  log-law  region  of  the  boundary  layer. 
Kline  further  concluded  that  these  structures  are  strongly  related  to  the 
production  process.  Robinson11  attributes  most  of  the  eight  structures 
listed  earlier  to  these  vortical  structures,  including  the  8-scale  shear 
layers.  Many  other  models  with  similar  features  have  been  proposed 
which  share  a  common  theme;  that  is,  sweeps  and  ejections  play 
significant  roles  in  maintaining  turbulence  and  that  hairpin-like  vortices 
appear  to  be  the  dominant  structures. 

Farabee12  showed  that  high-frequency  pressure  fluctuations  were 
associated  exclusively  with  sources  near  the  wall.  Farabee  also 
demonstrated  the  influence  of  large  scale,  outer  layer  disturbances  on 
the  low  frequency  pressure  fluctuations  as  well  as  on  the  value  of  the 
RMS  wall  pressure.  Karangelen13  confirmed  that  large  amplitude  wall 
pressure  events  are  footprints  of  the  near-wall  bursting  cycle. 


63 


Wilczynski’s14  analysis  suggested  that  positive  and  negative  peak  wall 
pressure  events  are  often  components  of  the  ejection/sweep,  or  burst 
cycle.  Johannson,  Her,  and  Haritonidis15  also  found  that  negative  wall 
pressure  peaks  were  associated  with  sweep-like  motions.  Schewe, 
who  visually  tracked  pressure  producing  structures  in  time  records 
from  an  array  of  pressure  transducers,  attributed  them  to  sources  near 
the  wall  (y+<21).  Kammeyer17  observed  the  presence  of  an  inclined 
vortical  structure  associated  with  large  amplitude  pressure  events. 

Repeatedly,  structures  associated  with  turbulence  production  have 
been  demonstrated  to  impart  a  pressure  signature  at  the  wall.  The 
primary  intent  of  the  experiments  documented  here  was  to  measure  the 
spatial  extent  of  both  the  structures  in  the  boundary  layer  and  that  of 
their  induced  wall  pressures.  Through  various  signal  processing 
techniques,  a  correlation  between  large  and  small  scale  turbulent 
motions  was  also  uncovered  which  is  consistent  with  many  of  the 
turbulent  boundary  layer  models  discussed  above. 


III.  THE  EXPERIMENT 

The  experiments  in  this  investigation  were  conducted  in  the 
Catholic  University  of  America  (CUA)  Low  Noise  Flow  Facility  shown 
schematically  in  figure  1. 


V////////////////////////// 


Figure  1.  CUA  Low  Noise  Flow  Facility  features  (1)  inlet  section  (2) 
test  section  (3)  diffuser  (4)  muffler  (5)  coupler  (6)  blower/motor  (7) 
turn  vanes  (8)  return  duct 


All  experiments  in  this  investigation  were  conducted  with  an 
equilibrium  turbulent  boundary  layer  and  a  free  stream  velocity  of 
approximately  16  m/s  (50  ft/s).  Detailed  boundary  layer  characteristics 
are  given  in  table  I.  Wall  pressure  measurements  were  made  using 
Endevco  model  8507-C2  piezo-resistive  pressure  transducers,  which 
are  described  in  detail  in  Russell.18  Boundary  layer  characteristics 
were  measured  using  a  TS1  type  1261  A-T1.5  miniature  boundary 
layer  probe.  All  two-component  velocity  measurements  were  made 
with  aTSI  type  1249  A-10  miniature  "X"  probe.  The  data  acquisition 
system  is  described  in  detail  in  Kammeyer.17 


Parameter 

SI 

English 

Freestream  Velocity,  U0 

15.33  m/s 

50.28  ft/s 

Shear  Velocity,  uT 

0.59  m/s 

1.93  ft/s 

uT/U0 

0.038 

Boundary  Layer  Thickness,  6 

2.73  cm 

1.075  in 

Viscous  TBL  Thickness,  8  T 

1026 

Displacement  Thickness,  8  * 

0.49  cm 

0.195  in 

Momentum  Thickness, 0 

0.34  cm 

0.133  in 

Reynolds  No.,  ReT 

3364 

Shape  Factor,  H 

1.4606 

Cf,  calculated 

0.00285 

Cf,  measured 

0.00295 

Table  I.  Boundary  Layer  Parameters 

The  purpose  of  the  wall  pressure  array  was  to  track  and  measure 
the  spatial  extent  of  near  wall  turbulent  structures.  To  resolve  the  small 
scales  at  which  these  structures  exist,  the  sensing  diameter  of  the 
transducer  had  to  be  minimized  (d+=39).  The  orientations  of  the  wall 
pressure  arrays  are  shown  in  figure  2. 

Two  sets  of  experiments  were  performed.  The  first  set  involved 
the  exclusive  measurement  of  fluctuating  wall  pressure  with  both 
streamwise  and  spanwise  transducer  arrays.  The  second  set  of 
experiments  involved  the  simultaneous  measurement  of  pressure  and 
velocity.  Figure  2  also  illustrates  the  orientation  of  the  hot  wire  system 
during  the  velocity  surveys.  To  map  the  flow  field  in  the  X-Y  plane, 
three  different  cross-wire  surveys  were  conducted  downstream  of  the 


Figure  2.  Sensor  Configuration  During  Wall  Pressure  and  Velocity 
Measurements. 

streamwise  transducer  array.  The  result  was  a  rectangular  grid  (18  x 
30)  at  which  wall  pressure  and  velocity  signals  could  be  simultaneously 
sampled  and  compared  using  correlation  and  conditional  sampling 
techniques.  A  similar  grid  (10  x  30)  was  generated  in  the  Y-Z  plane 
using  the  spanwise  transducer  array.  In  each  of  the  experiments,  the 
pressure  and  velocity  signals  were  sampled  simultaneously  at  a  rate  of 
32,768  Hz  for  a  period  of  10  seconds. 

Facility  noise  as  well  as  transducer  noise  were  first  removed  by 
filtering  with  a  broadband,  band-pass  digital  filter  (filter  0).  Based  on 
the  behavior  of  velocity  spectra  measured  outside  the  boundary  layer 
(see  Russell18)  a  filter  was  chosen  to  remove  the  scales  associated  with 
the  outer  “irrotational  bulge.”  These  motions  were  assumed  to  be 
passive  since  no  conclusive  evidence  exists  that  these  structures  are 
associated  with  turbulent  production.  This  band-pass  filter  (filter  1)  had 
cutoff  frequencies  of  100  and  300  Hz.  A  third  filter  was  chosen  with 
cutoff  frequencies  of  300  and  1200  Hz  (Farabee’s12  “universal” 
range).  Finally,  a  high  frequency  band-pass  filter  was  chosen  which 
best  duplicated  the  performance  of  Kammeyer's17  wavelet  filter.  This 
frequency  range  was  shown  by  Kammeyer  to  capture  the  near-wall 
burst/sweep  activity.  The  three  filters  are  listed  in  table  II.  Figure  3 
shows  the  spectral  effect  of  these  filters  on  a  typical  wall  pressure 
signal. 


Filter  Number 

Frequency  Band  (Hz) 

Spectral  Region 

0 

100-5000 

Broadband 

1 

100-300 

“Mid” 

2 

300-1200 

“Universal” 

3 

1200-5000 

“High” 

Table  II.  Bandpass  Filter  Break  Frequencies 


Figure  3.  The  Spectral  Effects  of  Band-Pass  Filters  on  a  Typical  Wall 
Pressure  Signal  (U0=15.3  m/s) 


64 


Another  form  of  scale  discrimination  or  filtering  was  applied  to 
pressure  and  velocity  signals  in  an  attempt  to  detect  turbulent  events. 
This  was  the  Variable  Interval  Time  Average  or  VITA  function, 
(Blackwelder19)  which  is  a  measure  of  the  localized  variance  of  a 
signal  over  a  time  window,  Tv,  an  adjustable  integration  time.  Tv  can 
be  changed  to  fit  the  time  scales  of  the  events  of  interest,  allowing  the 
VITA  method  to  be  applied  to  velocity  and  pressure  signals  which  have 
been  band-pass  filtered. 

IV.  SPACE  TIME  CHARACTERISTICS  OF  THE  WALL 
PRESSURE  FIELD 

Signals  from  the  streamwise  and  spanwise  wall-pressure  arrays 
were  analyzed  for  information  about  the  space-time  characteristics  of 
the  wall  pressure  field.  These  methods  included  spectral  analysis, 
cross-correlation  measurements,  and  conditional  sampling.  The  results 
successfully  demonstrate  the  spatial  extent  of  the  wall  pressure 
signatures  of  organized  structures.  Correlation  and  conditional 
sampling  results  are  also  presented  for  both  the  streamwise  and 
spanwise  transducer  arrays. 


Streamwise  Correlation  Results 

The  correlation  coefficient,  Rpp(x),  was  computed  between  the 
upstream-most  transducer  (pi)  and  each  of  the  remaining  transducers 
in  the  streamwise  array  (pi  to  p8).  This  computation  was  made  over  a 
segmented  time  span,  AT,  and  then  repeated  for  successive  time  spans 
until  the  end  of  the  time  record  was  reached.  The  individual  correlation 
functions  were  then  ensemble  averaged.  Typical  results  of  this 
computation  are  shown  in  figure  4  for  time  records  that  were  subjected 
to  filters  0,1,2  and  3. 


Filter  0 


1 

0.8 
0.6 
0.4 
0.2 
0 

-0.2 
-0.4 
-0.6 

-100  -50  0  50  100 


Filter  1 


Filter  2 


tau+ 


Filter  3 


tau+ 


fluctuations  increases  with  transducer  separation,  ie.,  the  turbulent 
structures  which  remain  well  correlated  across  the  length  of  the  array 
define  the  shape  of  the  correlation  function  between  first  and  last 
transducers. 

The  cross-correlation  function  computed  for  signals  subjected  to 
filter  1  are  shown  in  figure  4b.  The  shape  of  RpP(T)  changes 
dramatically  when  only  a  narrow  band  of  frequencies  is  considered. 
The  overall  shape  of  the  correlation  is  quite  different.  Rather  than  the 
pulse-like  shape  of  the  broad  band  (filter  0)  correlation  function, 
Rpp(x)  for  the  low  frequency  (filter  1)  appears  more  wave-like.  By 
removing  the  high  frequency  components  of  the  wall  pressure  signal,  a 
physically  relevant  correlation  function  of  the  pressure  sources  due  to 
the  irrotational  flow  is  exposed.  The  same  general  trend  is  observed  as 
the  filter  cutoff  frequencies  are  increased  (filters  2  and  3). 

The  spatial  decay  rates  of  the  maximum  cross-correlation  for  each 
of  the  filters  tested  are  re-plotted  versus  streamwise  distance  in  figure 
5a.  It  is  clear  from  these  curves  that  the  decay  rate  of  Rpp(T)max  of  the 
wall  pressure  signals  is  highly  dependent  on  the  filtering  applied.  From 
these  data  it  would  appear  that  high  frequency  (filter  3)  wall  pressure 
activity  is  only  correlated  out  to  one  half  the  boundary  layer  thickness 
(5/2)  in  the  streamwise  direction. 

The  convection  velocity  of  the  wall  pressure  field  can  be 
computed  from  the  time  delay  between  peaks  in  the  correlation 
functions  and  the  separation  distance  between  the  transducers.  Results 
of  this  computation,  using  the  upstream-most  transducer  as  the 
reference,  are  shown  in  figure  5b.  The  slightly  rising  convection 
velocity  with  transducer  spacing  is  also  consistent  with  Farabee’s 
spectral  results.  More  important  however,  is  the  variation  of  Uc  with 
the  choice  of  filtering.  Uc  computed  from  broadband  data  (filter  0)  as 
well  as  that  from  filters  2  and  3  appear  to  collapse  on  each  other.  The 
scales  associated  with  filter  1,  those  in  the  outer-irrotational  flow, 
convect  at  consistently  higher  velocities  across  the  array.  It  appears 
that  the  scales  associated  with  filters  2  and  3  convect  at  approximately 
the  same  speed  and  this  speed  corresponds  to  that  measured  by  cross¬ 
correlation  functions  of  the  broad-band,  (filter  0)  data. 


Streamwise  Distance  (x/delta) 


Figure  4.  The  ensemble  averaged  correlation  function  between 
transducer  pairs  in  the  streamwise  array,  (a)  unfiltered,  (b)  filter  1,  (c) 
filter  2,  (d)  filter  3. 

Figure  4a  shows  Rpp(t)  for  wall  pressure  time  records  subjected  to 
filter  0,  which  is  the  baseline  data,  free  from  background  and  electrical 
noise,  hereafter  referred  to  as  “unfiltered”  data.  Several  distinctive 
features  of  these  data  are  worth  noting.  First,  the  exponential  decay 
with  streamwise  distance  of  the  magnitude  of  the  maximum  correlation 
is  consistent  with  the  exponential  decay  of  the  coherence  function  seen 
by  other  investigators.12' 8  Second,  as  the  separation  distance  between 
the  transducers  is  increased,  the  width  of  the  correlation  function 
broadens.  This  is  also  consistent  with  the  spectral  results  which  showed 
the  measured  influence  of  the  large  scale,  low  frequency  pressure 


Figure  5.  Convective  features  of  the  cross-correlation  function  for  the 
streamwise  array,  (a)  mean  decay  of  peak  correlation  coefficients,  (b) 
convection  velocity  based  on  mean  time  between  peaks. 

As  shown  in  figure  5a,  the  magnitude  of  the  cross-correlation  of 
the  high  frequency  wall  pressure  signal  decays  rapidly  with  transducer 
separation.  These  pressure  signatures  are  generally  attributed  to  burst 
events  in  the  near  wall  region.  This  would  suggest  that  the  spatial 
influence  of  the  ejection/sweep  processes  are  limited  to  3  or  4 
transducer  spacings  in  the  streamwise  direction.  However,  this  is  not 
the  case.  The  spatial  influence  of  these  near  wall  structures  is  much 
larger.  A  shortcoming  of  the  standard  cross-correlation  function  is  that 
it  fails  to  illustrate  the  true  influence  of  these  scales  because  the 
pressure  signature  of  these  structures  changes  rapidly  as  they  convect. 


65 


A  more  appropriate  method  of  measuring  the  spatial  influence  of  these 
burst  events  is  to  correlate  the  wall  pressure  signals  based  on  a 
measure  of  the  localized  energy  contained  in  clusters  of  these  short 
time  events. 

Figure  6  shows  the  normalized  correlation  between  the  VITA 
functions  at  two  streamwise  transducers  computed  exclusively  from 
filter  2  and  filter  3  wall  pressure  signals.  The  results  for  filter  2-filter  2 
and  filter  3-filter  3  correlations  show  consistently  strong  correlations 
over  the  spatial  extent  of  the  streamwise  array  for  both  the  pressure 
signatures  of  the  larger  scale  structures  (filter  2)  and  the  near-wall 
burst  events  (filter  3). 

By  comparing  figure  4d  and  figure  6b  an  important  feature  of  high 
frequency  wall  pressure  signals  is  revealed.  That  is,  the  appearance  of 
individual  near-wall  burst  events  in  the  wall  pressure  signal  is  distorted 
as  it  convects  downstream,  deteriorating  the  temporal  correlation 
between  transducers.  However,  the  cluster  of  turbulent  activity 
associated  with  the  event,  identified  in  the  VITA  calculation  of  the 
signal's  variance,  remains  well  correlated  as  it  convects  the  length  of 
the  transducer  array.  And  as  shown  in  figure  5b,  this  cluster  of  burst 
activity  appears  to  convect  with  the  same  speed  as  the  larger  structures 
captured  by  filter  2. 


Filter  2 


Filter  3 


tau+ 


Figure  6.  Normalized  correlation  based  on  the  localized  variance 
(VITA)  functions  of  filtered  wall  pressure  signals  from  the  streamwise 
array,  (a)  filter  2,  (b)  filter  3. 

Streamwise  Conditional  Sampling  Results 

Conditional  sampling  and  ensemble  averaging  of  wall  pressure 
peak  events  can  also  yield  information  on  the  spatial  and  convective 
properties  of  the  wall  pressure  field,  however,  with  this  approach,  the 
intermittent,  high  amplitude  wall  pressure  fluctuations  can  be  extracted 
from  the  total  signal  and  examined  for  their  own  spatial  and  convective 
features. 

Conditional  sampling  results  from  the  streamwise  array  are  shown 
in  figure  7.  Wall  pressure  signals  from  each  transducer  were 
conditionally  sampled  based  on  the  detection  of  peak  events  (k=+3) 
occurring  at  the  upstream-most  transducer  (pi).  The  signals  from  each 
of  the  transducers  were  then  ensemble  averaged  over  a  fixed  time 
window  centered  at  the  peak  detection  time.  This  computation  was 
performed  on  time  records  that  were  subjected  to  filters  0,1,2,  and  3. 
The  conditionally  averaged  event  shapes  at  each  of  the  eight 
transducers  in  the  array  are  shown  in  separate  plots  for  each  of  the 
filtered  time  records.  The  average  shape  of  the  events  is  similar  to  the 
shape  of  the  corresponding  correlation  functions  in  figure  4.  The 
broadening  and  exponential  decay  of  the  filter  0  event  shapes  as  well 
as  the  clarifying  effect  of  the  other  filters  is  similarly  reflected  in  these 
data. 


Filter  0  Fitter  1 


Figure  7.  Downstream  wall  pressure  signals  conditionally  averaged  on 
peak  wall  pressure  events  (k=+3)  at  the  first  transducer  in  the 
streamwise  array,  (a)  unfiltered,  (b)  filter  1,  (c)  filter  2,  (d)  filter  3. 

The  mean  convection  velocity,  Uc,  can  also  be  determined  by 
measuring  the  time  delay  between  peaks  in  the  conditionally  averaged 
event  shapes.  The  results  for  each  of  the  four  filters  is  shown  in  figure 
8.  The  collapse  of  the  filter  2  and  filter  3  curves  on  the  filter  0  curve  is 
not  as  apparent  as  with  correlation  results,  however,  the  events 
sampled  in  the  filter  1  time  records  do  appear  to  convect  consistently 
faster  than  the  events  detected  in  the  other  (high  frequency)  signals. 


Figure  8.  Measured  convection  velocity  based  on  time  between  peaks 
in  the  streamwise  conditionally  averaged  wall  pressure  events. 

The  convection  velocity  results  presented  so  far  (cross-correlation, 
and  conditional  sampling)  consistently  show  that  wall  pressure  events 
associated  with  the  scales  defined  by  filters  2  and  3  have  similar 
convection  velocities  (Uc/Uo)  of  between  0.55  and  0.7.  This  places  the 
center  of  these  pressure  sources  at  (50<y+<250),  the  log-law  region  of 
the  boundary  layer. 

Spanwise  Conditional  Sampling  Results 

To  illustrate  the  spanwise  extent  of  the  wall  pressure  field,  results 
from  the  spanwise  conditional  sampling  experiments  are  presented. 
Absent  the  convective  effects,  the  conditionally  averaged  event  shapes 
resemble  the  shapes  of  the  streamwise  conditional  averages  in  figure 
7.  However,  rather  than  view  the  event  shapes  in  the  time  domain,  it  is 
possible  to  project  the  event  shapes  onto  the  X-Z  plane  using  Taylor's 
hypothesis.  By  assuming  a  frozen,  convecting  pressure  field,  the 
conversion  from  time  to  space  is  accomplished  simply  via  the  average 
measured  convection  velocity  by  X+=Uc+t+.  The  wall  pressure  signals 


66 


for  each  transducer  in  the  spanwise  array  (pi  to  p8)  were  conditionally 
sampled  and  ensemble  averaged  on  the  detection  of  peak  events 
(k=H-3)  at  p4,  a  transducer  at  the  center  of  the  array.  Time  was 
converted  to  space  using  the  average  convection  velocities,  computed 
for  each  filter  from  the  streamwise  cross-correlation  results.  Contour 
plots  from  the  resulting  ensemble  averaged  event  shapes  (P/P™)  are 
shown  in  figure  9.  The  streamwise  (x4)  scale  of  the  filter  1  curve  has 
been  expanded  to  accommodate  the  large  streamwise  extent  of  the 
wall  pressure  events  detected  in  that  signal.  The  average  spatial  extent 
of  high  amplitude  wall  pressure  events  from  the  unfiltered  (filter  0)  do 
not  appear  elongated  in  the  streamwise  direction  like  those  of  Kim20 
for  a  simulated  channel  flow,  however,  they  do  exhibit  the  same 
nominal  spatial  extent. 

(a)  Filter  0  (b)  Filter  1 


(c)  Fitter  2  (d)  Filter  3 


500 

:  0  : 
\  s' — \  C 

500 

& 

<9  0  2 

&  o 

- - 

4  0 

-500 

->  c°  ^ 
-200  0  200 

0  -500 

O'02 

-200  0  200 

Z+  Z+ 


Figure  9.  Contours  of  spanwise  wall  pressure  signals  conditionally 
averaged  on  peak  wall  pressure  events  at  P4  (k=+3),  (a)  unfiltered,  (b) 
filter  1,  (c)  filter  2,  (d)  filter  3. 

Examining  the  data  in  figure  9  collectively,  one  sees  the 
complexity  of  the  turbulent  wall  pressure  field.  Clearly,  the  wall 
pressure  signal  is  composed  of  many  large  and  small  scale  events.  The 
wall  pressure  signatures  of  these  events  varies  greatly  with  the  filtering 
performed  on  the  original  signal.  Not  suprisingly,  the  wall  pressure 
events  associated  with  scales  characteristic  of  the  irrotational  flow 
(filter  1)  have  a  much  larger  spatial  extent  than  the  streamwise  or 
spanwise  dimensions  of  the  transducer  array,  and  yet,  the  events 
detected  in  the  filter  3  data  are  nearly  too  small  to  resolve  with  the 
transducer  array  used. 

Correlation  of  Large  and  Small  Scale  Structures 

The  possibility  that  large  scale  (filter  2)  and  small  scale  (filter  3) 
wall  pressure  signatures  are  correlated  was  suggested  by  their  matched 
convection  velocities.  Several  of  the  turbulence  production  models 
discussed  in  Section  II  are  based  on  this  type  of  correlation  in  which 
there  is  a  causal  relationship  between  large  and  small  scale  turbulent 
activity.  Thomas  and  Bull,9  for  example,  correlated  the  passage  of 
large  scale,  inclined  shear  layer  with  small  scale,  near  wall,  turbulent 
production  activity.  The  relationship  between  the  scales  in  the  wall 
pressure  field  are  now  examined  using  the  cross-correlation  and 
conditional  sampling  methods  already  demonstrated. 

Streamwise  VITA  correlation  results  presented  earlier  illustrated 
that  small  scale  events  occur  in  clusters  of  large  amplitude  positive  and 
negative  peaks,  and  that  while  the  pattern  of  peaks  in  the  cluster 
changes  significantly  as  it  convects,  the  cluster  itself  remains  generally 
intact.  Figure  10  shows  the  normalized  correlation  of  the  low  and  high 
frequency  wall  pressure  VITA  functions  (filter  2-filter  3)  between  the 


transducers.  There  appears  to  be  consistent  correlation  between 
activity  in  the  filter  2  signal  of  the  upstream-most  transducer,  and  high 
frequency  (filter  3)  activity  at  the  downstream  transducers  in  the  array, 
the  magnitude  of  which  decays  very  gradually  with  transducer 
separation.  This  qualitative  observation  of  the  strong  VITA  correlations 
between  the  filtered  signals  suggests  that  the  filter  2  and  filter  3  wall 
pressure  activity  appear  to  be  components  of  composite  footprint  of  a 
single,  organized  turbulent  motion.  This  behavior  is  also  illustrated  by 
examining  sample  time  records  from  the  wall  pressure  array. 


Figure  10.  Normalized  correlation  based  on  the  localized  variance 
(VITA)  functions  of  filter  2  wall  pressure  at  PI  and  downstream  (PI¬ 
PS)  filter  3  wall  pressure 

A  sample  window  of  simultaneous  wall  pressure  time  records  from 
the  streamwise  array  is  shown  in  figure  11.  In  this  sample  there  are 
obvious  regions  or  clusters  of  high  frequency  activity  (filter  3)  which 
appear  to  convect  at  approximately  the  same  speed  as  the  peaks  in  the 
lower  frequency  signal  (filter  2).  At  each  of  the  downstream 
transducers,  the  turbulent  clusters  seen  in  the  high  frequency  signal 
appear  to  be  slightly  preceded  by  high  amplitude  positive  peaks  in  the 
low  frequency  signal.  Thomas  and  Bull9  observed  the  same  behavior  in 
high  and  low  pass  filtered  wall  pressure  signals. 


40  r 


Pi 


P8 


Figure  11.  Sample  filtered  wall  pressure  time  records  from  the 
streamwise  array  (PI  to  P8): ...,  filter  2;  — ,  filter  3. 

As  one  would  expect  based  on  the  streamwise  correlation  results, 
the  low  frequency  event  shapes  appear  almost  frozen  as  they  convect 
across  the  entire  span  of  the  array,  whereas,  the  peaks  within  the  high 
frequency  clusters  do  not  retain  their  shape  as  the  cluster  convects. 
Nonetheless,  the  high  frequency  cluster  remains  generally  intact. 


67 


The  low  and  high  frequency  VITA  functions  for  each  transducer 
in  the  streamwise  array  are  shown  in  figure  12.  The  time  sample 
shown  is  the  same  as  that  in  figure  11.  The  low  and  high  frequency 
events  seen  in  the  time  records  are  successfully  captured  by  the 
corresponding  VITA  functions.  As  observed  in  the  raw  time  records, 
the  high  and  low  frequency  VITA  functions  indicate  a  time  lag 
between  peak  low  frequency  and  peak  high  frequency  wall  pressure 
activity.  This  suggests  that  the  large  scale  component  of  the  structure 
passes  over  the  transducers  ahead  of  the  small  scale  component.  The 
signature  of  the  large  scale  head  and  small  scale  legs  of  an  inclined 
hairpin  vortex,  for  example,  would  satisfy  this  description. 


Figure  12.  Sample  VITA  functions  of  the  wall  pressure  time  records 
shown  in  figure  11:...,  filter  2;  — ,  filter  3. 

Although  the  sample  time  records  in  figure  1 1  are  typical  of  the 
entire  time  record  collected,  the  illustration  of  a  single  event  is  not 
sufficient  to  draw  general  conclusions.  Therefore,  conditional  sampling 
methods  were  also  applied  to  the  filter  2  and  filter  3  wall  pressure  time 
records.  Figure  13  shows  the  ensemble  averaged  data  from  the  high 
frequency  (filter  3)  wall  pressure  time  records  of  the  first  four 
transducers  in  the  streamwise  array  based  on  the  detection  of  low 
frequency  (filter  2)  high  amplitude  (k=+3)  peak  events  in  the 
upstream-most  transducer.  These  data  confirm  the  correlation  results  in 
figure  10  as  well  as  the  temporal  information  observed  in  the  time 


Figure  13.  Downstream  filter  3  wall  pressure  signals  conditionally 
averaged  on  peak  events  in  upstream,  filter  2  wall  pressure  signal, 
(k=+3) 


records  and  the  VITA  functions.  There  is  a  clear  correlation  between 
low  frequency  peak  events  and  high  frequency  wall  pressure  activity 
across  the  array.  On  average,  the  peak  high  frequency  activity  occurs 
slightly  after  the  low  frequency  peak  has  passed,  shown  by  the  offset 
of  the  dx=0  peak  from  t+=0. 

Collectively,  the  wall  pressure  findings  reveal  a  consistent  phase 
relationship  between  large  and  small  scale  wall  pressure  activity.  This 
phase  relationship  supports  the  idea  that,  in  many  cases,  small  and  large 
scale  wall  pressure  activity  are  components  of  the  wall  pressure 
signature  of  a  single,  large  scale,  turbulent  structure.  The  small  scale 
activities  were  characterized  by  intermittent,  convecting  clusters  of 
peaks  which  evolved  over  the  spatial  extent  of  the  array.  The  large 
scale  activity  accompanying  the  small  scale  events,  resembled  a 
frozen,  convecting  wave  train,  which  maintained  its  shape  as  it 
traversed  the  length  of  the  streamwise  array.  The  large  scale  wave 
trains  were  less  intermittent  than  the  high  frequency  events  and  usually 
contained  2  or  more  peaks  and  axis  crossings.  This  feature  made  them 
well  suited  to  VITA  detection. 

V.  IDENTIFICATION  OF  FLOW  STRUCTURES 

This  section  contains  the  results  from  the  simultaneous 
measurements  of  the  flow  field  and  wall  pressure  signatures.  The 
objective  here  was  to  identify  the  distinct  flow  structures  whose  wall 
pressure  signatures  were  measured  with  the  array.  These  flow 
structures  are  defined  using  the  same  analysis  tools  previously 
employed  including  cross-correlation,  and  conditional  sampling, 
applied  to  both  velocity  and  pressure  data. 

The  physical  extent  of  the  pressure-producing  structures  can  be 
illustrated  by  measuring  both  the  spectral  and  temporal  cross¬ 
correlation  between  wall  pressure  and  streamwise  (u),  as  well  as  wall 
normal  (v)  components  of  velocity  at  locations  across  the  boundary 
layer.  These  findings  are  presented  in  Russell.18  Many  of  the  same 
flow  characteristics  can  also  be  derived  from  the  results  of  the 
conditional  sampling  experiments  conducted.  In  this  section  the  results 
of  experiments  in  which  u  and  v  are  conditionally  sampled  based  on 
wall  pressure  peak  events  are  presented.  From  these  results,  a 
composite  picture  of  the  average  pressure  producing  flow  structures  is 
inferred.  In  addition,  by  conditionally  sampling  high  frequency  velocity 
signals  on  low  frequency  wall  pressure  events,  the  correlation  between 
large  and  small  scale  structures  seen  in  the  wall  pressure  data  is 
illustrated  in  the  ensemble  averaged  flow  field. 

Two  basic  techniques  for  flow  field  visualization  are  used.  The 
first  technique  utilizes  the  entire  array  of  transducers  to  produce  a 
database  of  pressure  and  velocity  time  records  in  the  streamwise 
measurement  grid.  At  each  station  in  the  streamwise  measurement 
grid,  the  velocity  vectors  (u  and  v)  are  sampled  at  times  corresponding 
to  large  amplitude  wall  pressure  events  (k  =  +2)  at  location 
(x+,y+)=(0,0).  The  velocity  samples  are  then'  ensemble  averaged. 
Vector  or  'quiver'  plots  of  the  average  velocities  are  then  plotted  in  a 
map  in  which  the  quivers  are  physically  located  at  the  measurement 
position  (x+,y+)  relative  to  the  fixed  reference  pressure  transducer. 
The  flow  fields  depicted  represent  flow  patterns  downstream  of  the 
transducer  array. 

The  second  technique  uses  a  single  pressure  transducer  and  a 
single  velocity  (u,v)  survey.  For  this  technique,  in  which  the  ensemble 
averaged  velocity  time  records  are  played  back,  an  effective 
streamwise  (x)  axis  is  computed  from  an  assumed  convection  velocity 
(x+-UcY).  The  average  velocity  time  record  from  each  y  location  in 
the  survey  is  then  vector  plotted  at  that  y  location.  The  “  Taylor  plots” 
created  using  this  method  are  based  on  an  assumption  of  a  frozen, 
convecting  flow  field  which  changes  negligibly  in  the  time  window 
viewed.  This  technique  has  the  distinct  advantage  of  an  essentially 
unlimited  streamwise  resolution,  limited  only  by  the  sample  time  (l/fs) 
and  will  prove  to  have  an  advantage  in  visualizing  the  small  scale, 
near-wall,  filter  3  flow  structures.  The  quivers  in  these  flow  maps  are 
scaled,  i.e.,  normalized  by  the  local  RMS  fluctuating  velocity  value. 
The  purpose  of  the  scaling  is  to  better  visualize  the  weaker  large  scale 
outer  structures  which  are  characterized  by  velocity  excursions  far 
less  violent  than  the  near  wall  structures  associated  with  large 
amplitude  wall  pressure  events. 

Flow  Field  " Mapping”  Results 

The  four  conditionally  averaged  flow  field  maps  in  figure  14  show 
the  filter  0  (unfiltered)  average  flow  field  conditionally  sampled  on 
filter  2  and  filter  3  positive  and  negative  peak  wall  pressure  events. 


68 


The  positive  pressure  event  in  figure  14a  is  characterized  by  a  reverse 
flow  and  ejection  motion,  whereas  the  negative  pressure  event  in 
figure  14b  is  characterized  by  a  sweep,  which  happens  to  follow  a 
negative  shear  stress  and  ejection  motion.  The  coupling  of  the  positive 
and  negative  peaks  as  components  of  the  total  footprint  of  large  scale 
ejection/sweep  type  motions  is  clearly  demonstrated  in  these  data. 


(a)  Filt  0  u,v  on  Filt  2  p,  k=+2  (b)  Filt  0  u,v  on  Fiit  2  p.  k=-2 


X+  X+ 


(c)  Filt  0  u,v  on  Filt  3  p,  k=+2  (d)  Filt  0  u,v  on  Filt  3  p,  k=-2 


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Figure  14.  Unfiltered  average  flow  field  conditionally  sampled  on 
filter  2  and  filter  3  positive  and  negative  peak  wall  pressure  events 


while  figures  15c  and  d  show  the  filter  3  average  flow  field 
conditionally  sampled  on  filter  3,  positive  and  negative,  peak  wall 
pressure  events.  The  filter  2  flow  structures  are  nominally  consistent 
with  the  unfiltered  flow  results  in  figures  14a  and  b.  However,  the 
filtered  flow  field  reveals  a  more  organized,  inclined  structure, 
exhibiting  the  same  ejection  type  motion.  It  also  exhibits  a  near-wall 
“splat”  feature  at  x+  ~  400  for  the  positive  peak  pressure  detection  in 
figure  15a  which  appears  to  be  a  component  of  the  ejection/sweep 
process  for  structures  of  filter  2  scale. 


(a)  Filt  2  u.v  on  Flit  2  p,  k=+2 


(b)  Flit  2  u.v  on  filt  2  p,  k=-2 


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The  maps  in  figure  14c  and  d  similarly  illustrate  a  relationship 
between  large  and  small  scale  structures.  In  these  figures,  the 
unfiltered  flow  field  is  conditionally  averaged  on  filter  3,  positive  and 
negative  wall  pressure  events.  Two  important  features  should  be 
noted.  The  first  is  the  familiar  large  scale,  near-wall  shear  stress 
region  which  extends  far  beyond  the  streamwise  extent  of  the  plots  (out 
to  at  least  x+  of  approximately  1800).  The  large  scale  sweep  of  fluid, 
coupled  with  the  near  wall  shear  stress  region  combine  to  form  an 
inclined  shear  layer  across  the  boundary  layer.  This  large  scale  shear 
layer,  by  virtue  of  its  strong  presence  in  these  data,  is  correlated  with 
high  frequency  (filter  3)  wall  pressure  activity. 

The  second  observation  is  of  activity  in  the  near-wall  region 
(y+<100  and  x+<200).  Upon  close  examination  of  figures  14c  and  d  in 
this  region,  the  near  wall  turbulent  structure  associated  with  the  filter  3 
wall  pressure  event  is  visible.  The  first  two  x  locations  of  velocity 
vectors  in  figure  14c  indicate  a  small  ejection  (Q2)  and  sweep  (Q4), 
respectively.  Since  the  scale  of  these  structures  are  on  the  order  of  the 
transducer  spacing,  their  detailed  shape  is  not  clear,  however,  they 
clearly  contain  Q2  and  Q4  motions.  The  flow  field  associated  with  a 
negative  pressure  event  shown  in  figure  14d  contains  further  evidence 
of  the  small  scale  structure  at  x+  -  200.  In  this  figure,  the  rotational 
motion  of  the  structure  is  weakly  visible.  It  appears  as  though  the  small 
scale  structure  rotates  clockwise  as  it  is  swept  along  by  the  large  scale 
shear  layer.  The  resemblance  between  figures  14c  and  d  is  strong, 
and  they  appear  only  to  differ  by  a  finite  phase  shift.  Though  the  small 
scale  activity  may  have  a  larger  vertical  and  streamwise  extent  than  is 
indicated  in  figures  14c  and  d,  the  dominance  of  the  large  scale  shear 
layer  in  these  data  appears  to  have  a  masking  effect  on  it.  It  is  hoped 
that  by  removing  the  large  scale  component  of  the  velocity  signals,  a 
more  refined  image  of  these  near  wall  structures  will  be  revealed. 

The  velocity  data  presented  in  figure  1 5  are  subject  to  the  same 
filtering  as  the  wall  pressure  on  which  their  sampling  was  based. 
Figures  15a  and  b  show  the  filter  2  average  flow  field  conditionally 
sampled  on  filter  2,  positive  and  negative,  peak  wall  pressure  events; 


Figure  15.  Filter  2  and  filter  3  average  flow  fields  conditionally 
sampled  on  positive  and  negative  peak  wall  pressure  events 

The  average  flow  field  downstream  of  filter  2  negative  wall 
pressure  events,  depicted  in  figure  15b,  contains  the  characteristic 
sweep  motion  above  the  reference  transducer.  This  is  followed 
downstream  by  an  ejection  which  occurs  upstream  of  a  region  of 
strong  near  wall  negative  shear  stress.  These  motions  combine  to  form 
an  inclined  shear  layer  similar  to  that  seen  in  the  filter  0  (unfiltered) 
flow  fields. 

The  unfiltered  flow  results  in  figures  14c  and  d,  showed  small 
scale  near  wall  ejection/sweep  motions  associated  with  high  frequency 
wall  pressure  fluctuations  associated  with  the  passage  of  larger  scale 
motions.  By  removing  the  larger  scales  from  the  velocity  signals,  a 
clearer  image  of  the  small  scale  motions  is  revealed.  This  is  illustrated 
in  figures  15c  and  d.  The  average  filter  3  flow  field  associated  with  a 
positive  peak  pressure  consists  of  a  strong  Q2  ejection  directly  above 
the  transducer  and  a  simultaneous  Q4  sweep  of  fluid  at  the  next 
transducer  (100  viscous  units  downstream).  Similarly,  the  negative 
wall  pressure  event  consists  of  a  sweep  and  ejection  motion  in  the 
opposite  order. 

Since  filter  3  peak  events  were  shown  to  occur  in  clusters,  one 
would  expect  to  see  a  multitude  of  ejections  and  sweeps  in  figures  15c 
and  d.  These  data  do  indicate  the  presence  of  additional  near-wall 
organized  activity,  however,  the  resolution  of  the  measurement  grid, 
combined  with  the  short  correlation  lengths  of  these  scales,  make  it 
difficult  to  map  the  entire  cluster  of  activity.  An  alternative  method  is 
needed  to  view  the  near  wall  turbulent  activity  with  greater  resolution. 

Flow  Field  Visualization  Using  Taylor's  Assumption 

The  Taylor  method  was  employed  to  both  qualify  the  results  from 
the  flow  field  mapping  technique  and  to  provide  better  resolution  of 
the  small  scale  turbulent  motions.  The  flow  fields  shown  in  figure  16 


69 


600 
500 
400 
£  300 
200 
100 
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600 
500 
400 
£300 
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t  0 

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-600  -400  -200  0  200  400  600 

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Filter  3  Flow  Field 


Figure  16.  Taylor  plot  of  unfiltered  and  filter  2  flow  fields  Figure  17.  Taylor  plot  of  unfiltered  and  filter  3  flow  fields 

conditionally  sampled  on  filter  2  positive  peak  wall  pressure  events  conditionally  sampled  on  filter  3  positive  peak  wall  pressure  events. 


are  a  Taylor  plot  of  the  filter  0  (unfiltered)  and  filter  2  average  flow 
fields  conditionally  sampled  on  filter  2,  positive  (k=+2),  peak  wall 
pressure  events.  The  ensemble  averaged  filter  2  wall  pressure 
signature  is  shown  at  the  bottom  of  the  figure.  The  general  features  of 
the  downstream  unfiltered  and  filter  2  flow  fields  (x+>  0)  in  these 
figures  are  consistent  with  the  equivalent  flow  maps  in  figures  14a  and 
15a.  This  observation  confirms  that  the  turbulent  motions  isolated  by 
filter  2  remain  generally  intact  as  they  convect  the  span  of  the 
streamwise  array.  Furthermore,  by  viewing  the  filtered  flow  field  with 
the  enhanced  streamwise  resolution  of  this  method,  the  rotational 
features  of  these  structures  is  revealed,  as  are  the  rotating  secondary 
motions  upstream  and  downstream  of  the  primary  structure.  Hence, 
rather  than  the  large  scale,  inclined  shear  layer  as  this  motion  appears 
in  the  unfiltered  flow  maps  (figure  14),  by  filtering,  the  vortical 
characteristics  of  these  structures  are  revealed.  It  is  possible  that  the 
backs  of  these  vortical  structures  comprise  the  shear  layers  described 
by  other  investigators. 

As  observed  in  the  flow  field  maps,  the  temporal  increases  in 
pressure  are  associated  by  ejection  motions,  while  a  drop  in  pressure 
signifies  an  inrush  or  sweep  of  fluid  toward  the  wall.  These  motions 
may  be  associated  with  the  passage  of  counter  rotating  vortical 
structures,  or  alternatively,  the  vortical  structures  could  be  a  product  of 
the  mean  flow  interaction  with  the  ejection/sweep  process.  This 
relationship  cannot  be  determined  from  these  data. 

The  two  flow  fields  shown  in  figure  17  are  the  filter  0  and  filter  3 
averaged  flow  fields  conditionally  sampled  on  filter  3,  positive,  peak 
wall  pressure  events.  The  ensemble  averaged  unfiltered  flow  field  in 
figure  17  is  nearly  identical  to  that  measured  by  Laadhari  etal. 

The  Taylor  plots  clearly  allow  a  much  improved  view  of  the  small 
scale  rolling  vortical  structure  below  the  shear  layer  in  the  unfiltered 
flow  field.  Filtering  the  flow  field  data  reveals  the  small  scale  vortical 
structures  which  are  masked  by  the  large  scale  motions  in  the 
unfiltered  data.  As  many  as  six,  counter-rotating  near-wall  vortical 
structures  can  be  identified  in  the  filter  3  flow  field.  The  wall  pressure 


signature  of  these  motions  also  follows  the  ejection  and  sweep  pattern 
demonstrated  by  the  larger  scale  motions. 

To  further  illustrate  the  correlation  between  large  scale  motions 
and  small  scale,  near-wall  turbulent  activity,  figurp  18  shows  the  filter 
3  average  flow  field  conditionally  sampled  on  filter  2  positive  wall 
pressure  events.  There  are  obvious  regions  of  organized  activity, 
primarily  ejection  and  sweep  type  motions  depicted  in  these  data. 
These  data  confirm  what  was  generally  observed  in  the  wall  pressure 
time  records.  That  is,  not  all  low  frequency  (filter  2)  peak  events  are 
accompanied  by  clusters  of  high  frequency  (filter  3)  activity,  however, 
a  sufficient  number  are  to  produce  the  patterns  shown  in  figure  18. 


Figure  18.  Taylor  plot  of  filter  3  flow  field  conditionally  sampled  on 
filter  2  positive  peak  wall  pressure  events 


70 


VI.  CONCLUSIONS 

The  distinct  features  of  the  “total”  wall  pressure  footprint  of  the 
small  and  large  scale  turbulence  producing  structures  are  not  easily 
defined.  Based  on  the  results  of  this  investigation,  it  is  clear  that  a 
simple  characteristic  signature  of  a  turbulent  producing  structure  is  not 
feasible.  A  hierarchy  of  structures  that  induce  wall  pressure  signatures 
exists  within  and  outside  of  the  boundary  layer,  however,  because  the 
large  and  small  scale  structures  appear  to  convect  together,  the  total 
streamwise  spatial  influence  of  the  large  and  small  scale  motions  are 
comparable. 

Although  dominant  Reynolds  stress  production  has  been  historically 
found  to  occur  near  the  wall,  the  large  scale  structures  across  the 
boundary  layer  associated  with  mid  frequency  wall  pressure  peak 
events  were  shown  to  exhibit  similar  Q2/Q4  motions  and,  more 
importantly,  appear  to  be  coupled  to  the  near  wall  burst  events. 

From  a  turbulence  control  or  drag  reduction  standpoint,  the  results 
of  this  investigation  are  promising.  Since  the  focus  of  any  active 
control  technique  would  most  likely  be  to  affect  the  near-wall,  small 
scale  production  motions,  the  findings  associated  with  these  scales  are 
of  primary  interest.  The  occurrence  of  these  motions  in  clusters  (best 
visible  in  a  filtered  time  record)  indicates  the  advantage  of  a  VITA 
type  detection  criteria.  Since  these  motions  were  also  shown  to  occur 
simultaneously  with  large  scale,  inclined  vortical  structures  or  shear 
layers,  the  possibility  is  raised  of  an  early  warning  mechanism  based  on 
the  detection  of  large  scale  motions.  These  large  scale  motions  were 
successfully  tracked  in  this  investigation  using  conventional  wall 
pressure  transducers. 

VII.  NOMENCLATURE 

Cf  coefficient  of  skin  friction 
d  diameter 

/  function  or  frequency,  Hz 
/s  sampling  frequency 
H  conventional  shape  factor,  570 
Kt  turbulence  kinetic  energy  (ui2+u22+u32)/2 
p  fluctuating  pressure 

Ree  Reynolds  number  based  on  momentum  thickness 
^  viscous  time  scale,  v/u/ 
u  fluctuating  streamwise  velocity 
uT  shear  velocity,  (xw/p)I/2 
U  mean  streamwise  velocity 
Uc  streamwise  convection  velocity 
U0  freestream  velocity 
v  fluctuating  wall-normal  velocity 
V  mean  wall  normal  velocity 

x,y,z  streamwise,  wall-normal  &  transverse  coordinates 
5  boundary  layer  thickness,  where  U=.99U0 

5*  boundary  layer  displacement  thickness 

0  boundary  layer  momentum  thickness 

k  peak-event  detection  threshold  (P/Pms) 
v  kinematic  viscosity 
p  density 

Tw  wall  shear  stress 
co  frequency,  rad/s 

T  time  delay  used  in  correlation  functions 
( )+  quantity  scaled  on  viscous  variables 

VIII.  REFERENCES 

1.  S.K.  Robinson  “Coherent  Motions  in  the  Turbulent  Boundary 
Layer”,  Annu.  Rev .  Fluid  Mech..,  23:601-639,  1991. 

2.  W.  W.  Willmarth  and  S.  S.  Lu,  “Structure  of  the  Reynolds  Stress 
Near  the  Wall”,  J.  Fluid  Mech. ,  55:65-92,  1972. 

3.  T.  Theodorsen,  “Mechanism  of  Turbulence”,  In  Proc.  Midwest  Co 
nf  Fluid  Mech.  2nd,  pages  1-18,  1952. 

4.  W.  W.  Willmarth  and  B.  J.  Tu,  “Structure  of  Turbulence  on  the 

Boundary  Layer  Near  the  Wall”,  Fluids ,  10:134-137,  1967. 

5.  G.  R.  Offen  and  S.  J.  Kline,  “A  Proposed  Model  of  the  Bursting 
Process  in  Turbulent  Boundary  Layers”,  J.  Fluid  Mech.,  70:209-228, 
1975. 

6.  J.  O.  Hinze,  “ Turbulence ”,  McGraw  Hill,  New  York,  1975. 


7.  A.  K.  Praturi  and  R.  S.  Brodkey,  “A  Stereoscopic  Visual  Study  of 
Coherent  Structures  in  a  Turbulent  Shear  Flow”,  J.  Fluid  Mech., 
89:251-272,  1978. 

8.  R.  E.  Falco,  “New  Results,  a  Review  and  Synthesis  of  the 
Mechanism  of  Turbulence  Production  in  Boundary  Layers  and  its 
Modification”,  AIAA  Paper  No.  83-0377,  1983. 

9.  A.  S.  W.  Thomas  and  M.  K.  Bull,  “On  the  Role  of  Wall-Pressure 
Fluctuations  in  Deterministic  Motions  in  the  Turbulent  Boundary 
Layer”,  J.  Fluid  Mech.,  128:283-322,  1983. 

10.  S.  J.  Kline,  “Boudary  Layer  Structure  -  a  Summary”,  In 
Turbulence  Research  -  Joint  AFOSR/ONR  Grantee  and  Contractors 
Meeting,  pages  157-173,  Illinois  Institute  of  Technology,  Fluid 
Dynamics  Research  Center,  1992. 

11.  S.  K.  Robinson,  “Kinematics  of  Turbulent  Boundary  Layer 
Structure”,  Ph.D.  thesis,  Stanford  University,  1990. 

12.  T.  M.  Farabee,  “An  Experimental  Investigation  of  Wall  Pressure 
Fluctuations  Beneath  Non-Equilibrium  Turbulent  Flows”,  Technical 
Report  DTNSRDC-86/047,  1986. 

13.  C.  C.  Karangelen,  “Temporal  and  Spectral  Features  of  Wall 
Pressure  Fluctuations  Beneath  a  Turbulent  Boundary  Layer”,  Ph.D. 
thesis,  The  Catholic  University  of  America,  1991. 

14.  V.  Wilczynski,  “Organized  Turbulent  Structures  and  their  Induced 
Wall  Pressure  Fluctuations”,  Ph.  D.  thesis,  The  Catholic  University  of 
America,  1992. 

15.  A.  V.  Johansson,  J.  Her,  and  J.  H.  Haritonidis,  “On  the  Generation 
of  High- Amplitude  Wall  Pressure  Peaks  in  Turbulent  Boundary  Layers 
and  Spots”,./.  Fluid  Mech.,  175:119-12,  1987. 

16.  G.  Schewe,  “On  the  Structure  and  Resolution  of  Wall-Pressure 
Fluctuations  Associated  with  Turbulent  Boundary  Layer  Flow”,  J.  Fluid 
Mech.,  134:311-328,  1983. 

17.  M.  Kammeyer,  “An  Experimental  Investigation  of  Organized 
Turbulent  Motions  and  Wall-Pressure  Fluctuations  in  Complex  Flows”, 
Ph.D.  theses,  The  Catholic  University  of  America,  1995. 

18.  S.  J.  Russell,  “Wall -Pressure  Signatures  of  Organized  Turbulent 
Motions”,  NSWCCD-TR-97/009,  14  July  1997. 

19.  R.  F.  Blackwelder  and  R.  E.  Kaplan,  “On  the  Wall  Structure  of  the 
Turbulent  Boundary  Layer”,  J.  Fluid  Mech.,  76:89-112,  1976. 

20.  J.  Kim,  “On  the  Structure  of  Pressure  Fluctuations  in  Simulated 
Turbulent  Channel  Flow”,  J.  Fluid  Mech.,  205:421-451,  1989. 

21.  F.  Laadhari,  R.  Morel,  and  E.  Alcaraz,  “Combined  Visualization 
and  Measurements  in  Transitional  Boundary  Layers”,  Eur.  J.  Mech., 
B/Fluids ,  13  No.  4:473-489,  1994. 


71 


STREAMFUNCTION  -  VORTICITY  CALCULATIONS  OF  NAVIER-STOKES 
EQUATIONS  AS  A  TOOL  FOR  HIGH  ACCURACY  STUDY 
OF  PRESSURE  -TENSION  RELATION 


Mickael  N.  Zakharenkov 
Central  Aero-Hydrodynamic  Institute 
140160  Zhukovsky,  Moscow  region,  Russia 
Fax:(095)5564337 


Abstract  -  This  paper  considers  the  problems  of  streamfunction  -vorticity  formulation  of  Navier-Stokes 
equations.  This  is  shown  that  the  boundary  condition  for  vorticity  which  had  been  assessed  many  authors  as 
“artifical”  boundary  condition  is  really  a  total  combination  of  the  no-slip  boundary  conditions  (b.c.).  and  some 
differential  conditions  outcoming  from  a  continuation  of  governing  equations  onto  the  boundary.  This 
conditions  are  necessary  for  all  high  accuracy  numerical  algorithms.  Two-parameters  approximating  formula 
for  the  boundary  vorticity  is  described  and  containes  the  parameter  optimizing  the  calculations.  The  no-slip  and 
slip-boundary  conditions  on  the  wall  are  in  the  problem  statement.  The  pressure  uniqueness  condition  is 
incorporated  into  proposed  algorithm.  The  formulation  of  necessary  boundary  differential  conditions  is 
spreaded  to  velocity-pressure  form  of  N-S  eqs.  The  influence  of  multidipole  far  field  flow  asimptotic  on  the 
viscous  flow  around  an  airfoil  is  considered.  The  thermodynamically  closed  boundary  condition  on  the  trailing 
edge  of  an  airfoil  is  discussed  in  connection  with  such  phenomena  as  a  surface  vorticity  waves, 
vortex/momentum/heat  spots  generation. 


1.  INTRODUCTION 

The  problem  of  accuracy  study  of  pressure-tension  relation  have 
the  fundamental  significans  in  the  theory  of  moving  bodies  and  closely 
related  with  the  problems  of  drag  reduction.  We  can  take  as  an  example 
the  known  Stokes  law  formulated  as  the  relation  between  the  tangential 
velocity  on  the  body  and  stress  tensor  [1]: 

^Vx‘=jTs‘  (1) 

where  Vx*.  is  a  tangential  velocity  vector  on  the  wall  s  ,  j  is  the  unit 
vector  in  the  direction  of  Vt‘,  ts  is  the  component  of  wall-shear  stress 
in  the  direction  of Vx\  X  is  the  slip  coefficient. 

This  relation  corresponds  to  no-slip  boundary  condition  for  X  ~  ao 
,  the  perfect  slip  relalizes  at  X  =  0,  and  the  slip  occures  at  0  <  X  <  oo 
.The  discussion  of  physical  and  theoretical  reasons  for  condition  (1)  is 
in  [1].  The  cases  of  new  rheological  laws  when  the  polymers  (or  some 
pollutions)  are  inserted  into  the  thin  layer  near  the  body  (for  drag 
reduction  purposes)  can  be  formulated  in  the  similar  form.  We  must 
note,  that  even  for  high  speed  flows  the  slip  condition  is  a  basic  law  for 
the  boundary  conditions  formulation  [2,  3].  On  this  reason  the  study  of 
the  viscous  flow  with  the  boundary  condition  (1)  have  the  wide 
application  and  may  be  easily  continued  onto  a  more  complex  flows. 

The  numerical  realization  of  the  law  (1)  proposed  by  Lugt  et  al.  [1] 
and  formulated  in  a  more  common  form  in  Section  4  of  this  paper  shows 
that  the  right  connection  of  wall-shear  stress  on  the  body  surface  with 
the  boundary  vorticity  (vortex  in  3-D  case)  defines  the  high  demands  to 
the  vorticity  calculations.  Consequently,  the  usage  of  vorticity  as  a  basic 
term  in  N-S  equations  formulation  is  very  desirable.  On  the  contrary,  the 
veloicity-pressure  formulation  must  be  complicated  by  some  differential 
conditions  which  are  necessary  for  thoroughly  approximation  of  law  (1) 
on  the  surface. 

The  boundary  condition  for  the  pressure  on  the  wall  is  the  second 
known  “artifical”  boundary  condition  as  well  as  a  boundary  vorticity 
condition  [4,  5].  These  condition  is  commonly  derived  as  a  consequence 
of  continuation  of  momentum  equations  onto  the  boundary.  This  had 
been  shown  by  Zakharenkov  [6]  that  the  pressure  boundary  condition  in 
a  numerical  formulation  is  completly  analogous  to  the  vorticity 
condition. 

In  other  hand,  we  have  the  necessity  to  know  both  the  pressure  and 
vorticity  on  the  wall  because  the  integral  characteristics:  drag,  lift, 
moment  of  force  -  are  in  interest  for  practice.  In  such  situation  we  have 
not  doubts  that  if  the  mentioned  above  boundary  conditions  are  well 
posed  then  we  must  employ  them  in  the  process  of  solution  of  N-S  eqs. 
formulated  in  any  form,  at  least  at  the  final  stage  of  boundary  vorticity 
and  pressure  calculations.  Moreover,  we  must  study  is  it  possible  to 


employ  the  solution  where  this  conditions  are  not  incorporated  into  a 
numerical  algorithm.  As  a  common  case  the  problem  of  high  accuracy 
study  of  pressure-vorticity  relations  on  the  wall  is  formulated. 

2.  PROBLEM  STATEMENT 

For  viscous  incompressible  flow  the  problem  statement  is 
wellknown  and  is  described  elsewhere.  The  usage  of  integrating 
function  for  continuity  equation  fulfillment  is  recomendated  by  theory 
because  this  allows  us  to  eliminate  this  equation  from  numerical 
solution.  Let  us  introduce  stream  function  'F  and  vorticity  Q  by 
relations 

V5  =  -H-'  d'i’/dn  ,  V„=  H"1  d'VIdl  , 
n  =  H-2[-d(HV5)/  an  +  a(Hvn)/  a?]  (2) 

where  H2=  (dxISQ1  +  (dy/dQ2  is  the  Jacobian  of  transformation  from 
Cartesian  coordinate  (x,  y)  to  curvilinear  orthogonal  coordinates  (£,  r|). 
The  coordinate  r|  is  a  cyclic  one,  and  £  is  orthogonal  to  the  body  and  r| 
coordinate;  and  Vn  are  the  velocity  components  in  (£,  rj). 
coordinates. 

Introduction  of  stream  function  fulfilles  the  continuity  equation 
and  (2)  gives  us  the  relation 

A'F  =  H2fi  (3) 

where  A  is  the  Laplace  operator. 

The  Navier-Stokes  equations  in  Gromeka-Lamb  form  are 

5p/a^=  Re-'an/cbi-50f/5t)/ari-5(V2/2)/S4+Oa^/5^  (4.1) 

dp/d<]=  -Re-|3n/3q+amat)/S4-S(V2/2)/ar|+n3'J'/OT|  (4.2) 

where  Re  =  Ua>  c/v,  U*,  is  the  freesteream  velocity,  c  is  the  airfoil 
chord,  v  is  the  coefficient  of  kinematic  viscosity. 

The  known  transformations  of  eq.  (4)  lead  to  vorticity  transport 
equation 

H2  5CllQl+8'VI&c\dClldird'Vldi1dClldr\  =  Re"1  AO  (5) 

and  Poisson  equation  for  the  pressure 

a(p+v2/2)  =  ao/ai;9¥/ai;+ao/^94'/an+H2n2  (6) 


©  Michael  N.Zakharenkov  2  April  1998 


73 


The  boundary  conditions  on  the  wall  s  will  be  formulated  for 
common  law  (1)  in  the  Section  4.  Hear,  the  case  of  no-slip  condition 
gives 

V4  =  -H-'  ffVId n  =  0  ,  Vr,  =  H'1  ffVld%  =  0  (7) 

The  far-field  flow  asimptotic  is  used  for  the  numerical  formulation 
of  boundary  conditions  on  the  outer  boundary  s»  of  computational 
domain  (the  “0”  type  mesh  is  considered  which  is  obtained  by  mapping 
of  an  airfoil  onto  the  circle 

&V/3E,  =  dx/d^sma  -  ay/a^cosa  -  Raf1!  Dx!  sin(r|-a)  + 

5 

+  Dy*  cos(q-a)]  +  X  Dxk  sin  k(q-a)  + 

k=2 

5 

+  X  Dym  cos  m(r|-a)  -  Tl2n  +  ...  (8) 

m= 2 


dQ/d^  =  0  (9) 

where  a  is  the  angle  of  attack,  Dxk,  Dym  are  intensities  of  multidipole 
terms,  T  is  the  velocity  circulation  around  an  airfoil  at  a  large  distance 
(on  Soo)  from  it,  R*  is  the  radius  of  a  circle  in  a  mapped  plane.  The 
source  terms  are  included  into  (8)  too,  but  are  omitted  here  because  the 
study  presented  below  is  restricted  by  given  form  (8)  only. 

The  initial  condition  are  follows.  The  body  and  fluid  are  in  the 

rest. 

y(0,x,y)=n(0,x,y)  =  0  (10) 

The  study  of  abrupt  start  of  the  body  and  slowly  start  of  the  body 
in  fluid  had  been  considered  in  [7,8].  This  study  shows  that  the  flow 
characteristics  are  the  same  in  a  both  cases  after  a  some  short  time 
period  after  start.  On  this  reason  there  are  not  considered  the  cases  of 
initial  conditions  with  the  given  vortex  sheet  on  the  airfoil  at  the  start 
which  is  recomendated  by  Ghia  et  al.  [9]. 

3.  NUMERICAL  ALGORITHM 

The  widespread  numerical  code  is  employed  for  solution  of 
eqs.(2),  (3),  (5)  with  boundary  conditions  (7)-(9).  The  ADI  method  [10] 
is  used  for  solution  of  eq.(5)  and  the  direct  method  [11]  is  used  for 
solution  of  eq.(3).  The  last  method  employes  the  expansion  into  a 
trigonometrical  polynom  in  coordinate  q,  Fast  Fourier  Transformation 
and  Thomas  algorithm.  The  method  of  solution  of  decoupled  equations 
(3),  (5)  is  very  suitable  in  this  case,  because  the  eq.(3)  is  solved  exactly 
and  this  allow  us  to  eliminate  the  distortions  in  stream-function 
calculation  which  are  very  dangerous  to  the  main  idea  of  introduction  of 
the  stream  function:  the  continuity  equation  must  be  fulfilled  exactly. 
Any  error  in  stream  function  calculation  leds  to  violation  of  continuity 
equation  and  as  it  will  be  shown  below  to  hardly  assessing  errors  in  a 
vorti city-pressure  relation  on  the  wall. 

The  second  derivatives  in  (3),  (5)  and  the  velocity  components  in 
(5)  are  approximated  by  central  differences.  The  one-sided  upwind 
differences  approximate  the  first  vorticity  derivatives  in  (5),  for  example 

d[(W/^)Q]/dq[j  ={3(aT//^)jQj+[3(aH//a^)j+]+ 

(d'¥/dZ)i]ci}  +i  -  (a^)J+inj+2}/2hn  (1 1) 

The  approximation  (11)  is  near  to  proposed  in  [12]  which  reveals 
the  property  of  enstrophy  coservation  in  the  flow. 

The  boundary  condition  %  =  0  (V$|s  =  0)  and  (8)  are  used  for 
solution  of  eq.(3).  The  given  velocity  (or  relation  (1)  on  the  wall)  and  (9) 
are  used  as  a  boundary  condition  for  eq.(5). 

The  iteration  process  couples  eqs.(3)  and  (5)  into  the  system  and 
simultaneously  solves  thoroughly  the  vorticity-pressure  relations  on  the 
wall  which  will  be  described  in  the  next  Section. 


4.  VORTICITY-PRESSURE  RELATIONS  ON  THE  WALL 

Let  us  consider  the  law  (1)  as  a  some  relation  known  from 
practice.  Then,  follow  to  Lugt  et  al.  [1]  we  can  write  the  expression  to 
the  vorticity  and  shear  stress 

n  =  H‘2[-3(HV^)/  dr\  +  3(HV„)/o?]  =  H'2A^  (12) 

x  =  3(V4/H)/3Ti  +  3(Vn/Hy^  (13) 

where  T=(c/pU«)T  ,  p  is  the  coefficient  of  dynamic  viscosity. 

Taking  into  account  relation  (2)  and  condition  V^|s  =  0  we  rewrite 
eq.(l)  as 

X.V„  =  3(H  ^dV/dQ/dli  (14) 

or,  taking  into  consideration  (12) 

XK 1  dTO^|s=94Vd^|5a(l  /H2)/c)^+n  (15) 

The  known  two-parameter  fomula  for  condition  &VI8 ^|s  =  H\VS 
is  described  in  [6,8,13]  and  has  the  form 

3 

HVrJs  =  5vF/3^|s  =  -H2EQs  +  h5‘2  E  1^  + 

j=° 

+  h5(2h^  -a)/3 !  33T'/^3|s+2h52(6h5  -P)/4!  d4^4  + ...  |(1 6) 

where  E=(6a-p)/22  is  the  Tarunin’  parameter,  Kj  are  defined  by 
expressions  in  [6,  8,  13],  a  and  p  are  parameters  (we  do  not  change  the 
original  notation  a  in  (16)  because  it  is  difficult  to  mix  this  parameter 
with  the  angle  of  attack  introduced  in  eq.(8)). 

After  some  transformations  we  obtain  the  formula  for  boundary 
vorticity 

3 

{H2E+[7.H-1-S(l/H2)/a4]'1}ns=  h5‘2  E  K^-H  (17) 

j= 0 

+  h5(2h5-ot)/3!  a3'F/943|s+2h52(6h5-P)/4!  94'f/5^4,+  ... 
and  for  tangential  velocity  on  the  body 

vn|s=  ns[x  +  H-3aH2/ay'  (18) 

Finally,  the  derivative  93'F/9^3 |s  in  (17)  must  be  expressed  as 

dV^3  is  =  3(H2Q)/9£|s  -  32(HVn)/3ti2|s  (19) 

where  3(H2Q)/3^|S  =  (-3H2S  Qs  +4H2,n,  -  H22n2)/2h» 

For  given  value  of  slip  coefficient  X  the  formulae  (17)-(19)  allow 
us  to  calculate  vorticity  and  tangential  velocity  on  the  surface  of  a  flown 
body.  The  pressure  on  the  wall  can  be  calculated  from  eqs.(4)  when  the 
¥  and  Q  are  known.  This  was  shown  by  Zakharenkov  [14,  16]  that 
two  pressure  distribution  on  the  s  ,  the  first  one  obtained  by  integrating 
eq.(4.1)  from  s  to  s®  and  the  second  one  obtained  by  integration  eq.(4.2) 
along  s  may  not  be  in  concidence  for  a  common  solution  of  eqs.(3),(5). 
On  this  reason  the  corrector  stage  of  algorithm  consists  in  the 
calculation  of  po  from  (4.1)  and  in  the  usage  of  expression  (k  is  the 
index  of  iterations): 

SO/34k+1  |s=(-3nks+40k+ 1 1 -nk+  '2)/2l^  = 

Re[-3po/3r|  +  3(34V5^k/a  -  3(V25/2)k/9n]|s  (20) 

(obtained  from  (4.2))  as  the  boundary  condition  for  eq.(5).The 
alternating  predictor-corrector  iterations  calculate  the  (17)-(19)  and  use 
(17)  as  a  b.c.  for  eq.(5)  at  the  first  stage,  and  calculate  (17), (18), (20)  and 
use  (20)  as  a  b.c.  for  eq.(5)  at  the  second  stage.  The  six-eight  iterations 
are  sufficient.  The  convergence  of  procedure  is  shown  by  Zakharenkov 


74 


[15].  This  algorithm  ensures  the  pressure  uniqueness  on  the  wall.  The 
pressure  uniqueness  n  the  flow  field  may  be  controlled  by  integrating 
eqs.(4)  and  by  comparision  of  po  from  (4.1)  and  pi  from  (4.2)  on  the 
coordinate  lines  %  -  £i. 

The  vorticity  dissipation  in  the  wake  is  the  next  dangerous 
phenomenon  which  can  desturbs  the  pressure  field.  This  problems  is 
solved  analogously  to  SIMPLE  procedure  for  pressure  correction.  The 
dissipating  vorticity  may  be  reconstracted  at  a  mesh  nodes  in  the  far 
wake  due  to  the  two  rules.  This  stage  of  corrector  algorithm  consists,  in 
the  first,  the  pressure  uniqueness  on  coordinate  lines  £  =  £i.  is  verified, 
in  the  second,  the  integral  law  of  vorticity  conservation  in  the  flowfield 
leds  to  condition  that  the  integral  of  vorticity  along  line  £  =  £j.  conserves 
its  value  in  far  wake  flow  (for  all  j  >jo)  for  positive  and  negative 
vorticity  separately  (condition  of  vorticity  neutralitty  in  the  steady  wake 
flow).  This  algorithm  ensures  that  the  pressure  compatibility  condition, 
see  [16],  is  really  fulfilled.  In  this  procedure  the  N-S  eqs.  in  form  (4)  are 
solved  correctly.  Therefore,  the  eq.(6)  which  is  derivative  form  of  eq.(4) 
will  be  fulfilled  automatically  if  we  carry  out  properly  the  differentiation 
of  eq.(4). 

The  last  remark  touch  upon  the  problem  of  pressure  boundary 
condition  on  the  wall.  The  eq.(6)  is  often  used  instead  of  continuity 
equation  (taking  into  account  that  the  continuity  equation  is  used  for 
simplification  of  eq.(6)  after  differentiation  of  eq.(4)).  But  this 
procedure  rises  the  issue  is  the  continuity  equation  ensured  really?  This 
problem  may  be  solved  directly  by  properly  formulation  of  pressure 
boundary  condition,  see  [6],  which  is  necessary  for  solution  of  eq.(6). 
The  final  form  of  this  condition  (for  no-slip  case)  is 

3 

0  =  5V^  =  -H2Ea2V^2|s  +  h4-2  E  Kj(V5)j  +  0(h25)  = 

j= o 

3 

-H2ERe(dp/dQ|s+V2  Z  Kj(V?)j  +  0(h25)  (21) 

j= 0 

The  relation  (21)  incorporates  the  next  conditions:  (i)  continuity 
equation  is  hold  on  the  wall  (this  is  correct  procedure  if  we  admit  the 
differentiation  of  (4)  and  any  kind  of  discretization  of  governing 
equations);  (ii)  the  continuation  of  momentum  equation  onto  the  wall. 
The  parametrization  of  (21)  is  attained  analogously  to  vorticity 
boundary  condition  [13]. 

In  such  a  way  we  must  solve  the  known  momentum  equations  and 
eq.(6)  (if  the  velocity-pressure  form  of  N-S  eqs.  is  used),  with  b.c.  (21) 
and  carry  out  the  pressure  correction  in  the  wake.  For  stream-function 
and  vorticity  form  of  N-S  eqs.  we  solve  the  vorticity  transport  eq.(5),  the 
eq.(3),  satisfy  b.c.(17)-(19),  corrects  solution  by  employing  (20)  as  a 
b.c.  for  eq.(5),  and  reconstruct  vorticity  in  the  far  wake  flow  (if  its 
necessary,  see  Section  5).  This  two  approaches  are  similar.  I  find  the 
advantage  in  the  stream-function  and  vorticity  formulation  because  the 
continuity  equation  is  fulfilled  exactly,  the  second  order  approximation 
for  vorticity  is  achived  by  employing  of  simple  finite-difference  scheme. 
The  same  level  of  solution  accuracy  demands  the  third  (fourth-)  order 
approximation  of  governing  equation  in  the  velocity-pressure 
formulation. 

5.  RESULTS  OF  CALCULATIONS 

Three  groups  of  results  may  be  distinguished  for  viscous 
incompressible  flow  around  an  airfoil/body.  The  first  ones  are  classic 
and  directed  to  verification  of  algorithm  and  to  study  of  basic  properties 
of  the  viscous  flow  around  a  body.  The  second  ones  deal  with  the  new 
physical  phenomena  which  are  revealed  by  analysis  of  computational 
results.  The  third  group  of  results  is  pointed  out  for  assessment  of 
correctness  of  problem  statement  and  for  study  of  the  problem  to  what 
extend  the  model  of  incompressible  medium  is  equivalent  to  a  problems 
under  study? 

The  volume  of  a  single  paper  does  not  sufficient  for  complete 
description  of  all  results  from  this  list.  On  this  reason  the  presentation  of 
results  from  the  first  group  are  limited  by  a  few  examples.  The  mesh 
used  in  calculations  have  128  or  256  nodes  in  ^-coordinate  and  80  or 


400  nodes  in  £  -coordinate.  The  outer  region  is  on  the  ten  (or  more) 
airfoil  chords.  The  mesh  is  compressed  to  an  airfoil  by  the 
transformation  £=d  tg(7t$/2)  where  d=0.5  for  N^=80  and  d=0.25  for 
N^=400.  The  first  mesh  will  be  mentioned  as  a  normal  mesh  and  the 
second  one  as  a  fine  mesh.  The  flow  around  airfoil  NACA0012  is 
studied. 

In  Fig.  1  the  pressure  coefficient  Cp  -  -  (p-po)/0.5pUoo  and  surface 
vorticity  are  presented  for  the  flow  at  Re=l  0,000,  a=5°  (no-slip 

boundary  conditions),  the  normal  mesh,  the  predictor-corrector 
algorithm.  The  Dxk  =  Dym  =  0  and  the  Fig.  la,  b,  c  corresponds  to  the 
values  of  circulation  T  are  equal  to  0,  -0.21,  -0.4.  This  results  show  that 
a  pressure  uniqueness  on  the  wall  is  fulfilled  (the  solid  line  corresponds 
to  pi  and  the  dotted  line  corresponds  to  po).  This  is  essential  that 
solution  at  T=  0  exists.  The  airfoil  lift  L  at  P=  0  is  equal  nearly  to  Lp/2 
(see  [14]),  where  Lp  is  the  value  of  lift  obtained  for  a  potential  ideal  flow 
at  a=5°.  The  maximum  of  lift  obtained  in  [14]  is  attained  at  F=  -  0.21 
and  is  equal  to  Cl-L/_0.5pU2oo  =  0.55  (when  the  predictor  stage  of  Qs 
calculation  had  been  used  only).  This  value  of  lift  is  near  to 
experimental  result  [17].  The  lift  calculated  for  p0  in  this  case  is  equal  to 
0.49.  The  predictor-corrector  algorithm  singles  out  the  lift  value  equals 
0.49  for  a  given  value  of  T=-0.21. 

The  problem  of  lift  maximum  is  very  complex.  The  results  of 
Huang  et  al.  [18]  show  that  the  lift  may  be  significantly  larger  if  the 
single  vortex  is  posed  near  the  airfoil  in  diffusor  part  at  leeward  side  of 
an  airfoil.  There  are  the  lines  of  equilibrium  positions  of  centre  of  this 
single  vortex.  This  vortex  can  exist  due  to  a  flow  separation.  The 
computational  simulation  in  viscous  incompressible  flow  confirms  the 
possibility  of  such  flow  at  Re=l 0,000,  a=5°,  Dy1;=4,  see  [19,  20,  21]. 
The  lift  is  increased  significantly.  The  problem  of  an  aerodynamical 
hysteresis  arises  in  this  connection,  see  [22]. 

The  second  group  of  results  is  presented  by  the  study  of  surface 
vorticity  waves.  In  Fig.  2  the  relative  surface  vorticity  (the  relative 
vorticity  is  defined  as  a  difference  between  vorticity  at  two  time 
moments  tl  and  t2)  is  shown  for  tl-t2=0.1,  Re=10,000,  a=5°.  The 
vorticity  waves  are  bom  at  the  leading  edge,  move  to  separation  point  at 
leeward  side  of  an  airfoil,  intensify  in  separation  region  and  greatly 
grow  in  the  region  near  a  trailing  edge  (TE).  At  windward  side  of  an 
airfoil  the  vorticity  waves  move  to  a  trailing  edge  and  amplify  at  a  small 
region  near  TE.  Two  vorticity  waves  having  a  different  sign  of  vorticity 
run  into  each  other  at  the  TE  (theangle  of  TE  is  not  zero  for  NACA0012 
airfoil).  This  process  boms  the  large  pressure  impulse  in  incompressible 
flow  at  the  TE.  The  point  of  zero  vorticity  oscillates  in  the  region  of  two 
neighbouring  mesh  nodes  on  an  airfoil  surface  (one  of  this  nodes 
consides  with  TE).  The  flow  is  locally  unsteady.  We  discuss  the  possible 
temperature  process  at  this  region  in  Section  6  and  substantiate  the 
realty  of  unsteady  behavior  of  the  flow  in  this  phenomenon. 

The  multidipole  asymptotic  used  in  (8)  as  a  far  boundary  condition 
for  the  velocity  plays  a  decisive  role  in  a  number  of  critical  physical 
processes  near  an  airfoil  in  the  stream  [22].  We  can  consider  the 
perturbation  of  upcoming  flow  (or  surrounding  flow)  as  the  perturbation 
of  coefficients  at  multidipole  terms  in  (8).  This  problem  had  been 
considered  by  Zakharenkov  in  [21].  The  predictor  stage  only  had  been 
employed  in  [21].  This  is  done  because  the  problem  of  pressure 
uniqueness  is  related  with  the  assignment  of  far  field  boundary 
condition,  see  Badr  et  al.  [23].  This  had  been  shown  in  [21]  that  for 
NACA0012  airfoil  at  Re=l 0,000  and  a=5°  the  pressure  uniqueness  on 
the  wall  cannot  be  achieved  by  variation  of  parameters  of  (8).  On  this 
reason  the  errors  in  calculation  of  pressure-vorticity  relation  on  the 
airfoil  are  picked  out  as  a  main  reason.  The  employment  of  predictor- 
corrector  algorithm  eliminates  this  errors  and  results  presented  in  [21] 
are  verified  because  the  pressure  distributions  corresponding  to  po  are 
conserved.  In  Fig.  3a,  b,  c  the  pressure  distribution  and  in  Fig.  3d,e,f 
the  surface  vorticity  which  correspond  to  the  flow  patterns  in  Fig.  4 
(Fig.4a,  b,  c  are  streamlines,  d,  e,  f  are  the  lines  of  equal  values  of 
vorticity)  are  shown  for  the  variation  of  a  single  dipole  term  in  (8):  Fig. 
3a)  Dyl=  4,  b)  Dx2  =  78,  c)  Dy2^  -64.  For  the  case  Dy1=4  the  results 
corresponds  to  predictor-corrector  algorithm  calculations.  The  variation 
of  this  coefficients  only  changes  the  flow  pattern  significantly. 
Variation  of  Dyl  and  Dx2<0  coefficients  provokes  the  strong 
separation.  Variation  of  Dx2>0  coefficient  moves  the  separation  point 
on  the  airfoil  toward  TE  and  conserves  the  form  of  flow  separation 


75 


which  can  be  characterized  as  a  weak  separation.  Variation  of  Dy2  term 
effects  the  width  and  thickness  of  separation  zone  and  suppress  the 
fluctuation  of  vorticity  field  near  the  trailing  edge.  In  connection  with  a 
surface  vorticity  waves  generation  we  can  conclude  that  the  presence  of 
Dy2  dipole  field  suppress  the  amplification  of  vorticity  waves. 

The  effectivness  of  predictor-corrector  algorithm  for  calculation 
of  unsteady  flow  at  Re=  10,000  is  shown  in  [15]  and  is  confirmed  herein 
by  presentation  of  the  pressure  coefficient  in  Fig.  3a  for  Dy1=4.  The 
next  example  is  in  Fig.  5,  where  a,b)  presents  the  pressure  coefficient 
and  c,d)  is  the  surface  vorticity  at  Re=l,000,  a=5°,  Dy1=24  for  two  time 
moments  tl  =39.25,  t2=42.25.  The  streamlines  and  lines  of  equal  values 
of  vorticity  are  presented  on  Fig.  6a,  b  and  Fig.  6c,  d  correspondingly. 
The  massive  flow  separation  is  visible  in  Fig.6.  The  uniqueness  of 
pressure  distribution  along  an  airfoil  is  correctly  fulfilled. 

The  unsteady  flow  in  the  region  of  TE  can  be  characterized  by 
formation  of  vortex  spots,  see  [24,  25],  The  running  one  into  another  of 
two  surface  vorticity  waves  (see  Fig. 2)  is  the  reason  of  oscillation  of 
point  of  zero  vorticity.  This  process  leds  to  complex  phenomenon  which 
shaw  itself  in  the  vorticity  field.  The  new  vortex  patterns  which  are 
intermediate  between  vortex  waves  and  a  vorticies  are  generated.  This 
vortex  patterns  are  shown  for  Re=30,000  and  a=0  at  Fig.  7  where  the 
lines  of  equal  relative  vorticity  are  shown  for  tl-t2=0.06  .  The  fine  mesh 
is  used  for  calculations  at  Re=30,000.  The  correspondence  between  a 
trailing  edge  vortex  spots  generation  and  fluctuations  of  lift  and  drag 
coefficients  is  picked  out  in  [24,  25].  For  zero  angle  of  attack  this 
correspondence  is  conserving  and  may  be  interpritated  as  a  periodical 
drag  accumulation  which  leds  to  the  shedding  of  vortex  spots. 

The  influence  of  slip-condition  on  the  viscous  flow  characteristics 
is  interested  as  a  process  of  possible  drag  reduction.  Simultaneously  we 
obtaine  an  interesting  case  of  the  flow  in  vicinity  of  TE.  If  we  take  into 
account  that  vorticity  at  the  TE  (or  near  TE)  must  be  zero  and  look  on 
the  formulae  (17),(18),  then  we  can  conclude  that  the  tangential  velocity 
at  the  TE  is  zero  even  for  slip-condition.  In  this  case  the  increase  of 
friction  in  the  inner  layers  of  the  viscous  flow  near  the  trailing  edge  is 
possible  because  the  friction  about  the  surface  is  reduced  and  the  last 
one  may  be  unsufficient  to  establish  the  tangential  velocity  to  be  a  zero 
at  the  TE.  In  Fig.  8  the  pressure,  tangential  velocity  and  vorticity 
distribution  along  the  airfoil  are  presented  for  the  flow  at  Re=l 0,000, 
a=5°,  >.=3,000  (T=-0.21).  The  streamlines  and  the  lines  of  equal 
vorticity  are  shown  in  Fig.9.  The  drag  coefficient  component  due  to 
pressure  Cdp  and  one  due  to  friction  CDf  for  no-slip  condition  are  equal 
to  3.4794*10-2  and  2.7247*10-2  correspondingly.  For  slip  condition  at 
>.=3.000  this  components  are  equal  to  4.0883*10-2  and  2.6748*10-2 
correspondingly.  The  fluctuations  of  CD  are  conserving.  The  slip  along 
the  surface  decreases  the  friction  drag  and  increases  the  pressure  drag 
components.  The  perfect  slip  at  A,=0  is  attainable  for  a  small  Reynolds 
number  only  (Re=200  in  [1]).  This  is  because  the  surface  vorticity 
grows  essentially  with  Re  increasing,  and  the  tangential  velocity  (related 
with  surface  vorticity  by  expression  (18))  achieves  a  too  large  values. 

6.  DISCUSSION 

The  results  presented  in  a  previous  Section  show  the  wide 
possibilities  for  the  study  of  different  complex  flows  around  a  body  at 
Reynolds  number  up  100,000.  But  the  number  of  complex  phenomena 
in  the  regions  of  leading  and  trailing  edges  of  the  body  initiates  us  to 
improve  the  problem  statement.The  refined  problem  statement  includes 
the  study  of  heat  process  in  a  boundary  layer  and  a  possible  viscous- 
temperature  dependence.  We  can  write  the  heat  transport  equation  in  the 
form 

DT/Dt  =  1/Pr  !/Re  AT  +  Ec  1/Re  O  (22) 

where  T  is  temperature,  Pr  is  the  Prandtl  number,  Ec  is  the  Eckert 
number  and  the  dissipation  function  d>  takes  the  form,  see  [26] 

0=  2(a2vF/3x3y)2  +  (O- 2d24Vdx2)2  (23) 

The  number  of  boundary  conditions  for  eq.(22)  on  a  wall  are 
possible.  The  continuation  of  eq.  (22)  onto  the  wall  can  not  be  employed 
for  every  kind  of  boundary  conditions.  But  we  can  consider  such 
continuation  as  a  special  b.c.  when  we  have  not  the  confidence  in  any 


other  relation  on  a  wall.  Then  for  a  steady  flow  (at  a  no-slip  conditions) 
we  obtaine  on  the  wall  y=0  the  relation 

1/Pr  l /Re  AT  +  Ec  1/Re  (H20S)2  =  0  (24) 

which  at  the  points  where  Qs=0  simplifies  to  AT=0.  This  is  essential 
that  the  last  relation  is  hold  for  a  very  small  region  near  the  TE  on  the 
centreline  (c.l.)  of  the  wake  where  D.  =  0. 

This  means  that  near  the  trailing  edge  where  a  convective  heat 
transfer  and  vorticity  are  equal  to  zero  the  realization  of  (24)  demands 
for  a  “O”  type  computational  mesh  the  fulfillment  of  condition 

s2T/an2|uppers,c.i  .=  32T/an2l'0W£Vi.  (25) 

The  eq.  (25)  is  additional  differential  relation  which  must  be 
fulfilled  in  computations.  But  this  relation  may  be  a  great  restrictive  (see 
discussion  of  analogous  problem  for  a  boundary  vorticity  at  the  vertex 
in  [4]).  For  example,  the  process  of  running  one  into  another  of  two 
surface  vorticity  waves  (while  such  processes  is  initiated  by  any  way) 
leds  to  a  large  growth  of  local  friction  on  the  surface  and  to  a 
corresponding  growth  of  heat.  This  is  preferably  to  suppose  that  the  heat 
transfer  in  the  region  of  TE  is  unsteady  in  this  case.  The  similar  analysis 
is  correct  for  a  boundary  vorticity.  There  are  not  an  evident  physical 
mechanism  which  stabilizes  the  flow  in  the  region  of  TE  if  any 
perturbation  initiates  the  spots  generation. 

The  heat  transfer  from  TE  should  be  essentially  easy  if  the 
tangential  velocity  at  the  TE  is  not  zero  *then  the  convective  transfer  is 
possible(.  We  can  consider  as  an  example  of  such  boundary  condu.on 
the  slip-condition  obtained  for  large  velocity  in  [2] 

ux(x,  0)  =  f(T)(Adu/3y|s  +  B(p(T)3  InT/dx)  (26) 

where  f(t)  cp(t)  are  known  functions  on  temperature,  A  and  B  are  some 
constants  defined  in  [2]  and  others  papers. 

This  relation  admits  the  non-zero  tangential  velocity  at  the  TE 
even  at  zero  value  of  vorticity  (  du/dy|s  =  0).  Moreover,  the  tangential 
velocity  may  be  different  if  we  consider  the  limits  upon  upper  and  lower 
surface  of  an  airfoil.  The  uniqueness  of  tangential  velocity  at  the  TE 
puts  the  additional  condition  which  may  be  employed  for  example  for 
the  determination  of  velocity  circulation  around  an  airfoil.  The  necessity 
to  take  into  account  the  viscosity-temperature  dependence  become 
evident 

The  theoretical  and  computational  results  show  the  wide 
possibilities  for  application  of  proposed  numerical  algorithm  to  the 
problem  of  drag  reduction.  The  new  rheological  laws  may  be  easily 
incorporated  into  the  problem  statement  including  the  boundary 
conditions  on  the  wall.  The  inclusion  of  heat  calculation  and  viscosity- 
temperature  dependence  which  are  conducted  in  a  present  time  supposes 
a  more  realistic  computational  results. 

The  inclusion  of  any  additional  turbulence  model  is  practicable. 
The  correct  pressure-vorticity  relations  on  the  body  surface  is  the  most 
attractive  property  of  proposed  approach  for  solution  of  Navier-Stokes 
equations. 

REFERENCES 

1.  H.J.Lugt  and  S.Ohring  “Laminar  flow  behavior  under  slip¬ 
boundary  conditions,”  The  Physics  of  Fluids,  Vol.18,  No.l,  January, 
pp.1-8,  1975. 

2.  M.N. Kogan  “The  dynamics  of  rarefied  gas,”  Moscow:  ”Nauka”, 
1967  (in  Russian). 

3.  M.A.Reynolds,  J.J.Smolderen  “Profile  measurements  in  the 
Knudsen  layer  for  the  Kramers  problem,”  for  Karman  an  Institute  for 
fluids  Dynamics,  1974. 

4.  PJ.Roach  “Computational  Fluid  Dynamics,”  Hermosa  publishers, 
Albuquerque,  NM,  1976. 

5.  S.Sundaresan  and  S.M.Deshpander  “On  pressure  compatibility 
condition  in  numerical  simulation  of  incompressible  viscous  flows 
using  primitive  variable  formulation,”  In  Book  of  Briefs  1st 
International  Conference  on  Numercical  Methods  in  Fluid  Dynamics, 
June  24-28,  1996,  Monterey,  California,  pp.  118-119,  1996. 


76 


6.  M.N.Zakharenkov  “Singularities  of  finite-difference  scheme  for 
two-dimensional  Navier-Stokes  equations  solution  connected  with  the 
boundary  conditions  statement  on  a  solid  surface”,  Zumal 
Vychislitel’noj  Matematiki  i  Matematicheskoj  Fiziki,  30,  8,  1224- 
1236,  1990  (in  Russian). 

7.  H.J.Lugt,  H.J.Haussling  “The  acceleration  of  thin  cylindrical 
bodies  in  a  viscous  fluid”  Journal  of  Applied  Mathematics,  V.45, 
pp.1-6,  1978. 

8.  M.N.Zakharenkov  “On  the  approximation  of  the  boundary 
condition  for  vorticity ,”  In  Sbomik  Chislennye  Metody  Mehaniki 
Sploshnoj  Sredy,  13,  2,  pp.61-81,  Novosibirsk,  1982  (in  Russian). 

9.  K.N.Ghia,  G.A.Osswald,  U.Ghia  “Analysis  of  two-dimensional 
incompressible  flow  past  airfoils  using  unsteady  N-S  equations,”  In 
Numerical  and  Physical  Aspects  of  Aerodynamic  Flows  III.  Ed.  by 
Tuncer  Cebeci,  1986. 

10.  A. A. Samarsky  “Theory  of  difference  schemes,”  Moscow: 
“Nauka”,  1977  (in  Russian). 

11.  D.Potter  “Numerical  Methods  in  Physics,”  Moscow:”Mir”, 
1975  (Translation  from  English  into  Russian). 

12.  B.Engquist,  S.Osher  “One-sided  difference  approximations  for 
nonlinear  conservation  laws,”  Mathematics  of  Computations,  V.36, 
No.  154,  pp.321-351,  1981. 

13.  M.N.Zakharenkov  “Approximation  of  the  boundary  condition 
for  vorticity  at  a  solid  body  surface  in  the  analysis  of  the  Navier- 
Stokes  equation,”  In  Sbornik  Chislennye  Metody  Mehaniki  Sploshnoj 
Sredy,  11,  7,  pp.56-74,  Novosibirsk,  1980  (in  Russian). 

14.  M.N.Zakharenkov  “Far-field  boundary  conditions  for  a  viscous 
incompressible  flow  past  a  profile,”  Matematicheskoe  Modelirovanie, 
2,  pp.  3-18,  1990  (in  Russian). 

15.  M.N.Zakharenkov  “Pressure  uniqueness  for  solution  of  Navier- 
Stokes  equations  in  terms  of  stream  function  and  vorticity,” 
Matematicheskoe  Modelirovanie,  V.10,  No.l,  pp.  3-10,  1998  (in 
Russian). 

16.  S. Abdallah  “Numerical  solution  for  pressure  Poisson  equation 
with  Neumann  boundary  condition  using  a  non-staggered  grid,”  Int. 
Journal  of  Computational  Physics,  70,  pp.  182-192,  1987. 


17.  Tuncer  Cebeci,  L.W.Carr,  H.M.Jang  “An  iterative  boundary- 
layer  procedure  for  oscillating  airfoils  including  transition  effects,” 
AIAA-89-0020,  27th  Aerospace  Sciences  Meeting,  January  9-12, 
Reno,  Newada,  1989. 

18.  M.-K.Huang,  C.-Y.Chow  “Trapping  of  a  Free  Vortex  by 
Joukovski  Airfoils,”  AIAA  Journal,  V.20,  No.3,  pp.292-298,  1982. 

19.  M.N.Zakharenkov  “The  calculation  of  a  separated  flow  around 
a  trailing  edge  of  an  airfoil,”  Preprint  TsAGI  No.4,  1991,  Moscow: 
Central  Aero-Hydrodynamic  Institute  (in  English,  translation  from 
Russian  1990). 

20.  M.N.Zakharenkov  “Unsteady  incompressible  viscous  flow  past 
an  airfoil,”  Arch.Mech,  V.42,  No.4-5,  pp.609-615,  1990. 

21.  M.N.Zakharenkov  “Influence  of  multidipole  asymptotics  of  far 
field  (employing  as  a  boundary  condition)  onto  the  flow  separation 
in  the  problem  of  viscous  incompressible  flow  around  an  airfoil,”  In 
Akustika  neodnorodnyh  sred-IV,  28-31  May  1996,  Novosibirsk  (in 
Russian). 

22.  M.N.Zakharenkov  “Simulation  of  airfoil  aerodynamic  hysteresis 
for  flight  safety  problems,”  4th  International  conference  “Aircraft  and 
Helicopters  diagnostics.  AIRDIAG’95.  Warsaw,  6-7  December  1995. 
Air  Force  Institute  of  Technology.-ITWL/Informator  ITWL  wewn 
338/96,  Warsaw,  1996. 

23.  H.M.Bard  and  S.C.R.Dennis  “Time-dependent  viscous  flow 
past  an  impulsively  started  rotating  and  translating  circular  cylinder,” 
J.fluid  Mechanics,  158,  pp.447-488,  1985. 

24.  M.N.Zakharenkov  “Small-scale  vortex  structures  in  numerical 
solutions  of  two-dimensional  Navier-Stokes  equations,”  Preprint 
TsAGI  No.69,  Moscow: Central  Aero-Hydrodynamic  Institute,  1993 
(In  Russian  and  in  English). 

25.  M.N.Zakharenkov  “Generation  of  vortices  and  vortex  spots  - 
spots  of  momentum  loses,  in  the  viscous  flow  around  an  airfoil,”  In 
Scientific  Papers  of  International  symposium  on  ship  hydrodynamics 
devoted  to  85th  anniversary  of  bithday  of  A.M.Basin,  pp.450-470, 
1995  (in  Russian). 

26.  H.Schlichting  “The  theory  of  boundary  layer,”  Moscow:”Nauka”, 
1974  (Translation  from  German  into  Russian). 


r 


77 


Figure  3.  Cp  -  a,  b,  c  and  surface  vorticity  -  d,  e,  f  corresponding  to  the  flo 

C,  f  -  Dy2= 


t 


Max=6561 


m i n=-35 


disturbed  by  multidipole  perturbations:  a,  d  -  Dyl:=4;  b,  e  -  D 


Figure  8.  a)  -  Cp,  b)  -  tangential  velocity ,  c)  surface  vorticity  on  NACA0012  airfoil  at  Re=l  0,000,  a  =  5°,  X  =  3000. 


81 


82 


FREQUENCY-WAVENUMBER  SPECTRAL  MEASUREMENT 
OF  TURBULENT  BOUNDARY  LAYER  WALL  PRESSURE. 


M.  Pognant  (1),  G.  Giovannelli  (2)  and  B.E.  Forestier  (2) 

(1)  MS  L.A.I.A.T.  Universite  de  Toulon,  LA  GARDE  -  FRANCE 

(2)  I.R.P.H.E  -  UMR  6594  CNRS,  MARSEILLE  -  France 


Abstract 

The  wavevector-frequency  spectral  estimation  of  wall  pressure  fluctuations  by  means  of  multiple  Fourier  transform  processing  of  multi  point  data 
is  discussed.  This  study  brings  up  front  the  interest  to  probe  the  pressure  field  using  pinhole  transducers  with  a  sensor  spacing  as  small  as 
possible.  The  investigations  are  carried  beneath  a  turbulent  boundary  layer  for  a  Reynolds  number  Rex  of  2,9  106.  Fluctuating  pressure 

measurements  are  made  synchronously  at  sixteen  equally  spaced  points.  The  convective  ridge  and  the  acoustic  peak  due  to  the  background  noise 
generated  by  the  wind  tunnel  form  the  dominant  energy  contributions  to  the  wall  pressure  spectrum.  The  spectral  level  at  low  wavenumbers  has 
been  previously  evaluated  in  [1].  We  use  both  these  experiments  in  the  subconvective  domain  and  the  present  measurements  in  the  convective 
part  to  fit  the  parameters  of  Chase’s  model  of  the  ©-k  spectrum.  We  show  that  the  bias  introduced  by  the  discrete  Fourier  transform  estimation  on 
Chase’s  model  integrated  over  the  transverse  wavenumbers  is  about  5  dB.  The  addition  of  Chase’s  model  and  the  acoustic  contamination  of  the 
facility  is  close  to  experimental  frequency-wavenumber  spectral  densities. 


NOMENCLATURE 

N 

number  of  sensors 

rx 

sensor  spacing 

x/c 

abscissa  normalized  by  the  long  model 

k 

wavevector  (kx,kz)  in  the  wall  plane 

Ak 

wavenumber  resolution 

kN 

Nyquist  wavenumber 

f 

frequency 

CO 

circular  frequency  co=27cf 

fN 

maximum  frequency 

v®) 

frequency  spectral  density 

^(M) 

wavenumber-frequency  spectrum 

8 

boundary  layer  thickness 

8* 

boundary  layer  displacement  thickness 

V 

cinematic  viscosity 

Uoo 

free  stream  velocity 

Uc 

convection  velocity 

Ux 

friction  velocity 

Rex 

Reynolds  number  Rex=xU00/  v 

Rex 

Reynolds  number  Rex=6Ux/  v 

()" 

measured  quantity 

L  INTRODUCTION 

Properties  of  fluctuating  pressure  in  fully  developed 
turbulent  boundary  layer  flow  at  low  Mach  numbers  are 
important  in  various  aero  and  especially  hydrodynamic 
applications.  Many  investigations  examine  changes  in  the 
fluctuating  wall  pressure  field  by  the  presence  of  LEBU,  riblet 
surface  or  by  the  introduction  of  polymers.  The  performance 
enhancement  addressed  in  these  investigations  is  often  the 
control  of  turbulent  wall  pressure  fluctuations  which  are  primary 
self  and  radiated  noise  source  for  undersea  vehicles.  It  rapidly 
appears  that  the  wavevector-frequency  spectrum  is  suitable  for 
description  of  the  wall  pressure  field.  In  this  paper,  the  <o-k 
spectrum  is  obtained  by  means  of  multiple  Fourier  transform 


processing  of  multi-point  pressure  data.  If  we  desire  measure  the 
spectral  modifications  in  the  co-k  domain,  it  seems  necessary  to 
proceed  the  understanding  of  the  limitations  and  the  performance 
of  the  Discrete  Fourier  Transform  (DFT)  estimation. 

IL  ESTIMATION  OF  THE  WAVENUMBER- 
FREQUENCY  SPECTRUM 

The  recovery  of  the  wavenumber  spectrum  at  a  given 
frequency  is  governed  by  the  separation  rx  between  the  centers 
of  adjacent  sensors  according  to  the  familiar  Shannon’s  theorem. 
The  Nyquist  wavenumber  and  maximum  frequency 

f^2vx  can  be  putted  back  to  2kN  and  2fN  if  the  co-k 

spectrum  is  predominantly  one-sided  i.e.  if  we  suppose  that  the 
spectrum  is  highly  attenuated  above  the  convective  ridge. 
Otherwise,  there  is  no  possible  compromise  ([2])  between  an 
efficient  low  pass  filtering  (large  sensor)  of  the  convective  part  a 
nd  limited  wavenumber  abasing  range  (small  spacing).  Owing  to 
these  constraints,  the  pressure  field  is  probed  in  this  study  using 
pinhole  transducers  of  small  size. 

H.l  Boundary  filter 

A  boundary  filter  is  conceived  to  sample,  spatially  and 
temporally,  the  pressure  fluctuation  signals  beneath  a  turbulent 
boundary  layer  for  obtain  the  wavevector-frequency  distribution 
of  the  pressure  field.  The  difficulties  for  the  computation  of  the 
actual  spectrum  Opp(k,<o)  from  a  series  of  determinations  of  the 

measured  spectrum  O^(k,oo)  have  been  presented  by  [3].  In 

the  temporal  domain,  the  sampling  frequency  and  the  number  of 
samples  as  numerous  as  desired  and  the  filter  can  be 
approximated  by  a  Dirac  distribution.  In  the  spatial  domain, 
sensors  are  few  and  the  separation  distance  is  imposed  by  their 
size. 

II.l.l  Relation  between  the  actual  and  the  measured  ©- k 
spectra 

For  an  array  of  N  transducers  in  the  x  direction,  the  relation 
between  the  true  and  the  measured  spectra  at  steering 


83 


longitudinal  wavenumber  kXQ  and  frequency  co0  according  to 

[3]  is  not  explicit.  If  we  consider  punctual  sensors,  the 
integration  over  the  transverse  wavenumbers  of  this  relation  is 
given  by  : 


^p(kXo,®o)  =  4^2^-T®pp(kx>®o)|A(kx-kx0)|2dkx  (1) 
-N  -00 


where  the  multiplicity  of  sensors  is  accounted  by  the 
wavenumber  filter  shape  function  classically  defined  by  : 


|2 


ZS„exp(-in(kx-kXo)rx) 

n 


(2) 


where  Sn  are  the  coefficients  of  the  DFT  filter  shape  for  the 
window  function. 

If  N  is  large,  the  window  bandwidth  is  narrow.  For  an  uniform 
window,  we  obtain  the  following  usable  relation  : 

Tsj2 

®pP(kx0>®o)  =  — 3-®pp(kx0>®o)  (3) 

871 

in.  MODELS  OF  THE  WALL  PRESSURE  SPECTRUM 

We  present  briefly  the  two  main  models  of  the  wall  pressure 
spectrum. 

The  Corcos  model  [4]  is  based  on  the  similarity  properties 
of  the  covariance  of  the  pressure  field.  He  made  the  assumption 
that  the  cross  density  function  could  be  written  in  a  separable 
form  where  the  coherence  loss  of  pressure  sources  is 
approximated  by  exponential  decay  functions.  The  decay 
constants  yx  and  yz  are  respectively  0,2  and  0,8  in  our  study. 

Chase  [5]  published  a  descriptive  model  of  the  turbulent 
boundary  layer  wall  pressure  spectrum  established  by  its  relation 
to  the  fluctuating  velocity  filed.  The  mathematical  model  for  the 
wavevector-frequency  spectrum  in  the  incompressive  inviscid 
domain  is  the  sum  of  two  components  relative  to  the  mean  shear- 
turbulence  and  turbulence-turbulence  interactions.  At  high 
frequencies  defined  by  (o8*/Uc>>4  or  ©8/Ux»100,  the 

integration  over  wavenumbers  gives  an  of1  evolution  for 
O  (©).  This  model  has  been  fitted  by  Chase  on  the 
experimental  data  of  [6]  :  h=3,  C^h=0,466,  Cjh=0,014  and 

b=0,75.  h  fixes  the  wavenumber  dispersion  of  the  energy  around 
the  convective  ridge.  The  spectral  maximum  is  determined  by 
the  constant  CM.  The  spectral  level  at  low  wavenumbers  is 

proportional  to  CTh3.  The  parameter  CTh  has  been  estimated  in 

[1]  from  acceleration  spectra  measurements  at  the  center  of  two 
plates  excited  by  a  turbulent  boundary  layer  in  a  hydrodynamic 
tunnel.  The  mean  value  which  results  of  this  experimental  study 
is  0,12  with  h=3  and  is  eight  times  as  much  as  the  value  issued 
from  the  data  of  [6].  Its  validity  is  discussed  in  [1]. 

IV.  EXPERIMENTAL  SET  UP 

The  investigations  were  conducted  in  the  elliptical  open 
wind  tunnel  of  I.R.P.H.E.  in  Marseille.  The  dimensions  of  the 
test  section  are  3,3x2, 2  m2.  The  measurement  device  is  located  at 
x/c=0,65  from  the  leading  edge  of  the  5,4  m  long,  0,8  m  diameter 
axisymmetrical  model.  The  wall  pressure  fluctuations  are 
measured  using  2,5  mm  diameter  piezoelectric  ENDEVCO 
transducers  whose  sensing  area  is  reduced  by  placing  a  cap 


perforated  with  a  0,3  mm  diameter  hole  in  its  center.  The 
extinction  frequency  of  the  single  point  spectrum  given  by 

cov/U?  *2,5  is  5,6  kHz.  The  Helmholtz  resonance  frequency 

for  the  pinhole  system  is  next  to  9,6  kHz.  Measurements  are 
unaffected  by  spatial  averaging  for  f<7,6  kHz  for  a  12  m/s  free 
stream  velocity.  The  frequency  response  of  each  transducer  has 
been  tested  using  Bruel  &  Kjaer  source  delivering  a  white  noise 
from  50  Hz  to  10  kHz.  The  comparison  between  the  response 
with  and  without  the  pinhole  cap  shows  that  the  instrumental  cut 
off  frequency  is  4  kHz.  Pressure  measurements  are  made 
synchronously  at  sixteen  equally  3  mm  spaced  points.  The 

Nyquist  wavenumber  kN  is  1047  m"1  and  the  frequency  fN  is 
1,2  kHz  (11^0,611^).  The  filter  bandwidth  Ak  is  equal  to 

131  m'1.  By  assuming  that  the  energy  is  not  truncated  and  the 
number  of  transducers  is  sufficient,  we  use  the  practical  relation 
(3)  in  order  to  estimate  the  o-k  spectrum.  The  ®-k  spectrum  is 
computed  from  the  periodogram  method.  64  blocs  of  1024 
temporal  points  for  each  sensor  are  recorded  with  an  uniform 
window  using  a  10  kHz  sampling  frequency  after  low  pass 
filtering  at  the  Nyquist  frequency  of  5  kHz.  The  resulting 
frequency  resolution  is  4,88  Hz.  The  time-series  are  digitally 
filtered  by  applying  a  low  pass  filter  of  80  dB/octave.  The  cross 
spectral  density  matrix  is  computed  from  32  averages  of  1024 
points  and  the  o)-k  spectra  are  represented  using  a  Fourier 
interpolation  with  64  points. 

V.  EXPERIMENTAL  RESULTS 

V.l  Flow  mean  properties 

Mean  characteristics  of  the  turbulent  boundary  layer 
obtained  from  the  velocity  profile  measurements  are 
recapitulated  on  table  1.  The  ratio  of  the  boundary  layer 
thickness  to  the  radius  a  is  small  (6/a=0,18)  and  therefore  effects 
of  transverse  curvature  are  negligible. 


8 

mm 

103Cf 

u* 

m/s 

xw 

Pa 

10’6Rex 

10'3Re. 

67,8 

2,84 

0,45 

0,26 

2,9 

2,12 

Table  1  :  flow  mean  properties 


V.2  Wavenumber-frequency  spectra  of  the  wall  pressure 
field 

The  experimental  spectral  densities  as  a  function  of  the 
longitudinal  wavenumber  kx  are  reported  in  figure  1  for  various 

frequencies.  The  structure  of  the  spectral  density  exhibits  a 
dominant  ridge  corresponding  to  convection  of  turbulent 
pressures.  The  convective  ridge  becomes  broader  and  its 
amplitude  decreases  as  the  frequency  increases.  Owing  to  the 

resolution  Ak  equal  to  131  m*1,  the  acoustic  peak,  due  to  the 
background  noise  generated  by  the  wind  tunnel,  is  always 
centered  around  kx=0  m“^.  The  difference  between  the  acoustic 

and  convective  levels  is  never  higher  than  5  dB  and  therefore, 
the  acoustic  contribution  may  contaminate  the  low  wavenumber 
domain.  At  low  frequencies,  the  two  peaks  are  close  and  tend  to 
disjoint  as  the  frequency  increases. 

The  basic  DFT  filter  shape  for  the  uniform  window  presents 
a  difference  of  1 3  dB  between  the  main  lobe  and  the  highest  side 
lobe  localized  at  kx=±200m_1.  The  ripples  observed  at  proximity 

of  tlie  acoustic  peak  and  especially  at  k^^OOm'1,  are 
interpreted  as  acoustic  energy  leaking  out  by  the  side  lobes  of  the 


84 


wavenumber  filter  shape  function.  The  distortions  located  in  the  the  sidelobe  leakage  is  concealed  by  the  first  effects  of  spectral 
vicinity  of  the  two  peaks  are  probably  due  to  acoustic  and  abasing, 
convective  energy  intercepted  by  the  side  lobes.  Above  0,8% , 


101og(O  (k  ,(o ))  1 01og(O  (k  ,oo ))  101og(®  (k  ,<o)) 

PP  X  pp  X  pp  X 


turbulent  boundary  layer  for  various  frequencies  (f<%). 


VL  PERFORMANCE  OF  THE  DFT  ESTIMATION  FOR 
THE  CORCOS  AND  CHASE  MODELS 

For  the  Chase  model,  the  correlation  matrix  is  obtained  *by 
inverse  512-point  Fourier  transform  over  the  longitudinal 
wavenumbers.  The  frequency-wavenumber  spectrum  is 
computed  with  16  points  in  order  to  take  into  account  the  same 
bias  as  the  experimental  estimation,  h  and  CMh  parameters  fit 

on  our  experimental  results  for  a  frequency  of  700  Hz  (figure  2) 
situated  at  the  middle  of  the  or1  behavior  of  the  auto  spectrum. 
The  values  obtained  for  h  and  CMh  are  respectively  4,9  and 

0,85  and  remain  superior  to  3  and  0,466  recommended  by 
Chase  with  the  data  of  [6].  But  in  the  approach  [6],  the  major 
part  of  the  convective  contribution  is  filtered. 

The  performance  of  the  periodogram  with  the  Fourier 
transform  estimator  is  shown  in  figure  3  for  the  Chase  and 
Corcos  models  at  (900  Hz). 


101og(<J>  (k  ,©)) 

pp  ^ 


Figure  2  :  determination  of  the  Chase  model  parameters  h  and 
CMh  at  700  Hz. 


The  values  of  CTh  equals  to  0,014  for  the  measurements  of 
[6]  and  0,12  for  the  data  issued  from  [1]  with  h=3  are 
respectively  adjusted  at  5,25  10“3  and  0,045  with  h=4,9  in  order 
to  follow  the  subconvective  level  proportional  to  CTh3, 
predicted  by  the  Chase  model. 

The  bias,  at  kz=0  m'1,  introduced  by  the  DFT  for  a  linear 
array  of  16  points  equally  3  mm  spaced  is  about  17  dB  if 
CTh=5,25  10"3  and  is  reduced  to  9  dB  for  CTh=0,045 
(figure  3a). 

The  difference  between  the  convective  and  subconvective 
levels  decreases  when  the  Chase  model  is  integrated  over  kz, 

whereas  it  remains  constant  for  a  model  of  rectangular  product 
form  as  the  Corcos  spectrum.  This  difference  is  about  29  dB  for 
the  figure  3a  and  23  dB  for  the  figure  3b  with  CTh=0,045. 

For  the  kz-  integrated  Chase’s  model,  the  error  due  to  the 

low  number  of  sensors  is  12  dB  for  CTh=5,25  10‘3  and  5  dB  if 
CTh=0,045  (figure  3b).  The  spectral  fidelity  of  conventional 
beamforming  using  the  Chase  model  with  CTh=0,045  is 
reasonably  correct. 

It  is  clear  that  the  subconvective  level  comparatively  to  the 
spectral  maximum  is  imposed  by  the  filter  shape  function.  For 
an  uniform  window,  the  difference  between  the  main  and  the 
highest  side  lobes  is  13  dB.  The  ratio  between  the  convective 
level  to  the  corresponding  subconvective  level  predicted  by  the 
Corcos  model  is  14  dB  (Figure  3c).  The  DFT  estimation  is  thus 
accurate  for  the  Corcos  model. 


85 


101og(<I>  (k  ,0,®)/®  (<o/U  ,0,a>» 

pp  X  pp  c 


101og(4>  (k  ,w)/O((0/U ,ro)) 

PP  x  C 


k 

X 


k 

X 


Figure  3  :  bias  introduced  by  the  DFT  estimation  at  <o8*/U00s4  (900  Hz)  a)  on  Chase’s  model  at  kz=0,  b)  on  the  kz-integrated  Chase’s 
model  c)  on  the  Corcos  model ;  d)  comparison  between  the  Chase  and  Corcos  models  estimated  by  DFT  and  the  experimental  density. 


When  the  parameter  CTh  grows  from  5,25  10'3  to  0,045 

the  subconvective  level  increase  resulting  from  the  periodogram 
beamforming  method  is  merely  1,8  dB.  The  DFT  estimation  on 
Chase’s  model  is  close  to  the  experimental  o-k  spectrum 
(figure  3d).  The  acoustic  contamination  of  the  facility  can 
explain  the  difference  between  the  experimental  and  computed 
spectra.  When  the  Corcos  model  is  used,  the  low  wavenumber 
level  is  overestimated. 

We  model  the  acoustic  contamination  of  the  facility.  This 
external  contribution  is  seen  as  a  plane  wave  propagating  in  the 
streamwise  direction.  We  add  this  excitation  on  Chase’s 
spectrum.  The  model  is  confronted  figure  4  to  the  experimental 
densities. 

The  evaluation  of  the  parameters  h  and  CTh  carried  at 

700  Hz  is  satisfactory  for  all  frequencies  included  to  the  -1 
slope  of  the  frequency  spectrum.  The  differences  between  the 
experimental  and  predicted  convective  levels  are  very  slight. 
Otherwise,  the  wavenumber  dispersion  of  the  energy  around  the 
convective  maximum  is  correctly  reproduced  by  the  model.  We 
show  that  the  DFT  estimation  on  the  integrated  model  is  close 
to  experimental  frequency-wavenumber  spectral  densities  for 
frequencies  inferior  to  0,8fN  (960  Hz).  At  1000  Hz  and 

1150  Hz,  the  aliasing  energy  predicted  by  the  model  remains 
slightly  inferior  to  the  experimental  one.  The  figure  shows  that 
the  periodogram  beamforming  method  is  adequate  as  an 
estimate  of  the  experimental  wavenumber  spectrum.  The 
disymmetry  of  the  convective  ridge  observed  in  experimental 
densities  is  questionable. 


VIL  CONCLUSION 

According  to  the  Shannon  theorem  and  given  that  the 
sensitive  sensor  size  cannot  act  as  a  pre-filter  to  attenuate  the 
convective  region  of  the  co-k  spectrum  [2],  the  sensor  spacing  in 
our  study  is  as  reduced  as  possible.  Moreover,  for  a  sufficient 
number  of  sensors  and  for  a  very  small  sensitive  sensor  surface, 
there  is  a  simple  relation  between  the  actual  and  the  measured 
spectra.  Consequently,  we  probe  the  pressure  field  using 
pinhole  transducers. 

In  the  convective  region,  the  DFT  method  is  adequate  for 
the  determination  of  the  spectral  maximum  reached  at  about 
kx=co/Uc  and  the  dispersion  of  the  energy  around  <d/Uc.  The 
convective  parameters  h  and  CMh  of  the  Chase  model  obtained 

from  our  experimental  results  are  4,9  and  0,85. 

The  subconvective  level,  previously  evaluated  in  [1],  is 
9  dB  higher  than  the  measured  one  by  [6].  These  experiments 
lead  to  a  parameter  CTh  of  about  0,045  for  the  present  study.  In 

this  case,  the  DFT  estimation  follows  the  general  trend  of  the 
kz-integrated  Chase  model  quite  well.  Otherwise,  the 

experimental  spectra  are  correctly  reproduced  by  the  sum  of  the 
integrated  Chase  model  and  the  acoustic  contribution  expected 
from  a  sixteen  sensor  beamformer.  The  acoustic  contamination 
is  responsible  for  a  slight  rise  of  the  subconvective  level,  about 
3  dB.  We  propose  to  infer  an  approximation  of  the  ratio 
between  the  convective  to  the  subconvective  levels  from  the 
model.  This  ratio  is  about  23  dB. 


86 


1 01og(O^(kx?G) ))  1 01og(Opp(kx?(D))  1 01og(<Dpp(kx,a>)) 


0  500  1000  1500  2000  x  0  500  1000  1500  2000  x  0  500  1000  1500  2000  x 


101og(O  (k  ,co))  101og(<D  (k  ?oo ))  101og(<I>  (k  ,©)) 

pp  X  PP  X  PP  X 


101og(O  (k  ,©))  101og(O  (k  ,®)) 


PP  X  PP  X 


Figure  4  :  comparison  between  the  experimental  densities  measured  with  the  synchronous  method  ( - )  and  the  computed  spectra 

from  the  addition  of  Chase’s  model  and  the  acoustic  contamination  ( - ). 

AKNOWLEDGEMENTS  number,  Journal  of  the  Acoustical  Society  of  America,  90  (2) 

This  work  was  supported  by  the  Centre  d’Etude  et  de  1991,  pp.  1032-1040. 

Recherche  en  Detection  Sous-Marine  (C.E.R.D.S.M)  at  the  6.  N.C.  Martin  and  P.  Leehey  HLow  wavenumber  wall  pressure 

Direction  des  Constructions  Navales  (D.C.N.).  Dr  Giangreco  C.  measurements  using  a  rectangular  membrane  as  a  spatial  filter”, 

is  gratefully  acknowledged.  Journal  of  Sound  and  Vibration,  52  (1),  1977,  pp.  95-120. 

REFERENCES 

1.  G.  Giovannelli,  A.  Iddir  and  B.E.  Forestier  "Effets  d’une 
couche  limite  turbulente  sur  le  comportement  vibroacoustique 
d’une  plaque  bafflee  couplee  a  une  cavite",  Actes  du  4ieme 
congres  ffan9ais  d'acoustique,  April  1997  pp.  1023-1026. 

2.  G.H  Wakefield  and  M.  Kaveh  "Frequency-wavenumber 
spectral  estimation  of  the  wall-pressure  field  beneath  a  turbulent 
boundary  layer",  ASME,  Shear  Flow-Structure  Interaction 
Phenomena,  A.  Akey  and  M.  Reischman  eds.,  1985. 

3.  G.  Maldanik  and  D.W.  Jorgensen  “Boundary  wave-vector 
filters  for  the  study  of  the  pressure  field  in  a  turbulent  boundary 
layer”.  Journal  of  the  Acoustical  Society  of  America,  42  (2), 

1967,  pp.  494-501. 

4.  G.M.  Corcos  "The  structure  of  the  turbulent  pressure  field  in 
boundary  layer  flows",  Journal  of  Fluid  Mechanics,  18,  1964,  pp. 

353-378. 

5.  D.M.  Chase  "The  wavevector-frequency  spectrum  of  pressure 
on  a  smooth  plane  in  turbulent  boundary  layer  flow  at  low  mach 


HIGH  REYNOLDS  NUMBER  TURBULENT  FLOWS 


Alexander  J.  Smits  Mark  V.  Zagarola 

Mechanical  and  Aerospace  Engineering  Creare  Inc., 

Princeton  University  P.O.  Box  71, 

Princeton,  New  Jersey  08544-0710  Hanover,  NH  03755 

asmits@princeton.edu  mvz@creare.com 

Abstract  -  New  scaling  laws  for  the  mean  velocity  profiles  in  pipe  flow  and  boundary  layers  are  discussed. 
These  laws  are  based  on  recent  measurements  in  the  Superpipe  facility  over  a  very  wide  Reynolds  number 
range.  For  the  inner  layer  scaling,  a  power  law  was  found  for  the  overlap  region  of  the  mean  velocity  profile 
at  low  Reynolds  numbers,  and  both  a  power  law  and  log  law  region  at  high  Reynolds  numbers.  The  power 
law  with  empirical  constants  determined  from  pipe  flow  data  was  also  in  good  agreement  with  boundary 
layer  data.  For  the  outer  layer  scaling,  a  new  outer  velocity  scale  given  by  Ucl  —  U  was  proposed  for  the 
pipe  flow  and  UqoS* / 6  was  proposed  for  boundary  layers.  These  scales  collapse  the  pipe  and  boundary  layer 
data  considerably  better  than  the  conventionally-used  friction  velocity,  over  very  wide  ranges  in  Reynolds 
number. 


1  Introduction 

The  behavior  of  turbulence  at  high  Reynolds  number  is 
interesting  from  a  fundamental  point  of  view,  in  that  most 
theories  of  turbulence  make  very  specific  predictions  in  the 
limit  of  infinite  Reynolds  number.  From  a  more  practical 
point  of  view,  there  exist  many  applications  that  involve 
turbulent  flow  where  the  Reynolds  numbers  are  extremely 
large.  For  example,  large  vehicles  such  as  submarines  and 
commercial  transports  operate  at  Reynolds  numbers  based 
on  length  of  the  order  of  109,  and  industrial  pipe  flows 
cover  a  very  wide  range  of  Reynolds  numbers  up  to  10T. 
Some  typical  values  are  given  in  table  1,  where  Ret  is 
Reynolds  number  based  on  length  given  by 

Ree  = 

M  * 

where  p  is  the  density,  i  is  the  length,  f/oo  the  speed,  p. 
is  the  dynamic  viscosity  and  v  is  the  kinematic  viscosity. 
Similarly,  Res  is  based  on  £/«>  and  the  expected  maximum 
value  of  the  boundary  layer  thickness,  ReD  is  based  on  the 
average  velocity  U  and  the  pipe  diameter,  and 


where  ur  is  the  friction  velocity  (=  y/r^Jpy  tw  is  the  shear 
stress  at  the  wall).  The  examples  listed  in  table  1  are 
of  engineering  interest,  but  very  important  applications 
pertain  to  atmospheric  and  other  geophysical  flows  where 
extremely  high  Reynolds  numbers  are  the  rule  rather  than 
the  exception. 

To  model  the  behavior  of  high  Reynolds  number  tur¬ 
bulence  it  is  often  necessary  to  extrapolate  laboratory 
results  obtained  at  considerably  smaller  Reynolds  num¬ 
bers.  This  scaling  process  is  fraught  with  uncertainty, 
as  we  shall  see,  even  for  relatively  simple  flows  such  as 
pipe  flows.  Here,  we  present  some  observations  regard¬ 
ing  the  Reynolds  number  dependence  of  turbulent  pipe 
and  boundary  layer  flows,  based  on  recent  experimental 
evidence  obtained  at  Princeton  and  elsewhere.  Here,  we 
concentrate  on  the  mean  flow  scaling. 


2  Scaling  of  the  Mean  Flow 

For  wall-bounded  turbulent  shear  flows,  the  shape  of  the 
mean  velocity  profile,  or  equivalently,  the  relative  frac¬ 
tion  of  the  flow  occupied  by  the  inner  and  outer  regions, 
changes  with  Reynolds  number.  If  the  Reynolds  number 
is  large  enough,  it  is  usually  assumed  that  the  interaction 
between  these  regions  vanishes  because  of  the  disparity  of 
length  scales,  and  consequently,  independent  similarity  so¬ 
lutions  may  exist  for  each  region.  Therefore,  most  theoret¬ 
ical  treatments  start  by  dividing  the  flow  into  an  inner  and 
outer  region.  For  each  region,  a  length  and  velocity  scale 
may  be  defined.  The  velocity  scale  in  the  near- wall  region 
is  typically  taken  to  be  the  friction  velocity.  The  length 
scale  associated  with  the  inner  region  is  then  the  kinematic 
viscosity  u  divided  by  the  friction  velocity,  i//uT.  For  the 
outer  region,  the  velocity  scale  is  also  typically  taken  to  be 
the  friction  velocity,  although  this  has  long  been  the  source 
of  controversy  ([1],  [2]),  and  the  length  scale  is  taken  to  be 
the  radius  of  the  pipe  R  or  the  boundary  layer  thickness 
6. 

Using  dimensional  analysis,  the  scaling  for  the  inner 
region  is 

u+  =  f  (y+) ,  (1) 

where  /  represents  the  functional  dependence  in  the  in¬ 
ner  region  [3].  Here,  (7+  =  U/ury  y+  =  yur/vy  y  is  the 
distance  from  the  wall,  and  U  is  the  mean  velocity  in  the 


Table  1:  Typical  Reynolds  numbers  encountered  in  prac¬ 
tice. 


89 


streamwise  direction.  Equation  1  is  known  as  the  “law- 
of-the-wall”  and  is  valid  only  in  the  inner  region.  It  can 
be  shown  from  the  Navier-Stokes  equation  that  /  is  lin¬ 
ear  near  the  wall,  and  we  may  expect  that  equation  1 
is  valid  further  from  the  wall  than  the  linear  region  but 
not  into  the  outer  region  (that  is,  equation  1  will  hold  for 
0  <  <IC  R+,  where  R' *  =  Rur/i '). 

The  dimensionless  scaling  law  for  the  outer  region  is 

=»m,  m 

Uq 

where  g  represents  the  functional  dependence  in  the  outer 
region,  and  for  a  pipe  77  =  y/R  and  Ucl  is  the  centerline 
velocity.  The  parameter  u0  is  the  outer  velocity  scale.  If 
1x0  =  ur,  then  equation  2  is  known  as  the  “defect-law” 
[3].  Equation  2  is  valid  only  in  the  outer  region  where 
viscosity  is  not  important  (that  is,  equation  2  will  hold  for 
0<T7  <  1). 

Equations  1  and  2  are  based  on  the  assumption  that 
R +  is  large  enough  for  both  regions  to  be  independent 
of  Reynolds  number.  If  we  assume  that  an  intermediate 
region  exists  where  both  scaling  laws  are  valid,  then  we 
can  define  two  different  matching  conditions. 

By  matching  the  velocity  gradients  given  by  equa¬ 
tions  1  and  2,  we  find 

y+f'  =  -A va,  (3) 


where  the  differentiation  in  equation  3  is  with  respect  to 
the  dependent  variables  and  A  is  the  ratio  of  the  outer  to 
inner  velocity  scales,  uq/ut-  If  uo  =  ur,  then  equation  3 
is  the  same  relation  used  by  Millikan  (1938)  to  derive  the 
classical  logarithmic  overlap  region. 

Alternatively,  if  we  simultaneously  match  the  veloci¬ 
ties  and  velocity  gradients,  the  matching  condition  is 


(4) 


Equation  4  is  the  same  relation  used  by  George  et  al .  [2] 
with  uo  =  C/00  to  support  their  assertion  that  the  overlap 
region  in  a  boundary  layer  is  given  by  a  power  law. 

At  low  Reynolds  numbers  that  are  still  high  enough 
that  an  overlap  region  exists,  we  expect  that  A  depends 
on  R+.  At  these  Reynolds  numbers,  equation  3  does  not 
define  an  overlap  region  that  is  independent  of  R+,  but 
equation  4  does.  By  integrating  equation  4,  the  velocity 
profile  in  this  region  can  be  written  using  inner  layer  vari¬ 
ables  as 

U+=C1(y+)\  (5) 


3  Turbulent  Pipe  Flow 

To  verify  these  scaling  concepts,  pipe  flow  measurements 
were  obtained  in  the  Princeton/DARPA/ONR  Superpipe 
apparatus  which  can  achieve  a  range  of  Reynolds  num¬ 
bers  spanning  three  orders-of-magnitude.  The  facility  uses 
compressed  air  as  the  working  fluid  to  achieve  very  high 
Reynolds  numbers  at  a  reasonable  cost.  A  closed-loop 
system  was  built  with  the  test  pipe  located  inside  high- 
pressure  piping  (see  figure  1).  The  test  pipe  had  a  nom¬ 
inal  diameter  of  129  mm,  with  a  length- to-diameter  ratio 


of  200.  Further  details  of  the  facility  are  given  in  [1]  and 

[41- 

The  results  show  that  the  values  of  G\  and  7  were 
independent  of  Reynolds  number  and  equal  to  8.70  and 
0.137,  respectively  (see  figure  2a).  Equation  5  with  these 
constants  was  shown  to  be  in  excellent  agreement  with 
pipe  flow  data  for  60  <  y+  <  500  or  y+  <  0.15/£+,  the 
outer  limit  depending  on  whether  is  greater  or  less 
than  9  x  103  [5].  With  these  limits,  a  power  law  can  exist 
only  if  >  400. 

At  even  higher  Reynolds  numbers,  it  was  shown  that 
uo/ur  approaches  a  finite  limit  [1].  For  this  case,  equa¬ 
tion  3  also  gives  an  overlap  region  which  is  independent 
of  Reynolds  number.  Equation  3  can  be  set  equal  to  a 
constant  (typically  1/n)  and  integrated  to  give  the  classi¬ 
cal  log  law  which  can  be  written  in  terms  of  inner  scaling 
variables  as 

U+  =  -\ny+  +  B.  (6) 

The  values  of  k  and  B  were  shown  to  be  0.436  and 
6.15,  and  as  shown  in  figure  2b  this  log  law  is  in  ex¬ 
cellent  agreement  with  experimental  pipe  flow  data  for 
600  <  y+  <  0.07R+  [5].  With  these  limits,  a  log  law  can 
exist  only  if  R+  >  9  x  103  which  is  a  very  large  Reynolds 
number  compared  to  most  laboratory  flows. 

For  the  preceding  argument  to  be  valid,  uo  must  be 
proportional  to  uT  at  high  Reynolds  number.  The  correct 
velocity  scale  for  the  outer  region  was  shown  to  be  the 
velocity  deficit  in  the  pipe,  or  Ucl  —  t/,  where  U  is  the 
average  velocity,  which  is  a  true  outer  velocity  scale,  in 
contrast  to  the  friction  velocity  which  is  a  velocity  scale 
associated  with  the  inner  region  which  is  “impressed”  on 
the  outer  region  [1],  The  comparisons  with  the  data  are 
shown  in  figure  3.  As  expected  on  the  basis  of  the  argu¬ 
ment  given  here,  the  collapse  of  the  data  for  y/R  >  0.1 
using  uq  is  considerably  better  than  that  using  ur. 


4  Turbulent  Boundary  Layers 

The  preceding  analysis  for  pipe  flow  may  also  hold  for 
boundary  layers  if  the  centerline  velocity  is  replaced  by 
the  freestream  velocity  and  the  radius  is  replaced  by  the 
boundary  layer  thickness  [6] .  Here  we  also  assume  that  the 
streamwise  dependence  of  the  velocity  profile  is  properly 
accounted  for  by  our  choice  of  length  and  velocity  scales. 
An  outer  velocity  scale  equivalent-  to  Ucl  —  U  can  be  ex¬ 
pressed  using  boundary  layer  parameters  as  follows. 

«  -  u~-0  =  '¥[{'--k)iy 

-  U~T  <7> 

This  new  outer  velocity  scale  can  be  accurately  determined 
from  the  velocity  profiles,  in  contrast  to  the  friction  veloc¬ 
ity  uT  which  is  not  easily  measured  accurately  in  a  bound¬ 
ary  layer.  The  new  outer  velocity  scale  is  related  to  the 
Clauser  or  Rotta  thickness  A  which  is  given  by 


A  = 


Uoo  —  U 
ur 


90 


Figure  1:  The  layout  of  the  SuperPipe  facility.  The  flow  direction  is  counter-clockwise. 


Figure  2:  Pipe  flow  velocity  profiles  normalized  using  inner  scaling  variables  for  26  different  Reynolds  numbers 
between  31  x  103  to  35  x  106  [1].  (a)  Log-log  plot;  (b)  Linear-log  plot. 


Figure  3:  Pipe  flow  velocity  profiles  for  Reynolds  numbers  between  31  x  103  to  35  x  106  [1].  (a)  Normalized  using 
the  conventional  outer  velocity  scale;  (b)  Normalized  using  the  proposed  new  outer  velocity  scale. 


so  that 


At  high  Reynolds  numbers,  we  can  expect  that  izo  oc  ur, 
or  equivalently  6* / 6  oc  y/Cf,  (or  A  oc  5)  for  a  logarithmic 
overlap  region  to  exist  (the  skin  friction  coefficient  C/  = 
2  (Ur/U^f). 

A  very  rough  basis  for  comparison  between  pipe  and 
boundary  layer  flows  is  to  estimate  the  equivalent  mo¬ 
mentum  thickness  of  a  fully-developed  pipe  flow  at  about 
l/10th  the  radius,  so  that  the  equivalent  value  of  Re&  « 
Reo/ 20.  However,  comparisons  between  boundary  layers 
and  pipe  flows  must  be  made  very  carefully.  Even  though 
a  similar  scaling  may  exist  for  boundary  layers  and  pipe 
flow,  we  can  not  expect  the  functional  form  of  the  velocity 
profiles  in  the  outer  region  g{f})  to  be  the  same  since  the 
equations  of  motion  and  the  boundary  conditions  are  dif¬ 
ferent.  This  is  true  even  in  the  infinite  Reynolds  number 
limit.  Furthermore,  any  limit  that  depends  on  Reynolds 
number  (R+  or  J+)  may  be  different  due  to  the  differences 
in  the  outer  region  (J+  =  5ur/u).  These  limits  include 
the  Reynolds  number  at  which  complete  similarity  exists 
in  the  outer  and  inner  region,  the  outer  limit  of  the  power 
law  or  log  law,  and  the  Reynolds  number  at  which  the 
overlap  regions  appear.  Conversely,  the  equations  of  mo¬ 
tion  and  boundary  conditions  of  the  inner  region  are  the 
same  for  both  flows  in  the  infinite  Reynolds  number  limit, 
and  we  may  therefore  expect  that  the  functional  form  of 
the  velocity  profiles  in  the  inner  region  /(t/+)  are  the  same. 

Data  from  three  separate  boundary  layer  investiga¬ 
tions  were  used  for  the  comparison  presented  here  (see 
table  2).  The  data  from  Purtell  et  al.  [7]  spanned  the 
range  470  <  Re$  <  5,100  (220  <  6+  <  1,700);  the  data 
from  Smith  [8]  spanned  the  range  4,600  <  Re#  <  13,00 
(1,500  <  <  4,000);  and  the  data  from  Fernholz  et 

al.  [9]  provided  the  data  at  Re$  —  21,000  and  58,000 
(6+  =  6,000  and  18,000). 


Table  2:  Boundary  layer  data  sources. 


In  figure  4,  the  velocity  profiles  reported  in  [7] ,  [8]  and 
[9]  are  shown  normalized  by  inner  layer  variables.  The  data 
at  lower  values  of  6+  (profiles  1  to  5  in  table  2)  are  not 
shown  since  it  is  doubtful  that  a  universal  overlap  region 
exists  at  these  Reynolds  numbers  (tf+  <  500).  The  power 
law  established  from  pipe  flow  data  is  also  shown,  as  are 
the  regions  marking  a  ±3%  error  in  uT  (representing  a  best 
estimate  for  the  uncertainty  in  uT)*  For  all  profiles  except 


92 


20 


12 

U_-U 


±  3%  of  ordinate 
at  y/5  =  0.1 


Purtell  et  al.  (650  <  8+  <  1.7  x  103) 

x  Smith  (1.5  x  103  <5+ <4.0x  103) 

•  Pemholz  et  al.  (6.9  X  103  <  5+ <  18  X 103) 


Figure  5:  Boundary  layer  velocity  profiles  normalized  using  traditional  outer  scaling  variables. 


V* 

±  3%  of  ordinate 
at  y/S  =  0.1 

i 

T 

- •“Purtell  et  al.  (650  <  8*<1.7xl03) 

\ 

x  Smith  (1.5 

x  103  <  5+  <  4.0  x  103) 

■  Pemholz  et  al.  (6.9  x  103  <  5*  <  18  x  103) 

Figure  6:  Boundary  layer  velocity  profiles  normalized  using  proposed  outer  scaling  variables. 


93 


y+ 

Figure  4:  Boundary  layer  velocity  profiles  normalized  using  inner  scaling  variables. 


at  the  highest  Reynolds  number,  the  data  are  nominally 
within  ±3%  of  the  power  law  for  some  range  of  y+  and 
deviate  from  the  curve  in  the  inner  region  where  viscosity 
dominates  and  in  the  outer  region  where  the  inner  scaling 
no  longer  holds.  At  the  highest  Reynolds  number,  the 
data  near  the  wall  deviates  from  the  other  profiles  by  more 
than  3%,  but  this  perhaps  can  be  attributed  to  an  error 
in  position  since  the  five  points  nearest  to  the  wall  are  all 
within  1  mm  of  the  wall.  The  log  law  established  from 
pipe  flow  data  is  also  shown  in  figure  4.  According  to  the 
analysis  of  pipe  flow  data,  the  log  law  should  be  apparent 
only  at  the  highest  Reynolds  number  since  a  log  law  should 
not  exist  until  6+  is  of  order  104.  The  uncertainty  in  the 
friction  velocity  prevents  us  from  drawing  any  definitive 
conclusions  here,  but  a  power  law  with  C\  =  8.70  and  7  = 
0.137  seems  to  be  in  good  agreement  with  these  boundary 
layer  data. 

In  figures  5  and  6,  the  velocity  profiles  are  normalized 
by  the  conventional  outer  velocity  scale,  uT>  and  the  pro¬ 
posed  outer  velocity  scale  UooS*  /6>  respectively.  In  each 
figure,  error  bars  are  shown  which  represent  a  ±3%  uncer¬ 
tainty  of  the  ordinate  at  y/6  =  0.1.  When  normalizing  the 
wall-normal  position  in  the  outer  region,  the  length  scale 
was  taken  to  be  the  boundary  layer  thickness  at  0.99C/oo, 
although  it  was  found  that  the  profiles  collapsed  equally 
well  when  using  the  displacement  thickness  or  momentum 
thickness.  Regardless  of  the  length  scale  used,  the  col¬ 
lapse  is  poor  in  the  outer  region  for  the  profiles  normal¬ 
ized  by  ur  and  much  improved  for  y/S  >  0.07  and  for 
650  <  <5+  <  18  x  103  when  using  U00S* /&. 

5  Discussion 

From  the  analysis  given  here,  and  the  experiments  in 
the  Superpipe  facility  for  Reynolds  numbers  ranging  from 


31  X  103  to  35  X  106,  Zagarola  &  Smits  [1]  proposed  a  new 
scaling  for  the  mean  velocity  profile  of  fully-developed  pipe 
flow.  Zagarola  &  Smits  [6]  recently  extended  this  analy¬ 
sis  to  turbulent  boundary  layers,  and  using  data  over  a 
large  range  of  Reynolds  numbers  (650  <  6+  <  18  x  103  or 
4.6  x  103  <  Re@  <  58  x  103)  suggests  that  it  is  in  good 
agreement  with  experiment.  For  pipe  flow  and  boundary 
layers,  the  new  scaling  leads  to  a  power  law  for  the  overlap 
region  of  the  mean  velocity  profile  at  low  Reynolds  num¬ 
bers,  and  both  a  power  law  and  log  law  region  at  high 
Reynolds  numbers.  The  power  law  witli  empirical  con¬ 
stants  determined  from  pipe  flow  data  was  in  good  agree¬ 
ment  with  boundary  layer  data,  at  least  within  the  uncer¬ 
tainties  in  the  data,  specifically  the  value  of  the  friction 
velocity.  The  proposed  scaling  requires  a  new  outer  veloc¬ 
ity  scale  given  by  Ucl  -  0  for  the  pipe  flow  and  UooS*/S 
for  boundary  layers. 

6  Outlook  for  the  Future 

Work  is  continuing  on  measurements  of  the  turbulence  in¬ 
tensities,  structure  functions,  space-time  correlations  and 
structure  angles.  We  hope  to  report  soon  on  the  applica¬ 
bility  of  the  new  scaling  suggested  here  to  the  turbulence 
data. 

In  addition,  we  are  currently  constructing  a  High 
Reynolds  Number  Testing  Facility  (HRTF)  using  com¬ 
pressed  air  as  the  working  fluid  and  featuring  a  Magnetic 
Suspension  Balance  (MSB).  The  work  is  supported  by 
ONR  through  the  DURIP  program.  The  facility  is  de¬ 
signed  to  study  lift  and  drag,  wake  formation  and  decay, 
unsteady  flows  typical  of  maneuvering  vehicles,  turbulence 
in  boundary  layers  and  wakes,  all  at  Reynolds  numbers 
typical  of  full-scale  ships,  submarines,  torpedoes  and  air¬ 
planes  (up  to  length  Reynolds  number  of  176  x  106).  Its 


94 


heat 

exchanger  pumping  section 


motor 


Figure  7:  Schematic  of  the  new  High  Reynolds  Number  Testing  Facility  at  Princeton. 


design  is  largely  based  on  the  Superpipe  apparatus  (see  fig¬ 
ure  1),  and  also  uses  compressed  air  as  its  working  fluid. 
A  plan  view  of  the  new  facility  is  shown  in  figure  7.  Such 
a  facility  is  not  currently  available  anywhere  in  the  world, 
and  it  is  expected  to  provide  vital  new  data  on  the  perfor¬ 
mance  of  submarines  and  torpedoes,  as  well  as  providing 
a  new  capability  for  minimizing  risks  in  the  development 
of  new  and  innovative  vehicles. 


[9]  Fernholz,  H.H.,  Krause,  E.,  Nockemann,  M.,  & 
Schober,  M.  Comparative  Measurements  in  the 
canonical  boundary  layer  at  Re&i  <  6  x  104  on  the 
wall  of  the  German-Dutch  Windtunnel.  Phys.  Fluids , 
7  (6),  pp.  1275-1281,  1995. 


Acknowledgments 

The  research  in  high  Reynolds  number  flows  is  supported 
by  ONR  through  grants  N000014-92-J-1796,  N000014-97- 
1-0618,  and  N000014-98-1-0325,  monitored  by  Dr.  L.P. 
Purtell. 


References 

[1]  M.V.  Zagarola  and  A.J.  Smits.  Scaling  of  the  mean 
velocity  profile  for  turbulent  pipe  flow.  Physics  Re¬ 
view  Letters ,  78  (2),  239-242,  1997. 

[2]  George,  W.K.,  Castillo,  L.,  &  Knecht,  P.  The  zero 
pressure-gradient  turbulent  boundary  layer.  Techni¬ 
cal  Report  No.  TRL-153,  S.U.N.Y.  Buffalo,  1996. 

[3]  Schlichting,  H.  Boundary- Layer  Theory.  McGraw- 
Hill,  1987. 

[4]  M.V.  Zagarola.  Mean  flow  scaling  in  turbulent  pipe 
flow.  Ph.D.  Thesis,  Princeton  University,  1996. 

[5]  Zagarola,  M.V.  &  Smits,  A.J.,  1998  Mean  flow  scaling 
of  turbulent  pipe  flow.  Submitted  for  publication. 

[6]  M.V.  Zagarola  and  A.J.  Smits.  A  new  mean  velocity 
scaling  for  turbulent  boundary  layers.  AS  ME  Paper 
FEDSM98-4950 ,  1998. 

[7]  Purtell,  L.P.,  Klebanoff,  P.S.  &  Buckley,  F.T.  Turbu¬ 
lent  boundary  layers  at  low  Reynolds  number  Phys. 
Fluids ,  24  (5),  802-811,  1981. 

[8]  Smith,  R.W.  Effect  of  Reynolds  number  on  the  struc¬ 
ture  of  turbulent  boundary  layers.  Ph.D.  Thesis, 
Princeton  University,  Princeton,  NJ,  1994. 


95 


Drag  Reduction  Physics 


97 


THE  LAMB  VECTOR  AND  ITS  DIVERGENCE  IN  TURBULENT  DRAG 

REDUCTION 


C.  H.  Crawford,  H.  Marmanis  and  G.  E.  Karniadakis 
Center  for  Fluid  Mechanics 
Division  of  Applied  Mathematics 
Brown  University 

email:  (H.  Marmanis  -  marmanis@cfm.brown.edu);  (G.  Karniadakis  -  gk@cfm.brown.edu) 

Abstract  We  analyze  high-resolution  numerical  data  bases  for  a  turbulent  channel  flow  with  one  wall  formed  by 
streamwise  aligned  V-grooves  (riblets).  The  simulations  cover  a  range  of  Rr  from  140  to  200,  and  are  based  on 
parallel  spectral  element-Fourier  discretizations.  In  order  to  study  the  effect  of  different  geometries  on  the  drag,  we 
have  used  various  heights  and  widths  for  the  riblets.  The  fact  that  the  divergence  of  the  Reynolds  stress  tensor 
equals  the  average  Lamb  vector  motivates  us  to  write  the  Reynolds  stress  gradient  that  dominates  over  a  flat  wall,  i.e. 
3(uV)/da 72,  as  the  sum  of  the  streamwise  component  of  the  Lamb  vector  and  the  spanwise  variation  of  the  turbulent 
stress  Tz  —  d(ufw’)ldx 3.  The  streamwise  component  of  the  Lamb  vector  consists  of  a  vortex  stretching  term,  i.e. 
w'uj2^  and  a  vortex  transport  term.  By  studying  spanwise  locations,  from  groove  valley  to  tip,  we  find  that  an  increase 
of  the  vortex  stretching  term  is  associated  with  an  increase  of  the  Reynolds  stress  and  shear  stress.  For  a  smooth  wall 
X3  is  zero,  but  for  the  non-smooth  wall  it  achieves  large  positive  and  negative  values  at  the  valleys  and  the  tips  of  the 
roughness  elements,  respectively.  The  above  analysis  suggests  two  ways  of  reducing  the  drag:  The  first  is  to  prevent 
the  appearance  of  normal  vorticity,  and  the  second  to  create  valleys  at  the  wall  so  that  the  X3  component  becomes 
negative.  In  addition  to  this  standard  approach,  we  invoke  the  concept  of  turbulent  charge,  which  is  by  definition  the 
divergence  of  the  Lamb  vector.  We  present  the  spatial  distribution  of  this  quantity  and  analyze  its  connection  to  the 
problem  of  drag  reduction. 


I.  INTRODUCTION 

The  current  status  of  developing  means  of  turbulent  drag 
reduction  is  based  largely  on  identifying,  and  following  the  evolu¬ 
tion  of  the  so-called  coherent  structures.  These  structures,  how¬ 
ever,  are  arbitrary  in  the  sense  that  their  selection  as  structures 
is  subjective,  based  primarily  on  visualization,  and  outside  the 
framework  of  a  turbulence  theory.  Their  spatial  distributions  axe 
not  quite  clear  and  vary  considerably  in  time,  covering  a  large 
range  of  scales  that  generally  increases  with  distance  from  the 
wall.  Thus  it  is  not  surprising  that  the  description  of  their  in¬ 
teraction,  and  thereby  the  solution  of  the  problem,  is  far  from 
complete.  If  we  consider  the  effect  of  non-smooth  surfaces  ([37], 
[8]),  we  will  certainly  have  to  modify  our  structures  in  a  way 
that  depends  on  the  particular  geometrical  characteristics  of  the 
surface  and  it  is  not  known  a  priori.  This  naturally  raises  the 
following  question:  Even  if  a  model  involving  all  these  features 
and  structures  is  completed,  will  it  be  able  to  be  used  robustly 
and  efficiently  in  practiced  applications?  We  will  not  attempt  to 
answer  this  question,  but  we  shall  present  an  alternative  in  the 
description  of  turbulent  boundary  flows  that  invokes  the  structure 
of  the  Lamb  vector  and  its  divergence. 

We  shall  consider  a  channel  geometry  with  one  wall 
smooth  and  the  opposite  wall  mounted  with  longitudinal  riblets, 
so  that  we  are  able  to  make  a  simultaneous  study  of  the  flow  over 
both  flat  and  deformed  walls.  This  type  of  geometry  was  first 
introduced  in  [ll]  and  was  used  in  subsequent  more  systematic 
studies  of  drag  reduction  in  the  work  of  [12],  [8],  and  [19].  In  order 
to  obtain  very  accurate  vorticity  fields,  our  new  numerical  data 
bases  were  built  at  a  higher  resolution  than  in  the  previous  stud¬ 
ies  of  [12]  and  [8].  We  shall  encounter  flow  quantities  that  involve 
derivatives  of  the  velocities  even  higher  than  the  first,  therefore 
high  accuracy  is  required  in  order  to  obtain  reliable  numerical 
results.  By  using  a  vector  identity,  we  can  express  the  divergence 
of  the  Reynolds  stress  tensor  as  being  equal  to  the  average  Lamb 
vector  (i.e.  1  =  u;  X  u).  This  motivates  us  to  write  the  Reynolds 
stress  gradient  that  dominates  over  a  flat  wall,  i.e.  d(u,v/)/dx2i 
as  the  sum  of  the  streamwise  component  of  the  Lamb  vector  and 
the  spanwise  variation  of  the  turbulent  stress  T3  =  d^w^/dxz. 
The  streamwise  component  of  the  Lamb  vector  consists  of  a  vor¬ 


tex  stretching  term,  i.e.  ti/u/j,  and  a  vortex  transport  term,  i.e. 
vfoj'3.  By  studying  spanwise  locations,  from  groove  valley  to  tip, 
we  found  that  an  increase  of  the  vortex  stretching  term  is  asso¬ 
ciated  with  an  increase  of  the  Reynolds  stress  and  shear  stress. 
It  is  well-known  that  in  the  case  of  the  smooth  wall  X3  is  zero 
due  to  the  statistical  homogeneity  in  the  spanwise  direction.  For 
the  non-smooth  wall,  however,  it  achieves  large  positive  and  neg¬ 
ative  values  at  the  valleys  and  the  tips  of  the  roughness  elements, 
respectively.  The  above  analysis  suggests  two  ways  of  reducing 
the  drag:  The  first  is  to  prevent  the  appearance  of  normal  vor¬ 
ticity  and  the  second  to  create  valleys  at  the  wall,  so  that  the  T3 
component  becomes  negative. 

In  addition  to  this  standard  approach,  we  invoke  the  con¬ 
cept  of  turbulent  charge ,  which  is  by  definition  the  divergence  of 
the  Lamb  vector.  We  present  the  spatial  distribution  of  this  quan¬ 
tity  and  analyze  its  connection  to  the  problem  of  drag  reduction. 
The  difference  between  the  two  approaches  is  fundamental.  On 
the  one  hand,  the  coherent  structures  of  vorticity  are  investigated 
in  the  hope  that  they  will  provide  the  ground  for  the  formulation 
of  a  turbulence  theory  [23].  However,  as  we  have  already  men¬ 
tioned  these  structures  are  intensely  three-dimensional  and  their 
identification  is  mainly  based  on  visualization  techniques,  which 
are  restricted  to  low  Reynolds  numbers.  Moreover,  even  if  their 
identification  was  an  easy  task,  the  classification  of  all  advected 
structures  by  modes  and  parameter  size  would  be  necessary  be¬ 
fore  any  reasonable  theory  could  be  developed.  Considering  the 
large  number  of  these  structures,  this  would  be  an  immensely  ar¬ 
duous  task  that  would  result  in  a  theory  of  dubious  effectiveness. 
On  the  other  hand,  the  turbulent  charge  is  an  essential  element 
of  a  new  theory  of  turbulence  [34]  and  the  fact  that  it  does  have 
a  characteristic  structure  is  more  than  promising.  The  advantage 
of  thinking  in  terms  of  this  quantity  is  that  it  represents,  in  the 
physical  space,  the  tendency  of  the  energy  to  “clump"  at  some 
regions  where  its  value  is  positive,  and  to  leave  some  other  re¬ 
gions  where  its  value  is  negative;  the  stronger  the  tendency,  the 
greater  the  magnitude  of  the  divergence.  Hence,  if  the  turbulent 
charge  is  negative  at  some  region,  it  means  essentially  that  at 
these  regions  we  have  dissipation  of  kinetic  energy  into  heat,  and 
therefore  the  link  between  the  turbulent  charge  and  drag  force  is 
physically  clear. 


99 


The  paper  is  organized  as  follows:  In  section  II  we  discuss 
the  simulation  parameters.  In  section  III  we  present  a  summary 
of  vorticity  statistics  for  three  cases  (A,  B  and  C)  that  we  have 
considered.  Case  A  corresponds  to  a  5%  drag  reduction  on  the 
deformed  wall,  case  B  represents  a  10%  drag  increase,  and  case 
C  corresponds  to  a  2%  drag  reduction.  In  section  IV  we  present 
numerical  evidence  that  the  stretching  component  of  the  Lamb 
vector  is  responsible  for  most  of  the  drag.  We  also  show  that 
the  T3  component  changes  sign  and  results  in  drag  reduction,  as 
we  go  from  the  tip  to  the  valleys.  In  section  V  we  examine  the 
relation  between  drag  reduction  and  the  distribution  of  turbulent 
charge.  In  section  VI  we  summarize  our  results. 

II.  SIMULATION  PARAMETERS 

The  simulations  presented  here  were  based  on  spectral 
element- Fourier  discretizations.  Detailed  resolution  tests  and  a 
complete  validation  can  be  found  in  [16].  Both  spatial  and  tem¬ 
poral  resolution  employed  are  higher  than  in  previous  studies 
[12],  [8],  [19].  For  example,  the  time  step  is  an  order  of  magni¬ 
tude  smaller  than  the  one  used  in  [8].  The  details  of  the  spectral 
element-Fourier  method  can  be  found  in  [24]  and  recent  develop¬ 
ments  of  spectral  elements  on  unstructured  meshes  in  [40].  All 
simulations  were  performed  in  parallel  on  the  IBM  SP2  (thin 
nodes)  with  one  or  a  group  of  Fourier  modes  assigned  to  a  pro¬ 
cessor;  a  typical  run  requires  4  to  5  seconds  per  time  step.  The 
details  of  the  parallel  implementation  are  presented  in  [15]. 


Figure  1;  Geometry  for  streamwise  aligned  grooves.  The  flow 
direction  is  denoted  by  x±,  the  normal  direction  by  X2,  and  the 
spanwise  direction  by  #3. 

The  roughness  elements  are  streamwise  aligned  grooves 
aligned  in  the  flow  direction  as  shown  in  figure  1 ;  such  a  surface 
modification  has  been  shown  to  reduce  the  shear  stress  in  turbu¬ 
lent  flows  by  several  researchers,  including  the  experiments  of  [52], 
[33],  [49],  [44],  and  the  simulations  of  [12],  [8],  and  [19].  These 
triangular  grooves  are  characterized  by  their  height  and  span  in 
wall  units  h+  and  s+ ,  respectively.  Grooves  with  /i+  =  s+  <  20 
have  been  shown  to  reduce  drag  while  those  with  h *  =  >20 

have  been  shown  to  increase  drag. 

For  these  simulations,  the  computational  domain  was  a 
channel  consisting  of  a  smooth  upper  wall  and  a  non-smooth 
lower  wall.  The  flow  is  perpendicular  to  the  (X2  —  273)  planes, 
which  are  discretized  with  spectral  elements.  Along  the  flow  di¬ 
rection  xi,  Fourier  expansions  are  employed.  With  this  type  of 
domain,  statistics  on  both  the  smooth  wall  and  the  non-smooth 
wall  can  be  computed  simultaneously  for  comparison.  Our  results 
also  indicate  that  the  presence  of  the  grooves  did  not  effect  the 
smooth  wall  statistics  in  these  simulations.  We  choose  two  cases 
with  groove  heights  in  the  drag  reducing  range  and  one  case  with 
relatively  large  grooves,  i.e.  in  the  drag  increasing  range.  Table 
I  summarizes  the  cases  studied. 

A  summary  of  the  computational  domain  dimensions  for 
each  study  is  shown  in  table  II;  in  each  case,  10  grooves  were 


Case 

h+ 

s+ 

Re 

Rer  (u-1) 

Drag 

A 

17.70 

20.41 

4280 

181  -  177 

-5% 

B 

31.01 

35.66 

3280 

148-  155 

+10% 

C 

18.57 

21.42 

3280 

144  -  143 

-2% 

Table  I:  Summary  of  streamwise  aligned  groove  cases  studied. 
Shown  are  the  geometrical  parameters,  Reynolds  numbers  for  the 
upper  (u)  and  lower  (1)  walls,  as  well  as  the  drag  decrease  (-%)  or 
increase  (+%)  observed.  Re  is  Reynolds  number  based  on  center- 
line  velocity  Ui  and  half- channel  width  £,  while  Rer  is  based  on 
the  skin-friction  velocity  uT  and  8. 


Case 

LXl 

Lx2 

Li? 

Li, 

A 

5.61 

2.05 

1.15 

1018 

372 

209 

B 

5.61 

2.1 

2.3 

830 

311 

340 

C 

5.61 

2.065 

1.5 

808 

297 

216 

Table  II:  Summary  of  turbulent  grooved  channel  domain  for 
all  cases  studied.  Shown  are  the  computational  domain  dimen¬ 
sions  (L)  in  global  and  wall  units  for  the  streamwise  (aq ),  normal 
(072),  and  spanwise  (073)  directions.  Note  that  the  wall  unit  nor¬ 
malization  uses  the  non-smooth  wall  span-averaged  skin  friction 
velocity. 


used  on  the  bottom  wall.  As  with  previous  channel  studies  the 
flow  is  periodic  in  the  x\  and  X3  directions  and  no-slip  bound¬ 
ary  conditions  are  used  on  the  upper  and  lower  walls.  In  the 
final  simulations,  240  spectral  elements  were  used  with  11  X  11 
grid  points  in  each  element  and  with  32  Fourier  modes  in  the 
streamwise  discretization.  Table  III  gives  a  summary  of  the  res¬ 
olution  for  each  case;  these  values  can  be  compared  with  tables 
2  and  3.  In  all  our  cases  Aaq  =  0.0877,  the  maximum  Ax2+  was 
less  than  seven,  and  the  maximum  Aa73  +  was  less  than  three  for 
both  the  smooth  and  non-smooth  walls.  The  time-step  used  was 
A tUi/8  =  0.005,  and  the  flow  was  driven  by  a  constant  flow  rate, 
Q ,  based  on  the  channel  cross-sectional  area  and  the  equivalent 
laminar  centerline  velocity  C/p 

We  define  an  average  quantity  as  an  average  in  time 
and  space.  Spatial  averages  are  constructed  by  collapsing  three- 
dimensional  time-averaged  data  onto  a  two-dimensional,  single 
“master  groove”.  Note  that  in  time- averaging,  samples  of  the 
data  are  taken  at  every  time-step  in  the  integration  of  the  Navier- 
Stokes  equations,  no  time-steps  are  skipped.  The  initial  con¬ 
dition  for  all  three  cases  came  from  previous  turbulent  channel 
data  used  in  [14].  These  flow  fields  were  already  turbulent  and 
the  velocity  and  pressure  data  was  simply  interpolated  spectrally 
onto  the  new  mesh.  The  simulations  were  run  for  more  than  700 
non-dimensional  time  units  ( tUi/8 ).  The  accuracy  of  the  simula¬ 
tion  was  monitored  using  the  global  momentum  error,  which  was 
bounded  by  O(10-6)  in  all  cases  [16]. 

III.  REYNOLDS  STRESS  AND  VORTICITY 
STATISTICS 

Results  are  presented  in  global  coordinates,  i.e.  normaliza¬ 
tion  with  Ui  and  8 ,  as  well  as  wall  coordinates,  i.e.  normalization 


Case 

Azq 

Axz 

A 

0.0011  -  0.0373 

0.0019  -  0.0085 

B 

0.0011  -  0.0364 

0.0038-  0.0170 

C 

0.0011  -  0.0371 

0.0024-  0.0111 

Table  III:  Summary  of  turbulent  grooved  channel  grid  spacing 
for  all  cases  studied.  Shown  are  the  computational  grid  spacings 
in  global  units  for  both  the  smooth  and  non-smooth  walls. 


100 


with  uT  and  8 .  Grooved  wall  quantities  are  normalized  by  the 
span- averaged  uT)Sp  and  the  non-smooth  wall  x+  is  defined  as 
x+  =  uT,sp(x 2  -  x2  v.o.)/^j  where  X2  v.o.  is  the  virtual  origin 
(see  [16]).  We  present  data  in  this  section  for  cases  A  and  B  to 
contrast  the  statistics  of  a  drag  decreasing  configuration  (A)  and  a 
drag  increasing  configuration  (B) .  Data  for  case  C  can  be  found  in 
[16].  The  non-smooth  wall  statistics  are  compared  to  the  smooth 
wall  statistics  of  the  same  case;  this  prevents  any  confusion  in 
plots  concerning  known  Reynolds  number  effects  ([53],  [43],  [3]) 
as  demonstrated  in  figure  2  for  the  Reynolds  stress.  Note  that  in 
this  plot  the  DNS  data  from  [8]  at  ReT  =  180  is  closest  to  our 
DNS  channel  data  at  Rer  =  200.  The  agreement  is  fortuitous 
and  it  may  be  due  to  the  rather  low  resolution  in  the  streamwise 
direction  used  in  their  study  as  compared  to  the  data  shown  here. 
More  specifically,  it  was  demonstrated  in  [16]  that  under- resolved 
simulations  (in  the  streamwise  direction)  tend  to  overpredict  the 
Reynolds  stress. 


Figure  2:  Profiles  at  the  smooth  wall  of  the  the  Reynolds  stress 
— u'v'^  plotted  in  wall  coordinates  for  the  channel  (Rer  ft*  200), 
case  A  (Rer  ft!  180),  case  B  (Rer  «  150),  and  case  C  (Rer  ft! 
150).  Points  are  from  the  DNS  data  of  Choi,  et.  al.  1993  (Rer  ft! 
180). 


Reynolds  shear  stress  profiles  normalized  by  Ui  and  uT 
are  shown  in  figures  3  and  4.  For  case  A,  there  is  a  slight  in¬ 
crease  in  the  peak  Reynolds  stress  as  profile  location  moves  from 
the  groove  valley  to  the  groove  tip.  In  [36],  experiments  showed 
that  the  Reynolds  stress  was  increased  in  profiles  taken  from  the 
groove  valley  to  the  groove  tip  as  well.  In  case  B,  the  increase 
in  peak  magnitude  is  more  pronounced  as  the  profile  spanwise 
location  changes.  In  case  A  there  has  been  a  reduction  in  the 
peak  Reynolds  stress  as  compared  to  the  smooth  wall.  In  case 
B,  the  Reynolds  stress  peak  has  been  increased.  These  trends 
for  drag  reducing  and  drag  increasing  cases  in  triangular  grooves 
have  been  reported  in  [44],  [12],  and  [8].  For  case  A,  in  plots  us¬ 
ing  wall  coordinates,  the  difference  between  the  non-smooth  wall 
and  the  smooth  wall  remains  almost  constant  out  to  x£  =80. 
For  case  B,  however,  the  non-smooth  wall  and  smooth  wall  data 
become  quite  similar  for  x%  >  40.  From  these  same  figures,  we 

also  observe  that  the  Reynolds  (— u'v'^)  stress  at  the  groove  tips 
has  been  decreased  for  case  A  but  increased  for  case  B.  Previ¬ 
ous  work  in  [16],  [8],  [12]  has  also  shown  that  the  spanwise  and 
normal  turbulence  intensities  decrease  in  drag  decreasing  config¬ 
urations  and  increase  in  drag  increasing  configurations.  These 
combined  findings  have  been  used  to  propose  a  possible  mecha¬ 
nism  for  drag  reduction.  The  hypothesis  is  that  the  reduction  of 
spanwise  motions  causes  near  wall  bursts  to  take  place  prema¬ 
turely  leading  to  reductions  in  their  duration  and  intensity,  and 
therefore  reductions  in  turbulent  shear  stress  [10]. 

Figures  5,  6,  and  7  show  profiles  of  root-mean-square 
vorticity  fluctuations  normalized  in  wall  variables  (totrns  = 
Wrms^/W))1  The  at  the  non-smooth  wall  is  measured  from 
the  virtual  origin.  In  both  case  A  and  case  B,  all  components  of 
the  vorticity  intensities  show  maximum  values  at  the  groove  tips. 
For  the  streamwise  vorticity  in  case  A,  the  maximum  ( u)\  )tms  has 
been  reduced  as  compared  to  the  smooth  wall.  The  opposite  is 
true  with  case  B,  where  (u>i)rms  has  been  dramatically  increased. 
This  leads  to  speculation  concerning  the  strength  and  structure 
of  the  streamwise  vortices  at  the  non-smooth  wall.  In  [28],  the 


Figure  3:  Reynolds  stress  profiles  plotted  in  a)  global  and  b) 
wall  coordinates  for  case  A. 


Figure  4:  Reynolds  stress  profiles  plotted  in  a)  global  and  b) 
wall  coordinates  for  case  B. 


101 


center  of  the  streamwise  vortex  was  postulated  to  coincide  with 
the  local  maximum  in  a  profile  of  (o'i)rms  data.  Using  such  a 
criterion,  we  see  that  for  cases  A  and  B  at  the  smooth  wall,  the 
center  of  the  streamwise  vortex  is  between  x£  «  15  —  20,  in  good 
agreement  with  [28].  For  case  A,  where  the  maxima  for  the  data 
has  not  changed  significantly  due  to  spanwise  plotting  location 
for  x2  >  12,  the  streamwise  vortical  structure  would  be  located 
at  x%  «  20.  This  is  in  good  agreement  with  [8]  for  a  similar 
non-smooth  wall.  For  case  B,  it  is  difficult  to  discern  where  the 
maximum  is  for  the  non-smooth  wall  data,  as  the  three  profiles 
continue  to  change  for  x+  >  20.  The  relative  strength  of  the 
streamwise  vortices  can  be  deduced  from  these  plots  as  well.  The 
peak  (wi)rms  at  the  smooth  wall  for  case  A  is  larger  than  the 
peak  ((jJi)rms  for  case  B  at  the  smooth  wall,  thus  showing  that 
as  the  Reynolds  number  increases  the  strength  of  the  streamwise 
vortices  increases,  a  Reynolds  number  effect  also  found  in  [4]. 
The  reduction  in  the  (u>i)rms  f°r  the  non-smooth  wall  in  case 
A  indicates  that  the  strength  of  the  vortices  has  been  reduced, 
while  the  increase  in  the  f°r  case  B  indicates  that  the 

strength  of  the  vortices  has  been  increased. 


Figure  5:  Profiles  of  root  mean  square  streamwise  vorticity 
plotted  in  wall  coordinates  for  cases  A  and  B. 


Figure  6:  Profiles  of  root  mean  square  normal  vorticity  plotted 
in  wall  coordinates  for  cases  A  and  B. 


IV.  LAMB  VECTOR  AND  REYNOLDS  STRESS 
ANALYSIS 


The  Lamb  vector  has  not  been  studied  as  extensively  as  vor¬ 
ticity,  especially  for  turbulent  flows.  In  the  context  of  fixed  points 
of  the  Euler  equations,  Kraichnan  &  Panda  [31]  introduced  a  de¬ 
composition  of  the  Lamb  vector  into  a  potential  and  a  solenoidal 
part,  and  compared  their  magnitudes.  A  large  potential  part  im¬ 
plies  a  high  probability  for  the  Fourier  image  of  the  Lamb  vector 
and  the  wave  vector  k  to  be  aligned,  and  the  argument  made  is 
that  purely  kinematic  properties  of  turbulent  flows  can  lead  to 
reduction  of  their  nonlinearity.  In  the  context  of  Reynolds  stress 
modeling,  Wu  et  al  [55]  have  examined  the  relation  between  the 
Lamb  vector  and  the  Reynolds  stress  tensor  and  concluded  that 
the  problem  of  modeling  turbulent  force  exclusively  amounts  to 
modeling  the  mean  turbulent  Lamb  vector.  In  a  recent  attempt 
to  study  the  problem  of  turbulence,  Marmanis  [34]  has  introduced 
a  closed  set  of  equations  that  involve  the  mean  vorticity  and  the 
mean  Lamb  vector.  His  closure  is  based  on  the  identification  of 
certain  nonlinear  quantities  as  sources  for  the  mean  fields.  We 
will  use  one  of  these  sources  in  the  next  section  and  suggest  how 
we  can  employ  them  in  turbulence  control. 

For  the  case  of  our  channel,  the  Navier-Stokes  equations 
written  for  the  mean  streamwise  component  of  the  velocity  in¬ 
volve  explicitly  the  streamwise  component  of  the  Lamb  vector. 
We  will  assume  that  the  streamwise  direction  is  homogeneous  as 
far  as  the  kinetic  energy  is  concerned,  i.e.  9(u  •  U.)/dx  —  0,  and 
write  the  equation  in  the  following  form 


a{«) 

dt 


-<M  -  <5~>  +  -v’w 


(1) 


where  lx  is  the  streamwise  component  of  the  Lamb  vector,  and 
we  used  (...)  to  denote  any  appropriate  averaging  operator.  This 
equation  immediately  shows  that  the  Lamb  vector  is  the  most  im¬ 
portant  agent  of  turbulence;  without  its  presence  the  above  equa¬ 
tion  would  describe  simply  a  Stokesian  flow.  Hence  the  analysis  of 
the  Lamb  vector  can  explicitly  provide  ways  of  altering  the  mean 
flow.  In  particular,  the  streamwise  component  of  the  averaged 
Lamb  vector  in  our  channel  can  be  written  as 


lx  —  —  w'usf2  ,  (2) 

and  the  terms  and  wfu>2  are  called  vortex  transport  and 

vortex  stretching  terms,  respectively. 


F igure  7 :  Profiles  of  root  mean  square  spanwise  vorticity  plotted 
in  wall  coordinates  for  cases  A  and  B. 


We  make  one  final  comment  on  the  smooth  wall  data  pre¬ 
sented  in  this  section.  At  the  beginning  of  this  section  the  point 
was  made  that  the  presence  of  the  non-smooth  wall  did  not  effect 
the  smooth  wall  data.  The  results  from  this  section  (especially 
for  case  B  -also  C  not  shown  here)  demonstrate  the  validity  of 
this  statement.  The  average  difference  in  the  turbulence  intensi¬ 
ties  between  cases  B  and  C  is  2%;  the  average  difference  in  the 
Reynolds  stress  is  less  than  4%.  Such  differences  could  be  at¬ 
tributed  to  the  slight  differences  X2-X3  plane  resolution  at  the 
smooth  wall  for  each  case.  In  cases  B  and  C  at  the  smooth 
wall,  the  X2  resolution  does  not  change.  However,  the  A X3  grid 
spacing  for  case  B  is  larger  than  that  of  case  C  (see  table  III). 
Results  from  the  channel  resolution  study  in  [16]  indicate  that  as 
the  spanwise  resolution  increases  (decreasing  ASC3),  the  Reynolds 
stress  magnitude  increases.  In  figure  2,  we  see  that  case  B  has 
lower  values  for  —  u,vt^  than  case  C  —  the  trend  that  we  expect 
from  the  resolution  study.  We  also  note  that  time- averaging  ef¬ 
fects  could  be  responsible  for  1%  differences  in  the  data  ([16]). 


Figure  8l  Profiles  of  the  transport  )  and  stretching 

( w'lu ' + )  terms  and  Reynolds  stress  derivative  for  case  A  at  the 
smooth  wall.  The  circles  correspond  to  direct  differentiation  of 
Reynolds  stress  while  the  solid  fine  corresponds  to  the  sum  of  all 
contributions. 

Figure  8  shows  the  transport  and  stretching  terms,  as 
well  as  the  Reynolds  stress  derivatives  in  wall  units  (j//uJ)  at  the 
smooth  wall  for  case  A.  This  plot  demonstrates  numerically  that, 
for  a  smooth  wall,  the  stretching  term  is  the  dominant  contribu¬ 
tion  to  the  positive  Reynolds  stress  derivative  for  x2  <  20.  The 
results  of  [29]  also  showed  that  the  stretching  term  contribution 
was  greater  than  the  transport  term  from  10  <  x2  <  20  in  a 
zero-pressure  gradient  flat  plate  turbulent  boundary  layer  flow  at 
Ree  -  2870. 

The  appearance  of  the  Lamb  vector  in  equation  (l)  implies 
that  the  lamb  vector  is  directly  associated  with  the  Reynolds 


102 


Figure  9:  Profiles  of  the  transport  v'u;'  +  ,  stretching 

w #u>2  »  and  turbulent  stress  derivative  terms  d(—u,v/  )/dx£} 
du'w'^ /dx^  =  T-s  for  cases  A  and  B  at  the  non-smooth  wall. 
Note  that  x  *  is  measured  from  the  virtual  origin. 


stress  tensor.  In  fact,  the  lamb  vector  is  the  divergence  of  the 
Reynolds  stress  tensor  minus  the  gradient  of  the  kinetic  energy 
per  unit  density.  This  is  proved  easily,  by  employing  a  well-known 
vector  identity  regarding  the  Lamb  vector,  i.e. 


djujui)  _  jj-  ,  1  djujUj) 

dxj  '  2  dxi 


If  we  assume  homogeneity,  as  we  did  before,  in  the  streamwise 
direction  (d/dx\  =  0)  and  set  i  =  1,  we  get  the  following  equation 
for  the  Reynolds  stress, 


d(-u'v’)  _  -rT 
dx2  v  "3 


-  diutw*) 

o'w>2  +  -V- — -  =  (.  +  T3 , 


dX3 


(4) 


and  if  we  also  assume  homogeneity  in  the  spanwise  direction 
(d/dxs  =  0)  we  get, 


d(— u'vf) 

dx2 


v'uj'z  —  w'uj!}  =  lx  , 


(5) 


where  the  last  equality  is  due  to  equation  (2).  Note  that  the  r.h.s. 
of  this  equation  is  the  same  as  the  r.h.s.  of  (2),  which  is  merely 
the  definition  of  the  Lamb  vector. 

Figure  9  shows  the  transport,  stretching,  and  turbulent 
stress  derivative  terms,  given  in  equation  (4),  for  profiles  from  the 
non-smooth  wall  virtual  origin  in  cases  A  and  B  (case  C  is  similar 
to  A).  At  the  non-smooth  wall  the  stretching  term  remains  domi¬ 
nant  over  the  transport  term,  and  the  T3  =  du*w,^r  / dx *  term  is 

in  competition  with  the  term  d(— u'v'  *  which  is  the  only 

term  of  the  divergence  of  the  Reynolds  stress  that  survives  in  the 
smooth  wall  case. 


Figure  10:  Profiles  of  the  Reynolds  stress  derivative, 

d(~ u'v,+  )/dx+ ,  for  cases  A  and  B  at  the  non-smooth  wall. 


Our  results  have  shown  that  peaks  in  the  Reynolds  stress 
profile  increase  as  profiles  are  taken  from  the  groove  valley  to 
the  groove  tip.  Profiles  of  the  derivatives  of  the  Reynolds  stress 
for  cases  A  and  B  are  shown  in  figure  10,  For  each  case, 
9(— u*vf+ ) / dx 2  increased  in  peak  magnitudes  from  profiles  taken 
at  the  groove  valley  to  profiles  taken  at  the  groove  tip.  Note  that 
in  case  B,  the  magnitude  of  d(— has  been  increased 
by  more  than  a  factor  of  two  compared  to  case  A  as  well  as  the 
corresponding  smooth  wall.  This  quantity  shows  the  first  sub¬ 
stantial  (more  than  10%  or  20%)  statistical  difference  between 
the  smooth  wall  and  the  non-smooth  wall  as  well  as  among  the 
three  non- smooth  wall  cases.  Figure  11  shows  that  the  wall  shear 
stress  increases  in  magnitude  from  the  groove  valley  to  the  groove 
tip.  This  quantity  also  shows  a  substantial  increase  in  magnitude 
as  the  spanwise  location  within  the  groove  is  varied.  It  seems 
likely,  then,  that  understanding  the  changes  that  occur  in  the 
terms  of  equation  (4)  may  provide  an  understanding  to  the  shear 
stress  modification  found  in  these  geometries. 


0.003  h 


£002 

* 


G 

CO 

£ 

CD 


— t  i  r  1  |  1 — i - 1 — 1 — | — r 

— 1 - 1 — 

— 1 — 1 - 

1  1  1  1 

• 

* 

0  Case  A 

O  _ 

•  Case  B 

• 

*  Case  C 

* 

- 

O 

- 

• 

- 

- 

* 

* 

- 

• 

O 

- 

- 

* 

- 

O 

• 

• 

8 

8 

•  8 

-•  ® 

_ 

.  VALLEY 

.  1  ....  1  . 

.  1  .  . 

.  .  1  , 

TIP  . 

3  0.1  0.2 

0.3 

0.4 

o.i 

x3/s 


Figure  11:  Wall  mean  shear  stress  in  global  variables  plotted 
along  the  master  groove  from  valley  to  tip  for  cases  A,  B,  and  C. 
Note  that  the  spanwise  position  has  also  been  normalized  by  the 
groove  spanwise  length- scale,  s. 


Figure  12:  Profiles  of  the  transport  term,  for  cases  A 

and  B  at  the  non-smooth  wall. 


0.05 

0.05 

Valley 

.+ 

+ 

rr . ^ 

3  0 

> 

> 

-0.1 

J 

-0.0S 

Case  A 

-0.15 

-Tip  l / 

J  20 

40 

flO  i 

10  C 

\  20 

40 

•0  * 

Figure  13:  Profiles  of  the  stretching  term,  ,  for  cases  A 

and  B  at  the  non-smooth  wall. 


103 


Figure  12  shows  vfi oi^  plotted  for  cases  A  and  B.  Profiles 
are  taken  at  five  positions  along  the  groove  from  the  valley  to 
the  tip.  In  all  cases,  the  magnitude  of  increases  from  the 

groove  valley  to  the  groove  tip,  with  the  largest  increase  coming 
in  case  B.  The  values  for  case  B  at  the  tip  are  more  than  a  factor 
of  two  greater  than  the  other  non-smooth  wall  cases  as  well  as  the 
smooth  wall.  The  transport  terms  at  the  groove  tip  for  case  A 
(similarly  for  C)  show  a  small  increase  compared  to  the  smooth 

wall  data.  Figure  13  shows  plotted  for  cases  A  and  B. 

As  with  the  transport  terms,  the  magnitude  of  the  +  peaks 
are  largest  in  profiles  taken  at  the  tips.  The  position  of  the  peak 
value  also  changes  with  the  profile  location.  The  stretching  term 
at  the  tip  for  case  B  is  more  than  twice  that  of  the  smooth  wall  or 
the  other  non-smooth  wall  cases  (note  the  change  in  axis  limits 
needed) .  However,  the  data  for  case  B  also  shows  that  deep  within 
the  groove  valleys,  the  stretching  term  is  almost  zero. 


Valley 

Tip 

Case  A  7 

Figure  14:  Profiles  of  spanwise  derivatives  of  the  turbulent 
stress,  dufwl+  /dx£,  for  cases  A  and  B  at  the  non-smooth  wall. 

Figure  14  shows  X3  =  dvJw^  plotted  at  the  dif¬ 

ferent  spanwise  locations  of  the  riblet,  for  cases  A,  B,  and  C;  at 
the  smooth  wall  this  term  is  zero*  These  plots  show  that  be¬ 
low  the  groove  midpoint  du'w^  / dx+  is  positive  and  works  to 
increase  the  gradient  in  the  Reynolds  stress.  This  behavior  in 
du'w,+ /dx+  could  be  related  to  secondary  motion  within  the 

groove  ([44]).  Above  the  midpoint,  du'w,[  /dx%  is  negative  and 
works  to  decrease  the  gradient  of  the  Reynolds  stress.  Again, 
case  B  shows  the  largest  positive  values  for  du'w'* /dx+  within 
the  groove  valleys  and  the  largest  negative  values  at  the  groove 
tip. 

In  order  to  determine  what  the  relationship  between  T3 
and  the  secondary  motion  is,  we  looked  at  spanwise  (w)  and 
normal  (v)  velocity  vector  plots  from  ensemble  averages  con¬ 
structed  from  the  entire  simulation  time  of  each  case  on  the  two- 
dimensional  master  groove.  At  the  smooth  wall,  averages  of  w 
and  v  are  zero;  close  to  the  non-smooth  wall,  w  and  v  have  non¬ 
zero  means  which  are  O(10~3)  smaller  than  the  mean  stream- 
wise  velocity  for  all  cases.  Figure  15  shows  these  vector  plots 
for  the  near- wall  portion  of  half  the  master  groove  domain  for 
cases  A  and  B.  Note  that  these  vector  plots  are  symmetric  about 
273  =  X3}tip-  We  see  that  in  each  case,  there  exists  a  roll-like 
structure  between  the  groove  valley  and  tip.  The  scaling  of  these 
structures  in  wall  units  can  be  determined  from  the  groove  height 
and  span  dimensions  given  in  wall  units  as  shown  in  table  I.  The 
centers  of  these  structures  appear  to  be  at  x\  w  10  above  the 
groove  virtual  origin,  slightly  closer  to  the  wall  than  the  stream- 
wise  vorticity  rolls  found  at  canonical  smooth  walls,  [28]. 

Profiles  of  dvJvT*  that  originate  near  the  groove 

valley  go  through  a  downward  motion  region  of  this  secondary 
structure  (vectors  pointing  towards  the  groove  wall).  Profiles  that 
originate  near  the  groove  tip  go  through  an  upward  motion  re¬ 
gion  of  the  structure  (vectors  pointing  away  from  the  groove  wall). 
Profiles  that  originate  near  the  groove  midpoint  go  through  the 
core  of  the  structure.  Therefore,  positive  values  of  du'w 1  /&£$ 
correspond  to  the  downward  motion  of  fluid  towards  the  wall; 
negative  values  of  dufw,+  /dx£  correspond  to  fluid  being  trans¬ 
ported  away  from  the  wall.  This  observation  is  consistent  with 
the  observations  in  [14]  for  smooth  walls  and  groove  walls.  In 
that  work,  an  inrush  of  fluid  towards  the  wall  was  determined 
to  increase  the  shear  stress  at  the  wall  and  fluid  motion  away 
from  the  wall  was  determined  to  decrease  the  shear  stress  at  the 
wall.  Since  positive  /dx+  increases  the  gradients  of  the 

Reynolds  stress  and  negative  dv/w^ /dx^  decreases  the  gradi¬ 


ents  of  Reynolds  stress,  the  same  conclusions  about  the  mean 
secondary  motion  at  the  non-smooth  wall  in  these  plots  can  be 
made  here.  Overall,  case  B  shows  the  largest  positive  values  for 
du’w,Jt  /dx^  within  the  groove  valleys  and  the  largest  negative 
values  at  the  groove  tip. 


Figure  15:  Mean  spanwise  and  normal  velocity  vectors  at  the 
master  groove  for  case  A  (left)  and  B  (right).  The  ensemble  mean 
was  constructed  from  25  samples  taken  over  the  entire  simulation 
time.  The  axis  dimensions  are  in  global  units.  The  domain  shown 
is  the  near- wall  region  of  one  half  of  the  master  groove. 


V.  THE  DIVERGENCE  OF  THE  LAMB  VECTOR 
AND  DRAG  REDUCTION 

Previous  works  in  the  area  of  turbulence  control  based  their 
concepts  primarily  on  observation.  That  is,  the  concepts  involved 
have  been  introduced  by  visualization  of  the  flow  and  have  been 
selected  due  to  their  spatial  structure;  no  matter  how  arbitrar¬ 
ily  the  latter  is  defined.  The  notion  of  the  turbulent  charge  [34], 
which  is  by  definition  the  divergence  of  the  Lamb  vector,  origi¬ 
nates  from  a  theory  of  turbulence  that  seeks  a  closed  set  of  equa¬ 
tions  involving  only  the  vorticity  and  the  Lamb  vector.  The  terms 
that  cannot  be  explicitly  expressed  as  a  function  of  either  the  vor¬ 
ticity  or  the  Lamb  vector  are  gathered  together  and  treated  as 
sources.  This  leads  to  a  set  of  equations  that  are  linear  in  their 
prime  variables.  Of  course,  the  determination  of  the  sources  needs 
to  be  done  outside  this  model  system.  Whenever  the  sources  are 
given  as  an  input  to  the  system,  the  system  responds  according 
to  the  model  equations.  Herein,  we  do  not  attempt  to  engage  the 
above  mentioned  theory  in  the  calculation  of  the  drag.  Neverthe¬ 
less,  it  turns  out  that  these  sources  have  remarkable  properties, 
which  deserve  some  attention  in  the  context  of  turbulent  drag 
reduction. 

The  divergence  of  the  Lamb  vector  is  a  completely  kine¬ 
matic  quantity.  Its  relation  to  the  dynamics  can  be  obtained  by 
applying  the  divergence  operator  on  both  sides  of  the  Navier- 
Stokes.  For  an  incompressible  fluid  we  get 

V  •  l(x,f)  =  ~V2$,  (6) 

where  $  is  the  Bernoulli  energy  function  (i.e.  $  =  (u2 /2)  +  p/p). 
Therefore,  the  divergence  of  the  Lamb  vector  is  connected  with 
the  “curvature”  of  the  Bernoulli  energy  function.  It  follows  that 
the  turbulent  charge  is  endowed  with  a  clear  physical  meaning: 
It  represents  the  tendency  of  the  energy  to  concentrate  at  some 
regions  where  its  value  is  positive,  and  to  be  destroyed  at  some 
other  regions  where  its  value  is  negative;  the  stronger  the  ten¬ 
dency,  the  greater  the  magnitude  of  the  divergence.  In  the  case 
where  the  Laplacian  is  zero,  the  energy  has  no  curvature  at  all 
and  its  density  arranges  itself  so  as  to  average  out  the  differences 
imposed  by  the  boundary  conditions.  Notice  that  for  an  incom¬ 
pressible  Newtonian  fluid,  the  divergence  of  the  Lamb  vector  is 
the  same  for  both  the  inviscid  and  the  viscous  case;  this  is  evi¬ 
dent  from  direct  calculation  of  the  equations.  In  what  follows,  we 
consider  this  quantity  for  the  case  of  the  channel,  and  examine 
a  reasonable  explanation  of  drag  reduction  in  terms  of  its  spatial 
distribution. 

The  importance  of  the  turbulent  charge  lies  on  its  property 
to  be  located  in  a  very  narrow  region  close  to  the  wall.  Indeed, 
it  is  well-known  that  in  wall-bounded  turbulent  flows,  there  is  a 
region  near  the  wall  where  viscous  effects  dominate.  This  viscous 
layer  that  extends  up  to  y+  «  5  is  the  region  in  space  where  most 
of  the  energy  is  dissipated,  consequently  we  would  expect  the 


104 


turbulent  charge  to  be  negative  there  and  achieve  its  maximum 
value  exactly  at  the  wall,  i.e.  y +  =0.  In  the  area  just  above 
the  viscous  layer  (5  <  <  20),  the  turbulent  motion  becomes 

intense  and  tends  to  accumulate  the  energy  of  the  mean  flow 
there.  The  rates  of  energy  production  and  dissipation  in  these  two 
regions  are  much  larger  than  those  anywhere  else  in  the  flow.  This 
implies  that  the  distribution  and  the  magnitude  of  the  turbulent 
charge  should  be  nearly  independent  of  the  weaker  motion  in  the 
center  of  the  channel,  and  they  should  be  determined  by  the  gross 
energetics  and  the  geometry  of  the  wall.  In  figure  (16)  we  present 
the  spatial  distribution  of  the  turbulent  charge,  in  the  case  of  a 
flat  smooth  wall.  It  should  be  noted  that  even  without  averaging, 
the  distribution  of  the  turbulent  charge  does  not  change  in  time, 
it  is  only  its  magnitude  that  varies  in  time.  This  is  essentially  a 
numerical  verification  of  our  plausible  qualitative  argument  given 
above. 


100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 


Figure  16:  Mean  profile  of  the  turbulent  charge  in  the  channel 
(Re=5000).  We  measure  the  normal  distance  in  wall  units  and 
show  only  half  the  channel. 

The  question  that  naturally  arises  is:  How  do  geometric 
modifications  of  the  wall  change  the  turbulent  charge  distribution 
?  We  can  show  analytically  that  if  we  require  the  enstrophy,  i.e. 
u ;2  and  the  strophokinesis,  i.e.  I2,  to  be  finite  along  the  tips  of 
the  riblets,  then  the  vorticity  and  the  Lamb  vector  will  behave 
singularly  at  these  tips.  This  is  confirmed  in  figure  (17)  where  the 
turbulent  charge  is  again  calculated  and  shown  to  be  concentrated 
at  the  tips  of  the  riblets.  This  means  that  most  of  the  dissipation 
takes  place  in  the  neighborhood  of  the  tips,  since  the  turbulent 
charge  achieve  its  maximum  negative  value  there.  The  areas  of 
positive  charge  just  above  the  tips  drain  the  kinetic  energy  from 
the  mean  flow  and  pass  it  to  the  areas  of  negative  charge  at  the 
tips. 


Figure  17:  Turbulent  charge  distributions  over  the  streamwise 
riblets. 


The  same  figure  shows  two  different  cases,  one  where  the 
drag  is  reduced  (case  A)  and  another  where  the  drag  is  increased 
(case  B).  Can  we  explain,  at  least  qualitatively,  the  different  ef¬ 
fect  of  the  riblets  on  the  drag  by  examining  the  structure  of  the 


turbulent  charge?  We  believe  that  the  answer  is  affirmative.  The 
reason  is  that,  although  both  cases  exhibit  the  singular  behaviour 
at  the  tips,  the  case  where  the  drag  is  reduced  exhibits  a  “cloud” 
of  negative  charge  that  bridges  the  maxima  of  the  neighboring 
tips  and  consequently  it  hides  the  valleys  of  the  riblets  from  the 
rest  of  the  flow.  This  layer  of  negative  charge  that  covers  the 
riblets  forms  a  pseudo-wall,  so  to  speak,  and  essentially  reduces 
the  height  of  the  channel.  Moreover,  the  average  thickness  of 
this  negative  layer  is  greater  than  the  one  that  corresponds  to 
a  flat  wall.  This  means  that  the  Reynolds  number  has  been  ef¬ 
fectively  reduced.  On  the  other  hand,  the  case  where  drag  has 
increased  is  lacking  this  negative  cloud.  Therefore,  the  effectively 
laminar  canals  formed  by  the  valleys  of  the  riblets  and  the  neg¬ 
ative  cloud,  in  the  drag  reducing  case,  do  not  exist  here.  This 
implies  that  the  kinetic  energy  accumulated  above  the  tips  can  be 
disposed  of  between  the  riblets,  in  the  valleys.  In  fact,  the  situa¬ 
tion  is  even  worst  in  the  cases  where  the  singularity  increases  so 
much  that  the  Reynolds  number  is  effectively  increased.  A  rule 
of  thumb,  according  to  the  above  analysis,  would  be  as  follows: 
Edges  are  good  (i.e.  drag  reducing)  if  they  can  form  a  uniform 
layer  of  negative  turbulent  charge  whose  thickness  is  greater,  and 
its  magnitude  is  smaller,  than  their  corresponding  quantities  in 
the  flat  wall  case.  For  this  to  be  accomplished,  the  key  parame¬ 
ters  are  the  angle  of  the  edge  at  the  tip  and  the  spacing  between 
the  tips.  The  angle  determines  the  magnitude  of  the  singularity, 
which  is  worst  for  the  degenerate  case  of  a  one- dimensional  riblet 
and  decreases  monotonically  as  the  angle  between  the  sides  of  the 
riblet  increases.  These  conclusions  are  supported  by  experimental 
evidence  [5]. 

VI.  SUMMARY 

We  have  presented  two  different  scenarios  regarding  the  na¬ 
ture  of  turbulent  drag  reduction  in  wall-bounded  flows  with  ri¬ 
blets.  The  first  is  related  to  the  decomposition  of  the  Lamb  vec¬ 
tor  into  two  components  and  their  relation  to  the  Reynolds  stress 
.tensor.  This  analysis  suggests  that  the  stretching  term  is 

the  dominant  contribution  to  the  drag  force.  It  also  provides  an 
explanation  regarding  the  role  of  bumps  and  dents  to  the  shear 
stress  distribution.  Bumps  like  the  tips  of  the  riblets  increase 
locally  the  shear  stress  (X3  <  0  whereas  dents  like  the  valleys 
decrease  it  (T3  >  0). 

The  second  scenario  involves  the  concept  of  turbulent 
charge,  i.e.  V  •  1.  This  quantity  identifies  the  regions  of  space 
where  most  of  the  energy  is  dissipated  and  the  regions  of  space 
where  most  of  the  turbulent  kinetic  energy  is  generated.  The  spa¬ 
tial  distribution  of  this  quantity  is  very  simple  and  therefore  it  is 
simple  to  model.  Drag  reduction  is  associated  with  a  redistribu¬ 
tion  of  the  turbulent  charge  due  to  the  geometrical  modifications. 
A  reasonable  argument  on  why  this  happens  has  been  given  and 
found  to  be  in  agreement  with  experiments.  The  advantage  of 
the  latter  approach  is  that  study  of  local  solutions  for  a  particu¬ 
lar  geometry  can  give  an  immediate  answer  and  lead  to  an  opti¬ 
mization  algorithm  regarding  the  best  (i.e.  most  drag  reducing) 
geometrical  shape. 

Acknowledgments 

This  work  was  partially  supported  by  the  Department 
of  Energy  and  the  National  Science  Foundation.  Computations 
were  performed  on  the  IBM  SP2  at  the  Cornell  Theory  Center, 
the  Maui  High  Performance  Computing  Center,  and  the  Center 
for  Fluid  Mechanics  at  Brown  University. 


105 


References 

[1]  ACARLAR,  M.S.  Sc  Smith,  C.R.  1987a  A  study  of  hairpin 
vortices  in  a  laminar  boundary  layer.  Part  1.  Hairpin  vortices 
generated  by  a  hemisphere  proturbance.  J.  Fluid  Mech.  175, 
1. 

[2]  Acarlar,  M.S.  Sc  Smith,  C.R.  1987b  A  study  of  hairpin 
vortices  in  a  laminar  boundary  layer.  Part  2.  Hairpin  vortices 
generated  by  fluid  injection.  J .  Fluid  Mech.  175,  43. 

[3]  Antonia,  R.A.,  Teitel,  M.,Kim,  J.  Sc  Browne,  L.W.B. 
1992  Low-Reynolds  number  effects  in  a  fully  developed  tur¬ 
bulent  channel  flow.  J .  Fluid  Mech.  236,  579. 

[4]  Antonia,  R.A.  Sc  Kim,  J.  1994  Low- Reynolds-numb er  effects 
on  near- wall  turbulence.  J.  Fluid  Mech.  276,  61. 

[5]  Bechert,  D.  W.  &  Bartenwerfer,  M.  The  viscous  flow  on 
surfaces  with  longitudinal  ribs,  J.  Fluid  Mech.  206,  105-129.. 

[6]  Bernard,  P.S.,  Thomas,  J.M.  Sc  Handler,  R.A.  1993  Vor¬ 
tex  dynamics  and  the  production  of  Reynolds  stress.  J.  Fluid 
Mech.  253,  385. 

[7]  Brown,  G.L.  Sc  Thomas,  A.S.W.  1977  Large  structure  in  a 
turbulent  boundary  layer.  Phys.  Fluids  10,  S243. 

[8]  Choi,  H.,  Moin,  P.  Sc  Kim,  J.  1993  Direct  numerical  simu¬ 
lation  of  turbulent  flow  over  riblets.  J.  Fluid  Mech.  255,  455. 

[9]  CHOI,  K.S.  1989  Near- wall  structure  of  a  turbulent  boundary 
layer  with  riblets.  J.  Fluid  Mech.  208,  417. 

[10]  Choi,  K.S.  1993  Turbulence  structure  revisited;  Results  and 
implications  from  riblets  research.  In  International  Conference 
on  Near- Wall  Turbulent  Flows.  Tempe,  Arizona,  eds.  Speziale, 
C.G.  Sc  Launder,  B.E. 

[11]  Chu,  D.C.  Sc  Karniadakis,  G.E.  1991  Numerical  investi¬ 
gation  of  drag  reduction  in  flow  over  surfaces  with  streamwise 
aligned  riblets.  AIAA-91-0518. 

[12]  CHU,  D.C.  Sc  Karniadakis,  G.E.  1993  The  direct  numerical 
simulation  of  laminar  and  turbulent  flow  over  riblets.  J.  Fluid 
Mech.  250,  1. 

[13]  COLES  D.E.  1978  A  model  for  flow  in  the  viscous  sublayer. 
Coherent  Structures  of  Turbulent  Boundary  Layers ,  (ed.  C.R. 
Smith  Sc  D.E.  Abbot).  AFOSR/Lehigh  University  Workshop, 
Dept,  of  Mech.  Engng.  Sc  Mech.,  Bethlehem,  PA. 

[14]  Crawford,  C.H.  1994  The  structure  and  statistics  of  tur¬ 
bulent  flow  over  riblets.  M.S.E.  Thesis  Princeton  University. 

[15]  Crawford,  C.H.,  Evangelinos,  C.,  Newman,  D.J.  Sc 
Karniadakis,  G.E.  1995  Parallel  benchmarks  of  turbulence 
in  complex  geometries.  Presented  at  Parallel  CFD  1995  and 
Computer  and  Fluids ,  vol.  25,  p.  677,  1996. 

[16]  Crawford,  C.H.  1996  Direct  numerical  simulation  of  near¬ 
wall  turbulence:  Active  and  passive  control.  PhD  Dissertation , 
Princeton  University. 

[17]  Crawford,  C.H.  Sc  Karniadakis,  G.E.  1997  Reynolds 
stress  analysis  of  EMHD-controlled  wall  turbulence:  Part  I: 
Streamwise  forcing.  Physics  of  Fluids,  9(3),  788. 

[18]  DEISSLER,  R.G.  1969  Direction  of  maximum  turbulent  vor- 
ticity  in  shear  flow.  Phys.  Fluids.  12,  426. 

[19]  Goldstein,  D.,  Handler,  R.  Sc  Sirovich,  L.  1995  Direct 
numerical  simulation  of  turbulent  flow  over  a  modeled  riblet 
covered  surface.  J.  Fluid  Mech.  302,  333. 

[20]  HAIDARI,  A.H.  Sc  Smith,  C.R.  1994  The  generation  and  re¬ 
generation  of  single  haipin  vortices.  J.  Fluid  Mech.  277,  135. 

[21]  Hama,  F.R.  1962  Progressive  deformation  of  a  curved  vortex 
filament  by  its  own  induction.  Phys.  Fluids  5,  1156. 

[22]  Head,  M.R.  Sc  BANDYOPADHYAY,  P.R.  1981  New  aspects  of 
turbulent  boundary  layer  structure.  J.  Fluid  Meek.  107,  297. 

[23]  Hussain,  A.K.M.F.  1986  Coherent  structures  and  turbu¬ 
lence  J.  Fluid  Mech.  173,  303-356. 

[24]  Henderson,  R.D.&  Karniadakis,  G.E.  1995  Unstructured 
spectral  element  methods  for  simulation  of  turbulent  flows. 
J.  Comp.  Phys.  122,  191. 


[25]  Kasagi,  N.,  Sumitani,  Y.,  Suzuki,  Y.  Sc  Iida,  O.  1995 
Kinematics  of  the  quasi- coherent  vortical  structure  in  near¬ 
wall  turbulence.  Int.  J.  Heat  and  Fluid  Flow  16,  2. 

[26]  Kida,  S.  Sc  Tanaka,  M.  1994  Dynamics  of  vortical  struc¬ 
tures  in  a  homogeneous  shear  flow  J.  Fluid  Meek.  274,  43. 

[27]  Kim,  J.  &  Moin,  P.  1986  The  structure  of  the  vorticity  field 
in  turbulent  channel  flow.  Part  2.  Study  of  ensemble  average 
fields.  J.  Fluid  Mech.  162,  339. 

[28]  Kim,  J.,  Moin,  P.  Sc  Moser,  R.  1987  Turbulence  statis¬ 
tics  in  fully  developed  channel  flow  at  low  Reynolds  number. 
J.  Fluid  Meek.  177,  133. 

[29]  KLEWICKI,  J.C.  1989  Velocity- vorticity  correlations  related 
to  the  gradients  of  Reynolds  stresses  in  parallel  turbulent  wall 
flows.  Phys.  Fluids  1,  1285. 

[30]  Kline,  S.J.  Sc  Robinson,  S.K.  1989  Quasi- coherent  struc¬ 
tures  in  the  turbulent  boundary  layer.  Part  1,  Status  report  on 
a  community- wide  summary  of  the  data.  In  Near  Wall  Turbu¬ 
lence.  eds.  Kline,  S.J.  Sc  Afgan,  N.H. 

[31]  Kraichnan,  R.H.  Sc  Panda,  R.  1988  Depression  of  nonlin¬ 
earity  in  decaying  isotropic  turbulence,  Phys.  Fluids  31,  2395. 

[32]  Launder,  B.E.  Sc  Li,  S.-P.  1992  A  prediction  of  riblet  be¬ 
havior  with  a  low-Reynolds  number  k-e  model.  Aeronautical 
Journal  November  1992,  354. 

[33]  Liu,  K.N.,  Christodoulou,  C.,  Riccius,  O.  Sc  Joseph 
D.D.  1990  Drag  reduction  in  pipes  lined  with  riblets.  A I  A  A 
J.  28,  1967. 

[34]  MARMANIS,  H.  1998  Analogy  between  the  Navier-Stokes 
equations  and  Maxwell’s  equations:  Application  to  turbulence, 
Phys.  Fluids  (in  print) 

[35]  MOIN,  P.  Sc  Kim,  J.  1985  The  structure  of  the  vorticity  field 
in  turbulent  channel  flow.  Part  1.  Analysis  of  instantaneous 
fields  and  statistical  correlations.  J.  Fluid  Mech.  155,  441. 

[36]  Park,  S.-R.  Sc  Wallace,  J.M.  1993  Flow  field  alteration 
and  viscous  drag  reduction  by  riblets  in  a  turbulent  boundary 
layer.  AIAA-93-3256. 

[37]  Perry,  A.E.,  LlM,  K.L.  Sc  Henbest  S.M.  1987  An  experi¬ 
mental  study  of  the  turbulence  structure  in  smooth-  and  rough- 
wall  boundary  layers.  J.  Fluid  Mech.  177,  437. 

[38]  Rajaee,  M.,  Karlsson,  S.  Sc  Sirovich,  L.  1995  On  the 
streak  spacing  and  vortex  roll  size  in  a  turbulent  diannel  flow. 
Phys.  Fluids  7,  2439. 

[39]  Robinson,  S.K.  1991  Coherent  motions  in  the  turbulent 
boundary  layer.  Ann.  Rev.  Fluid  Mech.  23,  601. 

[40]  Sherwin,  S.J.  Sc  Karniadakis,  G.E.  1995  A  triangular 
spectral  element  method;  Applications  to  the  incompressible 
Navier-Stokes  equations.  Comp.  Meth.  Appl.  Meek.  Engr ., 
123,  189. 

[41]  Smith,  C.R.  Sc  Metzler,  S.P.  1983  The  characteristics  of 
low-speed  streaks  in  the  near- wall  region  of  a  turbulent  bound¬ 
ary  layer.  J.  Fluid  Meek.,  129,  27. 

[42]  Smith,  C.R.  1996  Coherent  flow  structures  in  smooth  wall 
turbulent  boundary  layers:  Facts,  Mechanisms,  and  Specu¬ 
lation.  In  Coherent  Flow  Structures  in  Open  Channels ,  eds. 
Ashworth,  P.J.,  Bennett,  S.J.,  Best,  J.L.  Sc  McLelland,  S.J. 
John  Wiley  &  Sons  Ltd.,  1. 

[43]  SREENIVASAN,  K.R.  1990  The  turbulent  boundary  layer.  In 
Frontiers  in  Experimental  Fluid  Mechanics,  ed.  Gad-el-Hak, 
M.,  159. 

[44]  Suzuki,  Y.  Sc  Kasagi,  N.  1993  Drag  reduction  mechanism 
on  micro-grooved  riblet  surface.  In  International  Conference 
on  Near-  Wall  Turbulent  Flows.  Tempe,  Arizona,  eds.  Speziale, 
C.G.  Sc  Launder,  B.E. 

[45]  Taylor,  G.I.  1932  Diffusion  by  continuous  movements.  In 
Proceedings  of  ike  London  Mathematical  Society,  Series  2.  20. 

[46]  TENNEKES,  H.  Sc  Lumley,  J.L.  1972  A  First  Course  in  Tur¬ 
bulence.  The  MIT  Press. 


106 


[47]  THEODORSEN,  T.  1952  Mechanism  of  turbulence.  In  Proceed¬ 
ings  of  the  2nd  Midwestern  Conference  on  Fluid  Mechanics, 
Bull  No.  129.  Ohio  State  University,  Columbus,  Ohio. 

[48]  Townsend,  A.  A.  1976  The  Structure  of  Turbulent  Shear 
Flow.  Cambridge  University  Press. 

[49]  V UKOSLAVCEVIC,  P.,  WALLACE*  J.M.  &  BALINT,  J.-L.  1992 
Viscous  drag  reduction  using  streamwise  aligned  riblets.  AIAA 
J.  30,  1119. 

[50]  Wallace,  J.M.,  Eckelmann,  H.  &  Brodkey,  R.S.  1972 
The  wall  region  in  turbulent  shear  flow.  J.  Fluid  Meek.  54,  39. 

[51]  Wallace,  J.M.  1982  On  the  structure  of  bounded  turbulent 
shear  flow:  A  personal  view.  Developments  in  Theoretical  and 
Applied  Mechanics,  XI,  509. 

[52]  Walsh,  M.J.  1990  Riblets.  In  Viscous  Drag  Reduction  in 
Boundary  Layers,  Progress  in  Astronautics  and  Aeronautics. 
eds.  Bushnell,  D.  &  Hefner,  J.  123  203. 

[53]  WEI,  T.  &:  Willmarth,  W.W.  1989  Reynolds- number  ef¬ 
fects  in  the  structure  of  turbulent  flow.  J.  Fluid  Mech.  204, 
57. 

[54]  Willmarth,  W.W.  &  Tu,  B.J.  1967  Structure  of  turbulence 
in  the  boundary  layer  near  the  wall.  Phys.  Fluids  10,  S134. 

[55]  Wu,  J.Z.,  ZHOU,  Y.  &:  Wu,  J.M.  1996  Reduced  stress  ten¬ 
sor  and  dissipation  and  the  transport  of  Lamb  vector,  I  CASE 
Rept.  96-21. 


107 


ROLE  OF  HELICITY  AND  CHIRALITY  IN  DRAG  REDUCTION  IN  TURBULENT  FLOWS 


S.  Moiseev,  H.  Branover*,  O.  Chkhetiani,  A.  Eidelman*,  E.  Golbraikh* 

Space  Research  Institute,  Profsoyuznaya  st.,  84/32, 117810  Moscow,  Russia 
moiseev@mx.iki.rssi.ru 

^Center  for  MHD  Studies,  Ben-Gurion  University  of  the  Negev,  P.O.B.653,  Beer-Sheva  84105,  Israel 

eidel@bgumail.bgu.ac.il 

Abstract  -  The  behavior  of  Reynolds  stresses  in  the  mean  velocity  equation  of  a  turbulent  flow  is  studied.  We  have  derived  an 
expression  of  turbulent  viscosity  for  the  case  where  the  initial  small-scale  turbulence  is  helical.  The  helicity  decreasing 
turbulent  viscosity  leads  to  a  slow-down  of  the  direct  energy  transfer  and  to  the  formation  of  an  inverse  one.  Formation  of 
intermittent  mode  of  helical  turbulence  leading  to  the  localization  of  turbulent  regions,  as  observed  in  wakes,  is  also  studied. 
This  effect  is  enhanced  in  magnetohydrodynamic  flows  under  an  external  magnetic  field.  We  also  discuss  general  problems 
connected  with  so  called  chirality  and  its  consequences  for  turbulent  motions.  The  studied  phenomena  alter  energy  transfer  and 
dissipation  in  turbulent  seawater  and  affect  hydrodynamic  drag  of  moving  bodies. 


1.  Introduction 

An  essential  drag  reduction  in  turbulent  liquid  flow  with  small 
amounts  of  certain  polymers  was  observed  about  50  years  [1].  Further 
investigations  have  shown  a  considerable  drag  reduction  when  adding 
2.5-10  ppm  of  certain  polymers  [2]  or  2-3  orders  larger  amount  of 
surfactants  [3]  to  the  liquid  flow.  Although  the  properties  of  the  two 
mentioned  additives  are  rather  different,  their  common  basic  property 
is  an  ultimate  drag  reduction  value  reaching  ~  60-70%  in  both  cases! 
Note  that  drag  reduction  is  also  achievable,  if  the  turbulence  is 
affected  in  an  entirely  different  way,  namely,  in  magneto¬ 
hydrodynamic  (MHD)  flow.  In  this  case,  turbulence  control  is  realized 
at  the  expense  of  electromagnetic  forces  arising  at  the  interaction  of  a 
conductive  liquid  flow  with  the  magnetic  field.  Here,  just  as  in  case  of 
additives,  the  same  drag  reduction  value  of  60-70%  is  achievable  [4, 
5].  MHD  flow  investigated  at  a  laboratory  represents  a  convenient 
object  for  studying  the  properties  of  flows  with  a  reduced  drag. 

Since  it  is  just  in  the  boundary  layer,  not  far  from  the  wall,  that  the 
main  part  of  turbulence  energy  is  generated  and  dissipated,  -  the 
understanding  of  the  processes  in  this  flow  region  represents  the  key 
to  the  problem.  Visual  observations,  beginning  with  [6,  7],  point  to  a 
helical  character  of  motion  in  this  region.  Recent  progress  in  the  study 
of  helical  turbulence  makes  it  possible  to  develop  an  adequate 
physical  model  and,  hence,  a  mathematical  description  of  the 
influence  of  drag  reducing  additives  on  the  turbulent  motion. 

Not  only  visual  studies  demonstrating  the  helical  character  of  the 
motion,  but  also  important  integral  properties  of  flows  with  reduced 
drag,  inherent  to  helical  turbulence,  are  considered  below.  Changes  in 
the  shape  of  turbulence  spectrum  caused  by  a  decrease  in  the  small- 
scale  motion  energy  and  growth  of  the  large-scale  motion  energy, 
which  are  observed  in  drag-reduced  flows,  are  also  inherent  to  helical 
turbulence  due  to  the  inverse  energy  transfer  [8].  The  decrease  in 
Reynolds  stresses  noted  in  drag-reduced  flows  is  also  characteristic  of 
helical  turbulence  possessing  a  reduced  effective  viscosity  [9]. 

Despite  a  large  number  of  encouraging  experiments,  the  absence  of 
an  adequate  physical  model  prevents  a  significant  progress  in  this 
field.  This  circumstance  negatively  affects  the  attempts  of  using 
geometrical  means  of  turbulence  control,  such  as  riblets  and  outer 
boundary  layer  (OBL)  devices.  Riblets  lead  to  a  drag  reduction  of 
<10%  in  case  of  a  successful  choice  of  their  parameters.  But  we 
should  emphasize  an  encouraging  result  reported  in  [10]:  turbulent 
friction  on  the  surface  located  downstream  in  the  vicinity  of  OBL 
device  was  reduced  by  50%.  However,  in  this  and  other  experiments, 
the  change  in  net  friction  losses  including  OBL  device  overflow  losses 
fluctuate  about  zero.  The  study  of  OBL  devices  action  on  turbulent 
friction  gives  qualitatively  different  results  even  within  the  same 
laboratory.  We  believe  that  the  understanding  of  helical  turbulence 
properties  will  make  the  basis  of  more  efficient  decisions  in 
turbulence  control  by  geometrical  means. 

2.  Turbulent  viscosity 

Helical  turbulence  occupies  a  special  position  among  the  variety  of 
turbulent  motions.  Helicity 


v 


(here  u  is  the  velocity  and  co  =  rot  u  is  the  vorticity),  being  a  second 
invariant  of  Euler's  equation,  just  as  energy  [1 1],  has  a  great  influence 


on  the  evolution  and  stability  of  turbulent  and  laminar  flows  [12]. 
Apparently,  helicity  is  one  of  the  main  sources  of  magnetic  fields 
generation  and  maintaining  in  astrophysical  objects  [13].  Possibly, 
helical  mechanism  is  responsible  for  the  generation  of  some  intense 
large-scale  geophysical  vortices,  such  as  typhoons  and  tornado  [14, 
15]. 

Many  properties  of  systems,  having  helicity  are  explained  by  that 
the  last  effectively  reduces  action  of  nonlinear  processes  responsible 
for  the  transfer  and  the  redistribution  of  energy  between  various 
scales. 

Numerous  investigations  of  the  properties  of  helical  turbulence 
[16,  17]  also  demonstrate  that  non-zero  helicity  leads  to  the 
decrease  in  the  energy  flux  from  large  to  small  scales.  One  of  the 
principal  parameters  connected  with  the  energy  flux  from  larger  to 
smaller  scales  is  turbulent  viscosity.  Hence,  its  magnitude  should 
decrease  with  decreasing  direct  energy  cascade.  Additionally,  the 
decrease  of  energy  transfer  should  lead  to  another  energy 
redistribution  between  different  scales  involved  in  turbulent 
motions. 

To  study  mean  helicity  effect  on  turbulent  viscosity  value  in  a 
flow,  we  consider  incompressible  turbulent  fluid  flow  and  examine 
the  stability  of  initial  turbulent  field  u(())  with  zero  mean  flow  to  the 
weak  large-scale  inhomogeneous  disturbances.  We  write  the  total 
perturbed  velocity  u  as  a  sum  u  =  <u>  +  u(0)+  u(t),  where  <u>  is  the 
mean  part  of  the  disturbance  and  u(1>  is  the  fluctuational  part  of 
disturbance,  with  u(l)  «  u(0),  <u>  «  <(u(l)>)2>,/2.  One  can  derive  a 
system  of  equations  for  u(1)and  u(0)from  the  Navier-Stokes  equation 
for  the  total  velocity  u 

du  1 

— -^Au  =  -- Vp  -  (u  •  Vu)  +  F 
V  •  u  =  0 

where  p  is  pressure,  F  is  an  external  force,  p  and  v  are,  respectively, 
the  fluid  density  and  viscosity. 

The  evolution  of  the  initial  turbulent  field  u(0)  is  described  by 
equations 

^  u<»>-,Au<°)=  (1) 

_Ivp<°>+F<°> 

P 

V-u(o)=0,  (u<°>)=0. 

where  p(l,)  =  p  -  <p>  -  p(l>  is  the  initial  pressure  fluctuation  and  F<0)  = 
F  -  <F>,  <F(0)>  =  0  is  the  external  random  force  sustaining  the 
turbulent  field.  Correlational  properties  of  u<(,)  we’ll  discuss  later. 

For  weak  disturbances  of  the  velocity  we  have  linearized 
equations: 

?£>— „A(u>  =  — iv6»-  (2) 

((u<°)  •  V)u(1))  -  ((u(1>  •  V)u(0))  +  (F) , 

V  •  (u)  =0, 


109 


^-„AuW  = 

dt 

_IVpW  -  ((u)  •  V)  u(0)  -  (u'°>  •  v)  (u» 

-( (u(°>  •  v)  u(1)  +  (u'1’  •  V )  u<°>  (3) 

-  ((u<°>  •  V)u(1))  -  ((u^  •  V)u(0))), 


Let  us  make  the  following  substitution  of  coordinates: 
x  — ►  x  ■+*  £,  x— *  x  4-  x;/— *  x, 

+  +  t"  ->r 

then  d/dxt  -±d/d£>i  and  we  derive  an  expression  for  the  third"  moment 
from  the  equation  (5): 

Qi™(x  +  £,t  +  r,x  +  £',t  +  r',  x,  t)  = 


V-u(l)=0  .(u(1))  =° 

where  <p>,  p(1)  are  average  pressure  and  a  weak  disturbance  of  the 
pressure,  respectively. 

Let  us  introduce  the  following  notations 

Q?V,t',x,t)  =  (u^(x',t')uf\x,t)) 
Q}f(x',t',x,t)  =  (i4l)(x',t><0)(x,t)) 


Ql™(Z,T,Z',T',X,t)  = 

-T’ V*nim(<3“  (C,  r,  r')Q$(£,  r,  x,  t) 

+Qmj(Z,  n  x,  ■  r,  c',  r')+ 


.(6) 


QfP(^r,«',r')<3“(e,r,x,t)+ 


4%(&T,x,t)<]*p(e,T,ert) 

Here  nim  =  8im  -  is  the  projection  operator.  Relaxation  time 

t*  can  be  estimated  as: 


QijH(x",t",x',t',X,t)  =  (u[  l)(x",t")uf\x>lt')u]°\x,t)) 


r* 


(J-Lturf E 


1/2 
tur  i 


To  study  the  behavior  of  Reynold's  stress  tensor  and  turbulent 
viscosity,  we  apply  the  procedure  suggested  by  Krause  and  Rudiger 
[18].  Multiplying  (3)  by  u<0)  (x\  t')  and  averaging,  we  obtain: 

£-((uk(x,t))Q™(x,t,x',t')  (4) 

+  (ui(x,i)>Qjg(x,  t,x',t'))— 

^(QL°°(x.  t,  X,  t,.x',  t')  +  Qi™(x,  t,  X.  t,  x', «')) 

where  Pjl()(x,  t,  x',  t')  =  <p(l)(x,  t)  u/0)(x\  t')>. 

The  equation  of  the  third  moments  may  be  derived  in  a  similar  way. 
For  the  sake  of  simplicity,  we  assume  hereinafter  that  the  original 
turbulence  is  of  Gaussian  character.  In  this  case 

(|-*A  )QW(x,4,x',i',x".t")  = 

^  (*>  t,  x,  t,  x',  i',  x",  f")+  (5) 

Ql°°°(x,t,x,t,x',t',x",t"))- 
(Qi°(x,  t,x,  t)  +  Qjf.?(x,  t, X,  f))0“(x',  i',  x",  t")\ 

Here 

/%"(*,  «,  <'>(?< ‘>(x,  t)4V.  t><0)(x",  t"))- 

The  account  for  the  correlation  time  finit'eness  in  turbulence  may  be 
realized  in  various  ways  leading  to  similar  results.  In  the  present 
paper,  an  analog  of  Orszag  approximation  [19]  studied  by  Vainshtein 
in  the  theory  of  MHD-dynamo  [13,  20]  for  the  second  moments  has 
been  applied  to  close  the  series  of  equations  (4). 

Fourth  order  correlation  moments  can  be  represented  as  a  sum: 


where  L,ur  is  the  integral  scale  of  turbulence,  EIuf  is  the  mean  energy 
of  turbulent  motion,  p  is  a  constant.  Relaxation  time  is  a  open 
parameter  here,  but  under  simplifying  assumptions,  it  can  be 
determined  from  the  functional  equation  [20].  In  the  present 
problem,  turbulence  is  affected  by  a  weak  large-scale  disturbance 
becoming  weakly  inhomogeneous  and  weakly  anisotropic. 
Turbulent  relaxation  time  is  less  that  the  characteristic  evolution 
time  of  perturbation,  so  a  quasi  stationary  moments  distribution  is 
established  in  the  system.  In  this  paper  this  question  is  not 
discussed. 

Additionally,  we  have  noted  that  analogous  closure  methods  are 
used  in  phenomenological  theories  of  turbulence  [20,  21,  22],  It 
turns  out  that  the  3rd  order  moments  calculated  in  this 
approximation  describe  correlation  properties  of  different  turbulent 
flows  with  the  same  value  of  numeric  constant  p  *  0.44  [22], 

The  equation  (4)  for  the  second  moments  contains  a  combination 
Vp(Qipj100  +  Qpij100),  and  since  Vpnpm  =  0,  the  term  involving  third 
moments  will  be  of  the  following  form 

r‘ V* Vpnim(Q“  (£,  r,  r0Q°*°(£,  r,  x,  t) 

+Qm,(f  >  T,  X,  T,  T,)  + 

<2itP(£.  T,  (?,  T,  x,  t)+  (7) 

Ql°(€,  T,  X,  4)Q“p(£,  r,  r')) 

We  assume  that  the  external  random  force  F(0)  has  sustained  the 
initial  small-scale  turbulent  field  u(0)  in  stationary  state  with  the 
properties  of  homogeneity,  isotropy  and  non-zero  helicity.  The 
extremely  interesting  problem  of  the  mirror  symmetry  breaking  in 
fluid  dynamics  we  did  not  discuss  in  this  paper.  In  this  case  a  two- 
point  correlator  Q™  (x,  t,  x)  has  the  following  form  [23] 

Q°f  (x,  t,  r)  =  A(i,  T)6ij+  (8) 

£  =  |x  —  x'|  ,T  =  |f  —  t'l  • 

where  Sijk.  is  an  entirely  antisymmetric  tensor.  A(^,  x),  B(^,  x)  are 
scalar  functions.  C(^,  x)  is  a  pseudoscalar  function  (C(£|,  x)  =  -C(|- 
^|,  x)).  Applying  the  incompressibility  condition  (3)  and  taking  into 
account  that 


Q‘°(x,t,x,t)Q0p°(x',t',x",t")+ 

Q,p(x>  x’>  t')Qk°(x’ t*  x"< f") 
+Q}°(X,  t,  x",  t")Q°k°p(x,  t,  x',  t')+ 
Q!kpj(x,  *■<  x,  x'<  x",  t")cum, 

where  Q,kB,'“K,(x,  t,  x,  t,  x',  t',  x",  is  a  cumulant. 


-e,r-  r\_(y_T-,A(0, 0 )Skp  (9) 

VkQ°°p «  _t— >C(0, 0)e„,* 

we  obtain  from  (7)  the  following  expression  at  t,'  %  and  x'  x 

transition; 


110 


T*nim(VfcQi?p(^,  r,  €,  r)VpQ^(4,  r,  x,  t)+  (10) 

A<3mi(^'r.X,t)-4(0,0)  + 
Q%(t,T,t,T)VkVp<%i(t,T,X,t)  + 
C(0,0)empkVrQl°(e,T,x,t)) 

Assuming  that  spatial  and  temporal  scales  of  the  mean 
inhomogeneity  exceed  greatly  the  turbulent  field  correlation  length 
and  time,  we  may  take  Taylor  series  expansions  of  Qy10(5,  x,  x)  and 
<Ui(5,  t)>  in  powers  of  Restricting  ourselves  by  the  first  order 
terms,  we  obtain 


In  particular, 

^(0,0)  =  J  Ef(k,0)dk,  (16) 

£(0,0)  =  !  J  H/(k'  ®dk 

As  Eq.  (13)  shows,  helicity,  in  fact,  decreases  turbulent  viscosity. 

Considering  the  correlator's  time  dependence  in  the  form 
(pxCOr)exp(-(3|T|),  where  both  Tcor  and  x*  are  determined  by  the 
characteristic  scale  and  the  energy  of  turbulent  motion,  we  obtain, 
after  integrating  with  respect  to  time 


Qi°(£,T,£,r)  =  0  )+(i- 


dQ$(x,t,  0,0) 
dxi 


(11) 


r  fl  ■  fr'Tcr  7  (2 Ef(k)Mk*+fl  +  aH,(k)) 

‘  1  15  J  {is?k2  +  j3)2-a2k2  J 

ktur 


(Ui(x  +  £,t  +  T))  =  (Ui(x,t))+( , 


d(iti(x,  t)) 
dxi 


Substituting  (11)  into  (10),  and  the  result  of  it  -  into  (4),  we  derive 
the  equation  for  the  second  moments 


(^7  -  ("  +  v<t)^‘)^ik  -  a£ipkVp 


Ql°M’T,x,t)  = 


K(x,i))VpQ?°(tr.x,0- 

(Ui(x,  t ))  r,  X,  t)- 

^2;.v,«S(S,nx,,)+ 

r’V»{  J-<5S(x,  0)aj;M,  r,x,  I) 

dQl°Jx,t,0, 0) 

+  V>(e.Qg(€,r,x,0) 

+Q1k°p(x,t,OlO)VkQ$(t,T,x,t)} 


(12) 


where  v,°  =  A(0,  0)x*  and  a  =  C(0,  0)x*. 

A  similar  equation  arises  in  the  theory  of  magnetic  dynamo,  when 
using  Klyatskin-Tatarski's  method  [21].  However,  in  the  present  case, 
additional  terms  arise  in  the  right-hand  part,  proportional  to  one-point 
moments  of  disturbed  turbulence.  They  make  the  problem 
self-consistent. 

Solving  Eq.  (12)  for  Qjj,0(x,  t,  0,  0)  one  obtains  the  following 
expression  for  turbulent  viscosity  (coefficient  at  A<u>): 

"t  =  {i+ 


2  (0tcot) 

— 5 -  J  {[£>M  (17) 

\tf*+m(W+0)2  -  ^-T1- 

«*[§*/(*)  -  jk^ir-M^+p)2  -  a2k2\-i}dk 

It  can  be  easily  shown  that  the  transition  to  6-correlated  process  (p 
-»  oo)  under  the  condition  of  finite  Tcor  and  x*  does  not  result  in  the 
disappearance  of  the  helicity  contribution  to  the  turbulent  viscosity, 
as  it  would  be  in  case  of  initially  postulated  5-correlated  character. 
It  is  finite  and  determined  by  intrinsic  turbulence  characteristics. 

3.  Intermittency  in  helical  turbulent  flow 

It  is  well-known  that  turbulent  wakes  at  the  motion  of  bodies  in 
seawater  persist  for  a  long  time.  Below  we  consider  one  of  possible 
mechanisms  of  turbulent  wakes  formation  in  the  presence  of  non¬ 
zero  helicity  and  its  fluctuations.  According  to  the  theory  of  mean 
magnetic  field  generation  in  the  mode  of  so  called  rapid  dynamo 
[24],  preferential  growth  of  higher  moments  of  the  velocity  and 
magnetic  field  fluctuations  lead  to  large-scale  field  breaking.  This 
phenomenon  is  observed,  for  instance,  in  the  velocity  field  of 
magnetohydrodynamic  helical  turbulence  [29]. 

On  the  other  hand,  since  seawater  represents  a  heavily  stratified 
medium,  and  at  the  overflow  of  bodies  strong  shear  flows  are 
formed  in  it,  we  can  say  that  equations  for  mean  velocity  fields  are 
formally  similar  to  equations  of  dynamo  type.  In  fact,  an  equation  of 
a  vortex  co  =  rot  u  in  an  incompressible  fluid 

—  rot[v  x  tj]  +  ul\u  (18) 


oo  oo 

—  J  J  exp(— Vth2r)(2Ef{k,  r)Ch(akr) 

kc  nr  0 

^Mhllsh(akT))dkdr}-1  x 

OO  CO 

|  J  J exp(-i/t°fc2r)  {[£/(*:,  r)  (13) 

klnt.  0 

kdEr(k,  r),  f  . 

3  dk  ~  Ch(a^r) — 


2£^r)  _  l^M]sh(afcr)}cffcdT 

3  k  b.  ok 

where  EKk,  x)  and  Hf(k,  x)  are  related  to  symmetric  and  antisymmetric 
parts  of  Fourier-transform  of  the  undisturbed  turbulence  correlator 


fioolk  r\  _  Ef(k'T)(g..  _  Mi) 
Qij  (K,rl-  4jrfc2  1.2  > 


k2 


. Hf(k,T )  , 


where 


\Hf(k,T)\<2kEf(k,T). 


(14) 


(15) 


is  formally  similar  to  magnetic  field  equation 

^2  =  rot[v  x  B]  +  £>AB  (19) 

at 

However,  as  noted  in  [13],  the  formal  similarity  of  these 
equations  does  not  imply  identical  behavior  of  o)  and  B.  On  the 
other  hand,  in  an  inhomogeneous  helical  medium  of  seawater  type, 
dynamo-type  equation  can  also  take  place,  i.e. 

=C  rot  {u)+vA(u )  (20) 

at 

If  the  helicity  in  a  given  system  is  fluctuating,  then  it  is  necessary 
to  study  in  this  case  the  influence  of  so  called  multiplicative  noise 
on  the  evolution  of  the  non-equilibrium  system  [25],  Systems  with 
multiplicative  noise  include  those  where  random  fluctuations  of  the 
system  parameters  at  the  expense  of  external  energy  multiplied  by 
some  magnitude  Characterizing  the  state  of  the  system  exert  the 
most  considerable  influence.  If  we  present  helicity  in  Equation  (20) 
in  the  form  C  =  C0  +  C,  where  C  are  helicity  fluctuations,  then  the 
equation 

^M  =  (C0  +  C')r0i(u)  +  ^A(u)  (21) 

at 

will  also  fall  into  the  category  of  equations  with  multiplicative 
noise.  We  can  readily  show  that  the  equation  (21)  leads  to  the 


111 


following  expression  for  higher  moments  (of  the  order  of  n)  of  the 
velocity  field 

I  n  n  n  \ 

*(££11  ue(rot  u) /(rot  u )gJ 

\|=lm=l/=l  / 

/*« 

g^m 

where  D  is  defined  as  <  C'(t)  C'(t')>  =  D8(t  - t'),  and  for  the  chosen 
velocity  component 

^  (u")  ~  Dn2  (u"~2(V jUk)(V jUk))  (23) 

i.e.  higher  moments  grow  proportionally  to  the  square  of  their  order. 

As  established  in  [24],  preferential  growth  of  higher  moments  of  a 
random  velocity  field  represents  a  transition  of  a  turbulent  field  to 
intermittency,  i.e.  to  breaking.  Thus,  the  expression  (23)  points  out 
that  the  presence  of  helicity  fluctuations  leads  the  system  to  an 
intermittent  turbulent  field.  Simultaneously,  as  shown  earlier, 
turbulent  viscosity  in  the  present  system  decreases,  which  also 
contributes  to  intermittency  enhancement. 

Thus,  in  case  of  bodies  moving  in  seawater,  we  should  emphasize 
the  following:  if  a  wake  with  a  fluctuating  mean  helicity  can  be 
formed  behind  the  body,  then  it  should  be  expected  that  the  turbulent 
wake  will  become  strongly  intermittent  just  due  to  helical  turbulence 
properties. 

One  of  promising  trends  in  the  study  of  seawater  as  a  medium  with 
peculiar  symmetry  properties  is  the  study  of  its  chiral  properties. 

The  chirality  phenomenon  is  connected  with  a  global  violation  of 
mirror  symmetry  in  a  system  under  study.  In  this  sense,  helicity  is  a 
particular  case  of  chirality.  Chirality  is  a  wide-spread  property 
observed  in  quantum  physics  and  in  solid  state  physics.  It  is 
noteworthy  that  chirality  is  intrinsically  present  in  practically  all 
organic  substances,  including  living  matter.  Chirality  of  seawater 
results  from  the  latter.  In  fact,  it  is  well-known  that  seawater  contains 
a  large  amount  of  biomass,  which  imparts  chiral  properties  to 
seawater.  On  the  other  hand,  salts  containing  in 
seawater  make  it  a  well-conductive  medium.  As  is  known  [26],  at  the 
interaction  of  media  without  a  symmetry  center  with  an  external 
source  of  light,  current  structures  are  formed  in  a  conductive  medium. 
In  turn,  as  demonstrated  in  [27],  chiral  conducting  turbulent  medium 
(in  any  case,  the  seawater  surface  layer)  may  lead  to  the  growth  of 
mean  electric  field.  On  the  other  hand,  the  same  currents  generate  a 
ponderomotive  force,  which  forms  nonzero  mean  helicity  in  a 
turbulent  medium  [28].  Hence,  due  to  chiral  properties  of  seawater,  it 
can  be  practically  always  considered  helical  in  the  surface  layer. 
Motions  of  bodies  in  it  represent  large-scale  disturbances,  and  we, 
thus,  come  back  to  the  problems  discussed  in  the  previous  sections. 

4.  Conclusion 

We  have  computed  turbulent  viscosity  of  a  flow  involving  small- 
scale  helical  turbulence  and  a  weak  large-scale  disturbance.  When 
computing  higher  moments,  finite  correlation  time  is  taken  into 
account  within  Orszag’s  approximation.  It  is  shown  that  in  this  case 
turbulent  viscosity  is 
considerably  decreased  in  the  mean  flow. 

One  of  helical  turbulence  modes  is  intermittent.  This  mode  is 
realized  at  the  increase  of  helicity  of  motion  and  its  fluctuations.  Such 
a  mode  of  flow  entails  preferential  growth  of  higher  velocity  moments 
and  localization  of  turbulent  regions. 

The  study  of  these  phenomena  directly  affects  the  mode  of 
turbulent  motions  changing  their  structure  and,  hence,  energy  transfer 
and  dissipation  determining  hydrodynamic  drag. 

References 

1.  Toms,  B.A.  1949.  Some  observations  on  the  flow  of  linear 
polymer  solutions  through  straight  tubes  at  large  Reynolds  numbers. 
Proc.  of  the  1st  Internat.  Rheology  Congress,  II,  Part  2  (North- 
Holland,  Netherlands),  135-142. 

2.  McComb,  W.D.  and  Rabie,  L.H.  1982.  Local  drag  reduction  due 
to  injection  of  polymer  solutions  into  turbulent  flow  in  a  pipe.  Part  1 : 
Dependence  on  local  polymer  concentration.  Part  2:  Laser-Doppler 
measurements  of  turbulent  structure.  AIChE  J.,  v.  28,  547-565. 

3.  Dobrychenko,  V.M.,  Lobachev,  V.G.,  Povkh,  I.L.  and  Eidelman, 
A.E.  1976.  Drag  reduction  by  liquid  thickening  surfactant  admixtures. 


J.  of  Engineereing  Physics,  v.  30,  No.  2.  Transl.  of:  Inzhenemo- 
Fizicheskii  Zhumal,  v.  30,  No.  2,  240-245. 

4.  Klebanoff,  P.S.  and  McMichael,  J.M.  1976.  On  MHD  pipe 
flow.  Proc.  Bat-Sheva  Intemat.  Seminar  on  MHD-FIows  and 
Turbulence,  Beer-Sheva.  John  Wiley,  N.Y.,  p.  73. 

5.  Branover,  H.  1978.  Magnetohydrodynamic  flow  in  ducts.  J. 
Wiley  &  Sons,  N.Y.,  290  pp 

6.  Corino,  E.R.  and  Brodkey,  R.S.  1969.  A  visual  investigation  of 
the  wall  region  in  turbulent  flow.  J.  Fluid  Mech.,  v.  37,  p.  1,  1-30. 

7.  Kline,  S.J.,  Reynolds,  W.C.,  Schraub,  F.A.  and  Runstadler, 
P.W.  1967.  The  structure  of  turbulent  boundary  layers.  J.  Fluid 
Mech.,  v.  30,  p.  4,  741-773. 

8.  Chkhetiani,  O.G.,  Moiseev,  S.S.,  Petrosyan,  A.S.  and  Sagdeev, 
R.Z.  1993.  The  inverse  energy  cascade  and  self-organization  in 
homogeneous  turbulent  shear  flow.  Applied  Sci.  Research,  v.  51, 
67-72. 

9.  Belyan,  A.V.,  Moiseev,  S.S.  and  Chkhetiani,  O.G.  1994.  On 
turbulent  viscosity  in  helical  turbulence.  Dokl.  Akad.  Nauk,  v.  334, 
No.  1,34-36. 

10.  Yajnik,  K.  S.  and  Acharaya,  M.  1976.  Structure  and 
mechanisms  of  turbulence,  Vol.  1,  Lecture  notes  in  Physics  76 
(Springer,  N.Y.),  p.  249  (from  Balakumar,  P.  and  Widnall,  S.E., 
1986). 

11.  Moffatt,  H.K.  1969.  The  degree  of  knottedness  of  tangled 
vortex  lines.  J.  Fluid  Mech.,  v.  35,  p.  1,  1 17-129. 

12.  Moffatt,  H.K.,  Tsinober,  A.  1992.  Helicity  in  laminar  and 
turbulent  flow.  Annu.  Rev.  Fluid  Mech.,  v.  24,  281  -312. 

13.  Vainstein,  S.N.,  Zeldovich,  Ya.B.  and  Ruzmaikin,  A. A.  1980. 
Turbulent  Dynamo  in  Astrophysics.  Moscow:\  Nauka  (in  Russian). 

14.  Moiseev,  S.S.,  Sagdeev,  R.Z.,  Tur,  A.V.,  Khomenko,  G.A. 
and  Yanovskii,  V.V.  1983.  Theory  of  the  origin  of  large-scale 
structures  in  hydrodynamic  turbulence.  Sov.  Phys.  JETP,  v.  58,  No 
6,1149-1153. 

15.  Khomenko,  G.A.,  Moiseev,  S.S.  and  Tur,  A.V.  1991.  The 
hydrodynamical  alpha-effect  in  a  compressible  medium.  J.  Fluid 
Mech.  v.  225,  355-369. 

16.  Chkhetiani,  O.G.,  Moiseev,  S.S.,  Petrosyan,  A.S.  and 
Sagdeev,  R.Z.  1994.  The  large  scale  stability  and  self-organization 
in  homogeneous  turbulent  shear  flow.  Physica  Scripta,  v.  49,  214  - 
220. 

17.  Levich,  E.,  Shtilman,  L.and  Tur,  A.V.  1991.  The  origin  of 
coherence  in  hydrodynamical  turbulence.  Physica  A,  v.  176,  241- 
296. 

18.  Krause,  F.  and  Rudiger,  G.  1974.  On  the  Reynolds  stresses  in 
mean-field  hydrodynamics.  I.  Incompressible  homogeneous 
isotropic  turbulence.  Astron.  Nachr.,  v.  295,  No.  2,  93-99. 

19.  Orszag,  S.A.  1970.  Analytical  theories  of  turbulence.  J.  Fluid 
Mech.,  v.  41,  p.  2,  363-386. 

20.  Vainshtein,  S.I.  1983.  Magnetic  fields  in  space.  Moscow: 
Nauka,  (in  Russian). 

21.  Klyatskin,  V.I.  and  Tatarsky,  V.I.  1972.  Statistical  theory  of 
the  light  propagation  in  turbulent  medium.  Izv.  VUZov. 
Radiofizika,  v.  15,  1433-1442. 

22.  Launder,  B.E.,  Reece,  G.J.  and  Rodi,  W.  1975.  Progress  in 
the  development  of  a  Reynolds-stress  turbulence  closure.  J.  Fluid 
Mech.,  v.  68,  p.  3,  537-566 

23.  Batchelor,  G.K.  1953,  The  theory  of  homogeneous 
turbulence.  Cambridge  Univ.  Press,  L. 

24.  Molchanov,  S.A.,  Ruzmaikin,  A.A.  and  Sokolov,  D.D.  1985. 
Kinematic  dynamo  in  a  random  flow.  Sov.  Phys.:  Uspekhi,  v.  145, 
No.  4,  593-627. 

25.  Moiseev,  S.S.,  Chkhetiani,  O.G.  and  Shavva,  1. 1.  1990.  On 
the  effects  of  fluctuational  ’’negative  viscosity"  in  some  problems  of 
plasma  physics  and  hydrodynamics".  Preprint  of  Space  Research 
Institute  No.  1667. 

26.  Sturman.  B.I.  and  Fridkin,  V.M.  1992.  Photogalvanic  effect 
in  media  without  a  symmetry  center  and  related  phenomena", 
Moscow,  ’’Nauka’',  208  pp. 

27.  Belyan,  A.V.,  Moiseev,  S.S.,  Pungin,  V.G.  and  Chkhetiani, 
O.G.  1997.  Anomalous  growth  of  electric  fields  in  a  chiral  medium. 
Moscow,  Space  Research  Institute  Preprint  No.  1999. 

28.  Chkhetiani,  O.G.,  Moiseev,  S.S. and  Golbraikh,  E.  1997.  On 
helicity  generation  in  shear  turbulent  MHD\  flows  (in  press,  JETP) 

29.  Eidelman,  A.,  Branover,  H.,  Golbraikh,  E.  and  Moiseev  S. 
MHD  turbulence  experiments,  drag  reduction  and  application  to 
non-MHD  experiments.  Proc.  Seawater  Drag  Reduction  Symp. 


112 


METHODS  OF  INFLUENCE  ON  COHERENT  VORTICAL  STRUCTURES  OF  A  BOUNDARY  LAYER 


Viktor  V.  Babenko 

Department  of  Hydrobionics  and  Boundary  Layer  Control,  Professor, 
Dr.Tech.Sc.,  Head  of  Department,  8/4,  Zheliabov  str.,  252057,  Kiev,  Ukraine, 
E-mail:  vb@bionics.kiev.ua 

A  study  was  made  of  the  mechanisms  of  coherent  structure  formation  in 
boundary  layer  during  laminar-turbulent  transition.  Coherent  structure  features 
under  mentioned  types  of  external  disturbabces  are  analyzed.  A  special  attention 
was  payed  to  the  study  of  the  vortex  form  character.  There  were  elicited  three 
forms  of  vorticity  associated  with  the  characteristic  stages  of  a  traditional 
boundary  layer.  A  model  of  the  disturbing  motion  development  for 
characteristic  transition  stages  with  and  without  mentioned  disturbing  factors  is 
presented.  Similar  to  the  vortex  development  in  a  transitional  boundary  layer 
there  were  considered  disturbance  structures  in  a  wall  region  of  the  turbulent 
boundary  layer.  Mechanisms  of  the  coherent  structure  development  and 
interaction  along  the  boundary  layer  thickness  were  investigated.  A  table 
accumulates  some  methods  of  the  active  control  of  the  bo-undary  layer  flow 
character  including  local  separations  and  separating  flows.  They  are  methods  of 
coherent  structure  introduction  and  control,  methods  of  wall  jets  including  the 
polymer  solution  delivery,  vibration  methods,  plane  oscillation  methods. 
Experiments  were  carried  out  using  tellurium-method,  thermo-  and  laser 
anemometry  both  for  a  flat  plate  in  a  low-turbulence  hydrodynamic  bench  and 
for  three-dimensional  bodies. 


Actual  problem  is  study  of  regularities  of  coherent  structures 
generation  in  turbulent  boundary  layer  and  determination  of 
mutual  influence  of  vortical  coherent  structures  in  near-wall  and 
outer  regions.  Such  research  permits  us  to  substantiate  the 
mechanisms  of  control  of  coherent  structures  in  boundary  layer, 
on  which  basis  one  can  work  out  the  methods  of  their  control.  It 
is  known  fact  that  turbulence  production  in  boundary  layer  exists 
mainly  in  near-wall  region  which  coherent  structures  are 
characterized  by  stastically  alternated  in  transverse  direction 
longitudinal  areas  of  low-speed  and  high-speed  fluid.  In  near-wall 
region  there  are  other  coherent  formations  like  "pockets"  and 
Kline's  vortices  too.  However,  still  here  is  not  clear  understanding 
of  spatial  character  of  the  coherent  structures  and  their 
dependence  both  between  each  other  and  on  coherent  structures 
of  outer  part  of  boundary  layeris  subjected  to  disturbances  of 
difeerent  type  from  outer  and  inner  boundaries.  Let  the 
disturbances  to  be  called  deteriorating  factors  in  comparison  with 
idealized  conditions  for  flat  palte  flowing  by  indisturbed  flow. 
The  basic  idea  of  present  investigations  is  based  on  resukts  of 
experimental  research  that  have  allow  us  to  put  forward  the 
hypothesis  that  viscous  sublayer  of  turbulent  boundary  layer  can 
be  represented  as  quasi-laminar  boundary  layer.  In  1980  we  put 
forward  the  hypothesis  [1]  that  in  viscous  sublayer  of  turbulent 
boundary  layer  development  of  coherent  structures  happens 
approximately  in  the  same  way  as  in  transitional  boundary  layer 
with  influence  of  deteriorating  factors.  Since  measuring  in  viscous 
sublayer  is  difficult  then  taking  into  account  mentioned 
hypothesis  it  is  enough  to  learn  the  development  of  coherent 
structures  in  transitional  boundary  layer  when  it  is  subjected  to 
influence  of  deteriorating  factor,  for  example  in  form  of  increased 
turbulence  of  free  stream  and  vibration  of  flowing  surface. 
Really,  increased  vortical  disturbances,  which  are  in  outer  part 
and  in  the  core  of  turbulent  boundary  layer,  influence  the  viscous 
sublayer  from  iuter  side.  To  model  this  situation  one  should,  in 
transitional  boundary  layer,  create  the  increased  turbulence  of 
free  stream  or  disturb  outer  boundary  layer  by  plane  of  three- 
dimensional  finite  disturbances.  From  another  side,  permanent 
bursts  of  deccelerated  fluid  from  viscous  sublayer  create  as  if  the 
extra  disturbances  from  the  lower  boundary  of  viscous  sublayer. 
This  may  be  modelled  in  transitional  boundary  layer  by  means  of 
generation  of  vibration  of  flowing  boundary. 

This  fundamental  idea  is  being  illustrated  on  fig.  1 .  In  lower 
part  of  the  figure  there  is  schematic  picture  of  structure  of 
development  of  disturbing  motion  at  different  stages  of 
transitional  boundary  layer  development.  Shown  in  viscous 
sublayer  of  turbulent  boundary  layer  is  disturbances  development 


pattern  which  is  analog  to  and  characteristic  for  transitional 
boundary  layer.  Besides,  through  the  thickness  of  turbulent 
boundary  layer  there  are  generated  three  areas  of  coherent 
vortical  structures.  This  is  large  vortices  in  outer  part,  ordered 
vortical  systems  in  buffer  zone  and  systems  of  vortices  in  viscous 
sublayer. 

In  upper  part  of  the  figure  there  is  distribution  of  friction 
coefficient  corresponding  to  vortical  coherent  structures  of 
boundary  layer  at  different  stages  of  transition.  Dotted  lines 
denote  measurements  of  longitudinal  pulsative  velosity  at 
different  stages  of  transition  by  other  authors.  We  see  that  data 
on  upper  picture  correlate  well  with  development  of  coherent 
vortical  structures  at  different  stages  of  transition.  Hence  it  may 
be  suggested  that  controlling  vortical  coherent  structures  one  can 
influence  the  integral  and  fluctuative  characteristics  of  boundary 
layer. 

Except  the  idea  of  structural  character  of  disturbances 
development  at  different  stages  of  transition,  the  idea  of  influence 
the  frequency  characteristics  of  oredered  vortical  structures  lays 
in  the  base  of  control  methods  development.  As  we  said  before, 
fluid  particle  has  dual  property  of  its  motion:  it  moves  along  a 
definite  trajectory  and  has  a  spectrum  of  oscillatios  during 
motion  where  one  can  separate  the  definite  energy-carrying 
frequencies  for  each  stage  of  transition  or  for  every  type  of 
coherent  vortical  structures. 

In  accordance  with  these  two  approaches  the  methods  of 
influence  the  coherent  vortical  structures  have  been  elaboreted. 
As  the  principal  factor  (third  approach  or  principle  of  influence), 
the  influence  energy  must  be  of  the  same  order  as  the  energy  and 
dimension  of  disturbing  motion  at  corresponding  stage  of 
transition.  In  table  there  are  having  been  developed  methods 
consisted  of  seven  groups:  mechanical  (I),  dynamic  (II),  kinematic 
(III),  electric  (IY),  acoustical  (Y),  combined  (YI)  and  active  ones 
with  feedback  system  (YII).  Let  consider  mechanic  methods. 
Oscillating  surface  has  to  contribute  to  ordering  or  damping  the 
corresponding  vortical  structures.  Oscillated  my  be  the  part  of  the 
surface,  for  example  forepart. 

Transverse  projections  or  indentations  are  intended  to 
generate  transverse  vortexes  which  have  the  axis  of  rotation  in 
transverse  direction. 

Longitudinal  projections  or  indentations  are  intended  for 
generation  of  longitudinal  vortices.  The  most  studied  for  those 
purposes  are  riblets  of  different  type. 

Longitidinal  stationare  vortex-generators  differ  from  riblets 
by  discreteness  of  longitudinal  size  and  variety  of  forms. 


113 


Methods  of  influence  on  the  cohrent  structures  of  boundary  layer 


114 


Longitudinal  oscillatory  vortex -generators  differ  from  previons 
ones  by  ability  of  dynamic  influence  the  boundary  layer. 

Ordered  roughness  serves  for  the  same  goals:  organization 
of  longitudinal  and  transverse  vortices. 

Lunes  are  new  little-studied  method  of  influence  the  vortical 
structure  of  biundary  layer.  Depending  on  task  setted,  the  lunes 
may  be  arranged  in  longitudinal  or  transverse  order. 

Change  of  shape  of  surface  flowed  around  may  be  either 
cyclic  or  stationary.  Stationary  plates  may  be  put  into  the 
boundary  layer  in  order  to  destroy  the  large-scale  vortices.  As  an 
example  of  such  plates,  there  are  LEBU  that  is  rings  mounted 
equidistantly  from  flowed  cylindric  surface. 

Oscillatory  paltes  are  the  oscillatory  LEBU.  Dynamic 
methods  are  based  on  principle  of  mass  transfer  and  differ  from 
known  ones  by  that  that  influence  is  fulfilled  on  the  part  of  flowed 
surface.  Concerned  to  those  methods  is  slot,  perforate  or 
distributed  suction  of  boundary  layer. 

Injection  or  blow  in  to  the  boundary  layer  are  made  on 
discrete  parts  too.  Injection  may  be  done  by  means  of  blowing  the 
stratified  or  uniform  fluids  as  well  as  water  solution  of  polymer, 
surfactants  and  chemically  active  fluid.  Method  of  injection  may 
differ  from  each  other  in  particular  jet-method  or  using  Coanda 
effect. 

Kinematic  methods  are  based  on  principle  of  momentum 
transfer.  They  consists  of  injection  as  in  previous  case,  mounting 
discrete  surface  cavitators,  regulation  of  temperature  of  flowed 
surface  by  heating  or  resulting  from  chemical  reactions  with  free 
stream  fluid.  Separate  class  is  elastic-damping  surfaces:  one-layer 
o  multi-layer,  isotropic  or  not,  passive  or  active. 

Related  to  electric  methods  are  setting  ion  flux  in  boundary 
layer  and  generation  of  electro-magnetic  field  around  the  flowed 
body  in  case  of  small  conductivity  of  free  stream  fluid.  Acoustical 
methods  may  be  distributed  or  concentrated.  These  methods  are 
based  on  principle  of  generation  of  additional  pulsative  specially 
directed  field  of  pressure. 

The  most  perspective  are  combined  methods  which  use 
simultaneously  the  combination  of  different  considered  methods 
and/or  combination  with  active  methods  of  control. 

Some  of  methods  considered  have  been  studied 
experimentally. 

MEASURING  METHODS  OF  BOUNDARY  LAYER 
PARAMETERS 

Boundary  layer  velocity  field  is  visualized  with  tellurium 
method  [3]  and  with  coloured  streaks.  Velocity  measurements  are 
carried  out  with  the  laser  Doppler  anemometer  (LDA)  and  DISA 
thermoanemometer  [2]. 

The  hydrodynamic  bench,  equipment  and  devices  are 
described  in  Fig.  2. 

A  low-turbulence  hydrodynamic  test  bench  comprises 
special  equipment  and  devices.  The  following  are  the  basic 
technical  data  of  the  test  bench:  length  of  test  bench  7  m,  length  of 
test  section  3  m,  cross-section  of  test  section  0.09x0.25  m,  range  of 
operating  speeds  0.05-5-1.5  m/sec,  effuser  contraction  factor  equal 
to  10.  Mounted  on  the  test  bench  are  the  following  main  devices: 
a  duplex  bottom  of  the  test  section,  a  removable  cover  of  the  test 
section.  The  test  bench  is  equipped  with  a  boundary-layer  bleed  in 
the  corners  of  the  test  section.  The  cover  of  the  test  section  can  be 
tilted  to  various  angles  and  rails  are  laid  out  along  the  test  section, 
over  which  the  car  with  special  apparatus,  LDA  and  DISA 
moves. 

Small  oscillations  of  various  types  were  introduced  into  the 
boundary  layer  with  the  help  of  specially  designed  oscillators  for 
measuring  neutral  oscillations.  Supports  were  arranged  further 
downstream,  making  it  possible  to  obtain  small  tellurium  jets.  The 
oscillator  vibrational  frequency  changes  in  the  course  of  the 
experiment,  the  amplitude  of  the  tellurium  jet  oscillations  being 
recorded. 

The  method  of  investigation  of  natural  transition  at 
nonlinear  stages  consists  in  the  following.  First  of  all  a  boundary 
layer  is  examined  in  different  aspects  with  the  tellurium  method 
along  the  test  section. 

Simultaneus  photography  of  velocity  profiles  in  vertical  and 
transverse  directions  and  also  of  longitudinal  tellurim  small  jets 
gives  the  possibility  to  construct  the  spatial-temporary  picture  of 
exciting  motion  and  velocity  field  during  different  stages  of 
transition. 

Analysis  of  profiles  U(z)  gives  the  possibility  for  determining 
the  characteristic  points  along  y  and  z  axes  where  the  boundary 
layer  kinematic  parameters  are  measured  with  LDA  and  DISA. 


All  these  measurements  are  made  under  a  low  turbulence  level 
(s<0,05%). 

PHYSICAL  PATTERN  OF  STAGES  OF  LAMINAR- 
TURBULENT  BOUNDARY  LAYER  TRANSITION 

We  have  the  large  enough  amount  of  experimental  data  in 
order  to  conclude  that  at  the  low  turbulence  level  the  transition 
process  is  characterised  by  the  succesive  change  of  disturbing 
motion  types.  The  model  of  this  succession  was  developed 
(Fig.  $  )  on  the  basis  of  the  study  of  the  natural  boundary  layer 
transition  and  the  well-known  results  of  Knapp  and  Roach, 
Klebanoff  and  oth.,  Tani,  Morkovin,  Kline  and  many  others.  The 
wave  transformation  process  during  transition  to  turbulence  can 
be  devided  into  the  following  stages  (Fig.  3): 

-  plane  disturbances  amplification; 

-  wave  modulation  in  phase  -  three-dimensional  effect 
emergency; 

-  generation  of  the  longitudinal  rows  of  A-shaped  vortices; 

-  arrangement  of  the  longitudinal  vortex  system; 

-  transformation  of  votices  in  form  and  intensity,  indulation  of 
vortices; 

-  breakdown  of  peripherical  parts  of  undulating  vortices; 
generation  of  turbulent  spots,  their  growth  confluence  and 
turbulent  boundary  layer  development. 

At  present  there  are  two  concepts  explaining  the  successive 
development  of  the  transition  process: 

-  it  is  defined  by  modes  development  and  interaction  in  a 
boundary  layer; 

-  it  is  defined  by  the  vortex  filaments  behaviour. 

Both  concepts  are  reasonable  -  the  conditions  and 
mechanism  of  their  interaction  are  discussed  in  detail  in  my  book. 

Small  particle  of  liquid  contains  double  information 
concerning  its  movement: 

-  as  the  vibrating  element  it  is  characterized  by  frequency-wave 
and  other  parameters; 

-  as  the  moving  element  it  is  characterized  by  vorticity,  i.e.  by 
the  trajectory  of  its  movement. 

In  any  case  it  is  necessary  also  to  analyse  the  structure  of 
disturbances:  for  example,  the  form  of  linear  and  nonlinear 
waves,  the  form  and  direction  of  vortices  and,  besides,  the 
disturbing  motion  intensity. 

FORMATION  OF  THREE-DIMENSION  DISTURBANCES 
IN  A  BOUNDARY  LAYER  OF  FLAT  PLATES  WITH 
VARIOUS  PROPERTIES 

According  to  results  shown  in  [2],  it  is  obvious,  that  the 
allocated  way  of  longitudinal  vortical  systems  formation  in  a 
boundary  layer  (BL)  will  be  effective  at  concurrence  of  sizes  and 
intensity  of  generated  and  natural  disturbances.  The  longitudinal 
wire  and  the  stripes  covering  them  still  created  additional 
roughness  in  [2],  and  to  some  extent,  their  influence  on  BL  was 
similar  to  action  of  riblets. 

It  is  expediently  to  increase  intensity  of  influence  of  these 
stripes  on  the  BL,  not  increasing  at  that  their  hydraulic 
roughness.  Results  of  numerous  experience  with  riblets  of  the 
various  form  are  widely  known.  Two  other  ways,  different  from 
riblet,  raising  intensity  of  influence  on  the  BL  are  offered  below. 

One  of  them  consists  in  weak  heating  of  longitudinal  wires. 
The  other  one  consists  in  using  of  a  composite  elastic  plate,  an 
outside  layer  of  which  made  in  form  of  longitudinal  alternating 
strips  with  the  various  modules  of  elasticity. 

Before  estimation  of  a  boundary  layer  reaction  on  periodic 
on  z  structure  of  plates,  influence  to  a  flow  of  a  similar  plate  10 
made  from  the  similar  material  as  outside  layers  of  plates  7  was 
investigated  with  the  help  of  visualization.  The  simultaneous 
visualization  of  three  jets  in  a  plane  xz  has  shown  extremely  stable 
it's  behavior  along  the  whole  plate.  The  jets  parallelism  of  a 
streamline  surface  was  not  practically  broken  even  at  passage 
them  through  a  lattice  of  vortex  generators  Bl  (d).  A  small  jets 
closing  among  themselves  is  visible  in  a  plane  xz  on  x=0,4  m,  that 
is  displayed  irrespective  of  presence  or  absence  of  vortex 
generators. 

The  visualization  of  natural  distribution  of  U(z)  has  also 
reflected  the  specific  character  of  disturbances  development.  If  a 
undulation  of  a  structure  U(z)  is  fully  displayed  on  a  rigid  surface 
at  Re»M05  ,  here  it  is  poorly  planned  only  at  distance  from  a 
wall.  The  maximum  bend  of  a  tellurium  cloud  is  observed  at 
y=0,01  m  »5/2;  the  further  influence  of  a  wall  becomes  weaker 
together  with  reduction  of  intensity  of  a  disturbing  movement.  It 
is  necessary  to  note  small  speeds  of  three-dimension  disturbances 


115 


increasing,  that  is  expressed  in  an  extremely  weak  stretching  of 
tellurium  clouds  at  moving  them  downwards  on  a  flow.  The 
opposite  effect  was  observed  at  a  flow  over  the  membrane  surface 
not  having  a  damping  properties.  The  reduction  of  speeds  of  flat 
disturbances  increasing  in  a  boundary  layer  of  damping  surfaces 
[2]  was  found  out  at  research  of  linear  stability. 

It  is  possible  to  conclude  from  here,  that  the  elastic  surfaces 
with  large  factor  of  damping  interfere  with  the  fast  changes  of  the 
kinematics  characteristics  of  a  flow  bypassed  them.  This  effect  is 
similar  to  one  found  out  at  a  rigid  ribbed  surface  allocated 
influence  on  a  boundary  layer. 

The  similar  results  are  received  for  a  plate  7,  a  with  a  cross 
regularity  of  properties:  the  dark  longitudinal  strips  correspond  to 
edges  of  rigidity  of  about  2*1  O'4  m  height  on  fig.  4  (d-h).  The  first 
three  photos  (a-c)  characterize  a  field  of  current  before  an  elastic 
insert  (Re=  1,1-1 05),  the  other  -  over  it  (Re=l,4105).  It  is  visible, 
that  even  at  greater  Reynolds  number  the  distortion  of  a  current 
fields  less  over  the  insert.  At  the  tellurium  cloud  movement  in 
direct  affinity  from  a  plate  a  small-scale  toothed  is  not  displayed 
in  it,  that  was  observed  at  visualization  in  a  case  of  a  rigid  ribbed 
surface.  Apparently,  the  distinction  in  mechanical  properties  of 
longitudinal  strips  in  aggregate  with  microroughness  or  ribbing  of 
a  surface  appears  the  insufficient  reason  for  creation  of  vortical 
system  type  disturbances  in  a  boundary  layer  at  the  specified 
values  of  Re  and  Xy. 

At  the  analysis  of  received  results  it  is  necessary  to  mean  the 
fact  concerning  to  specificity  of  measurements.  Oscillatory 
movements  in  a  plane  of  xz  characteristic  for  a  stage  of  nonlinear 
disturbances  development,  result  in  fact  that  the  statistically 
average  parameters  are  registered  in  vertical  planes  of  structures 
u‘(y)  and  U(y)  measurement.  The  visualization  of  U(z)  frequently 
shows  the  wavy  lines  displacement  on  z  with  compelled  length  of 
a  wave.  At  accepted  geometry  of  ribbed  plates  with  rather  narrow 
longitudinal  paths,  the  change  of  kinematics  parameters  over 
them  can  be  fixed  both  by  strengthening  of  distinction  between 
properties  of  strips,  or,  probably,  by  increasing  their  width. 

In  this  connection  the  heating  of  rigid  edges  of  a  plate  7,  a 
was  undertaken  with  the  help  of  an  electrical  current.  It  is 
necessary  to  note,  that  the  rubbery  materials  in  the  best  way 
correspond  to  the  purpose  of  experiment  owing  to  their  high  heat- 
insulating  qualities:  the  preservation  of  a  positive  difference  of 
temperatures  between  edges  and  elastomer  will  create  the  regular 


on  z  change  of  kinematics  parameters  of  a  boundary  layer, 
connected  to  occurrence  of  convection  flows  along  edges  (change 
of  8,  u\  U,  speeds  values  of  distribution  and  increase  of 
disturbances).  Besides,  it  was  specified,  that  the  absorbing  ability 
of  soft  rubbers  decreases  with  growth  of  temperature,  that  should 
also  stimulate  formation  of  three-dimensional  disturbances  with 
set  parameters.  However,  at  a  movement  of  a  tellurium  cloud  over 
a  plate,  peculiarities  of  current  are  accumulated  in  it  and  a 
waviness  with  Xz=0,012m  is  displayed  at  absence  of  fluctuations 
or  it’s  moving  on  z.  The  influence  of  an  elastic  plate  is  expressed 
above  usually  in  an  alignment  of  a  structure  U(z).  The  further 
heating  forms  such  powerful  field  of  disturbances  that  there  is  the 
erosion  of  clouds  in  irregular  longitudinal  bunches  at  once  behind 
a  tellurium  wire. 

Thus,  experiments  have  shown  the  longitudinal 
reinforcement  of  a  streamline  surface  with  a  small  step  X7<& 
reduces  non-uniformity  of  kinematics  parameters  of  a  boundary 
layer  in  TpaHCBepcaJibHOM  direction  at  the  expense  of  primary 
orientation  of  a  disturbances  field  lengthways  x.  It  follows  from 
increase  of  u'  in  aggregate  with  results  of  current  on  z 
visualization:  the  absence  of  a  small-scale  regularity  of  tellurium 
lines  speaks  about  reduction  of  v',  that  is  naturally  caused  by 
damping  properties  of  a  streamline  surface;  the  termination  of  an 
oscillatory  movement  on  z  -  about  reduction  of  w\  Heating  of 
reinforced  elements  creates  conditions  for  formation  and 
maintenance  of  longitudinal  vorteces  system,  which,  however, 
differs  from  smaller  intensity  similar  to  one  on  a  rigid  surface:  the 
compelled  periodicity  on  z  of  a  tellurium  line  is  displayed  at 
moving  it  downwards  a  flow,  at  least,  on  twice  greater  distance 
than  on  a  rigid  ribbed  surface. 

Further  on  it  is  necessary  to  continue  study  of  proposed 
mechanism  of  influence  the  coherent  vortical  structures. 

REFERENCES 

1.  Babenko  V.  V.tfOn  interection  of  flow  with  elastic  surface^ 
Mechanisms  of  turbulent  flow,  Moskow:  Nauka.  1980,  p.  292- 
301. 

2.  Babenko  V.  V.,  Kanarsky  M.  V.,  Korobov  V.V^Boundary  layer 
on  elastic  plates?  Kiev,  Naukova  dumka,  1993  -  264  p. 

3.  Wortmann  F.  X.  Eine  Methode  zur  Beobachtung  und  Messung 
von  Wasserstromung  mit  Tellur.  -Z.  Fur  Angew.  Phys.^  1953,  5, 
No 6,  -s.  200-206. 


116 


Figure  2 .  The  sketch  of  the  hydrodynamic  channel  test  section  with  devices 

1  -  the  te/st  section;  2  —  vortex  generators;  3,4  -  tellurium 
wire  with  a  holder,  5  -  anode  (visualization  system)  ,  6,7  - 

photor eg i s trati on  system,  8-11  -  mOving  truck  with  devices, 
12-19  -  system  of  laser  anemoptry. 


118 


LL  •=> 


^*6-3  The?  physical  model  of  the  disturbances  type  successive  transformation  during  the  tran¬ 
sition  to  turbulence:  a  —  amplification  of  plane  disturbances;  b  —  phase  modulation  of  the 
wave,  three-dimensional  effects  appearance;  v  —  amplitude  modulation  of  the  wave,  ’’peaks” 
and  ’’valleys”  forming,  formation  of  longitudinal  rows  of  A  —  shaped  vortices;  d  —  organiza¬ 
tion  of  the  longitudinal  vorteces  system,  e  --  vorteccs  form  and  intensity  changes  in  space  and 
time;  transition  to  a  zigzag  trajectory  of  the  vorteces  movement;  breakdown  of  peripherical 
parts  of  the  meandering  vortices.  Active  formation  of  turbulent  spots,  their  growth,  amalga¬ 
mation  and  turbulent  boundary  layer  development, 


119 


Visualization  of  U(z)  at  U«,=0.05  m/s  before  a  plate  7a:  x=1.6  m;  y=0.002  m 
(a),  0.004  m  (b),  0.008  m  (c);  and  over  it:  x=2.18  m;  y=0.002  m  (d),  0.004  m 
(e),  0.006  m  (f),  0.008  m  (g),  0.01  m  (h). 


DRAG  REDUCTION  WITH  SUBMERGED  RIBS  AND  ITS  MECHANISM 
IN  A  TURBULENT  BOUNDARY  LAYER  OVER  D-TYPE  ROUGHNESS 


Shinsuke  MOCHIZUKI  and  Hideo  OSAKA 
Faculty  of  Engineering,  Yamaguchi  University 
Tokiwadai  2557,  Ube  755-861 1,  Japan 
shinsuke@po.cc.yamaguchi-u.acjp 


A  turbulence  management  device,  submerged  ribs  inside  transverse  grooves,  for  a  d-type  rough  wall  is  proposed  based  on 
observations  of  coherent  motions,  and  tested  experimentally  in  a  turbulent  boundary  layer  under  zero  pressure  gradient.  The  skin 
friction  measurements  with  a  direct  drag  balance  clearly  show  that  the  present  device  is  effective  with  a  maximum  drag  reduction  rate  of 
10%  of  the  original  d-type  roughness.  Moreover,  the  present  method  provides  for  even  less  skin  friction  over  a  rough  wall  with  a 
maximum  reduction  rate  of  just  3%  compared  with  smooth  surface.  The  turbulent  intensities  and  Reynolds  shear  stress  measurements 
prove  that  the  submerged  ribs  suppress  the  turbulent  production  and  dissipation  process,  and  our  proposed  model  for  momentum 
exchange  near  the  rough  wall  is  reasonable.  A  conditional  averaged  analysis  shows  that  strength  of  ejection  associated  with  a  pair  of 
streamwise  vortices  is  reduced  and  as  is  bursting  frequency  by  the  submerged  ribs  in  a  drag  reduction  case. 


1.  INTRODUCTION 

Management  of  fluid  flows,  governed  by  the  nonlinear  partial 
differential  equation,  is  a  major  subject  in  fluids  engineering,  and  for 
wall  turbulence  we  have  seen  remarkable  advancement  in  drag  reduction 
techniques  [1].  New  ideas  classified  as  active  methods,  which  need  a 
certain  amount  of  extra  energy,  such  as  spanwise  wall  oscillation  and 
selective  suction  programmed  by  sophisticated  control  schemes  have 
been  proposed  and  tested  in  DNS  and  experimental  studies  [2]. 
Furthermore,  by  a  number  of  tests  involving  practical  aircraft  flight  the 
array  of  micro  streamwise  grooves  or  “riblets”  were  shown  to 
substantially  reduce  of  the  skin  friction  by  8-10%  [3,4], 

Experimental  and  numerical  approaches  to  elucidating  the 
mechanisms  of  the  drag  reduction  phenomenon  over  riblets  over  the  last 
decade  [5,6]  have  been  unable  to  establish  a  consensus  as  to  the  sense  of 
the  dynamics  of  turbulence.  Since  the  early  days  of  research  into  the 
turbulence  field  over  riblets,  coherent  structures  such  as  bursting 
phenomenon,  streamwise  vortical  structure,  and  hairpin  eddy  have  been 
investigated  based  on  flow  structures  of  dynamical  significance  which 
often  depend  on  the  investigator.  There  are  two  major  problems 
preventing  agreement  on  the  mechanisms:  (1)  in  most  of  the 
experiments  the  wall  shear  stress  was  determined  with  indirect  methods 
assuming  similarity  in  mean  quantities  or  estimated  from  results 
provided  by  other  studies,  (2)  up  to  now  kinematics  of  coherent 
structure  has  been  viewed  as  relatively  easy  to  perform  and  described  in 
detail  [7],  whereas  dynamics  of  the  quasi-periodic  three-dimensional 
vortical  motions  can  be  hardly  discussed  with  well-defined 
mathematical  expressions. 

By  regarding  riblets  as  a  kind  of  roughness,  one  may  conclude 
that  roughness  can  alter  the  structure  in  the  wall  layer  and  reduce  drag. 
In  fact,  by  recalculating  Nikuradse’s  pipe  flow  data,  Tani  [8]  pointed  out 
that  with  sand  grain  roughness  submerged  in  the  viscous  sublayer,  skin 
friction  becomes  smaller  compared  with  that  of  a  smooth  wall  pipe. 
Recently,  management  with  wall  protrusions  chosen  to  excite  the 
appropriate  propagating  mode  for  the  sublayer  waves  was  led  by 
numerical  simulations,  and  in  an  experimental  test  in  a  two-dimensional 
turbulent  channel  flow,  random  array  of  the  protrusions  achieved  about 


10%  drag  reduction  [9].  That  three-dimensional  roughness  gives  less 
skin  friction  compared  with  smooth  surface,  has  practical  applications  in 
engineering,  and  requires  that  alternative  formulations  be  made  to 
represent  the  roughness  effect  on  the  mean  velocity  profile  for  small 
values  of  roughness  Reynolds  number. 

In  the  present  study,  based  on  experimental  observations  on 
coherent  structure,  we  propose  a  drag  reduction  control  device 
submerged  into  transverse  grooves  of  d-type  roughness,  and  test  its 
effectiveness  by  direct  drag  balance  measurement  in  a  zero-pressure 
gradient  turbulent  boundary  layer.  Then,  we  investigate  the  turbulent 
structure  altered  by  the  wall  modification  using  conventional  time 
averages  and  a  conditional  sampling  analysis. 

2.EXPERIMENTAL  APPRATUS  AND  TECHNIQUES 


Figure  1:  Schematic  of  flow  field,  nomenclature  and  coordinate  system. 


121 


2.1  Experimental  Set-up  and  Measurement 

Experiments  were  performed  in  a  low  turbulence  wind  tunnel 
0.5m  wide,  0.3m  high,  and  4m  long  in  Yamaguchi  University.  Free 
stream  turbulence  was  kept  below  0.3%  and  static  pressure  in  the  free 
stream  was  adjusted  to  be  constant  along  the  wind  tunnel  (pressure 
coefficient  r  was  within  0.5%).  Figure  1  shows  overall  flow  field, 

p 

nomenclature  and  the  coordinate  system.  A  d-type  rough  wall  is  of  a 
two-dimensional  roughness  which  consists  of  rectangular  bars  closely 
arrayed  with  the  same  streamwise  space  as  the  element  width,  namely, 
the  pitch  ratio  ( b  +  w)//cr  of  2.  The  roughness  height  kr,  element 
width  b,  and  groove  width  w  are  all  3mm  and  the  rough  wall  was  made 
by  machining  transverse  grooves  out  on  a  1 8mm-thickness  bakelite 
plate. 

The  wall  shear  stress  was  measured  with  a  direct  drag  balance 
which  provides  an  excellent  skin  friction  data  set  for  a  smooth  wall 
turbulent  boundary  layer  under  zero  pressure  gradient  [10].  The 
floating  element  of  the  balance  has  a  60mm  diameter  surface  containing 
1 0  pitches  of  a  roughness  element.  Velocity  measurement  was  carried 
out  with  constant  temperature  anemometers  and  single  and  crossed  hot¬ 
wire  probes.  A  5^  diameter  and  1mm  length  tungsten  filament  was 
employed  as  a  sensor  and  a  pair  of  filaments  were  welded  on  prongs  of 
the  crossed  hot-wire  probe  with  0.5mm  separation  at  about  a  90°  cross 
angle.  The  velocity  signal  from  the  anemometers  was  recorded  on 
optical  disks  as  sets  of  digital  data  by  a  12  bit  AD  converter  and  a  PC, 
and  then  mean  velocity  and  Reynolds  stresses  were  obtained  by  taking 
the  average  of  100,000  data  sampled  at  a  rate  chosen  for  the  frequency 
band  of  the  fluctuating  velocity  signals  (typically,  10kHz  at  the  highest 
Reynolds  number,  and  4kHz  at  the  lowest). 

2.2  Drag  Reduction  Device  Proposed  by  Observations  of 
the  Coherent  Eddy 

A  cross-stream  view  of  a  model  for  momentum  exchange  between 
a  boundary  layer  and  a  groove  is  sketched  in  Fig.2  with  arrangement  of 

_ Table  1  Experimental  uncertainties _ 


U  u2  o2  w2  uv  Cj 


Side  view  End  view 

Figure  2:  A  model  for  momentum  exchange  over  a  d-type  rough  wall 
and  turbulence  control  with  the  submerged  ribs  inside  transverse 
grooves. 


submerged  thin  ribs  to  prevent  the  induced  spanwise  fluid  movement. 
By  using  the  conditional  sampling  technique  [11],  a  pair  of  streamwise 
vortices,  often  referred  to  as  a  typical  coherent  eddy  in  the  near  wall 
region  over  a  smooth  surface,  can  be  detected  over  d-type  roughness  on 
which  a  so-called  quasi-smooth  flow  is  established.  A  pair  of 
streamwise  vortices,  probably  being  two  legs  of  a  hairpin  vortex, 
associated  with  the  bursting  phenomenon  play  a  significant  role  in 
turbulence  production  as  well  as  momentum  transport  in  the  wall  layer. 
Therefore,  the  strength  of  the  streamwise  vortices  is  supposed  to  be 
proportional  to  the  amount  of  turbulence  production  during  a  busting. 
Over  d-type  roughness,  plausibly,  flow  induced  inside  the  grooves 
makes  the  bursting  stronger  with  the  aid  of  low  momentum  fluid 
pumped  out  of  the  grooves.  By  preventing  induced  spanwise 
momentum  transport  inside  the  grooves  with  the  submerged  longitudinal 
thin  ribs,  the  strength  of  the  vortices  is  reduced  and  the  turbulence 
production  and  dissipation  rate  decrease.  The  spanwise  spacing  of 
arrangement  of  thin  ribs  should  be  of  the  same  order  of  magnitude  of  the 
spanwise  scale  of  the  streamwise  vortices,^  ,  which  is  usually 
characterized  with  the  viscous  wall  unit  »  100).  The  spanwise 
spacing  Wr  was  chosen  to  be  3mm  corresponding  to  a  rib  Reynolds 
number  w*  (==  Wr  u  j v )  *n  the  range  35-150  in  the  present  experiment. 
Experimental  uncertainties  in  the  present  measurement  procedure  are 
given  in  Table  1. 

3.  RESULTS  AND  DISCUSSION 

3.1  Skin-Friction  Measurement 

The  local  skin  friction  coefficient  is  plotted  as  a  function  of 
the  Reynolds  number  based  on  momentum  thickness  =  Ux0/v 
Fig.3.  The  solid  line  represents  Karmdn-Schoenherr’s  semi-empirical 
formula  for  a  zero  pressure  gradient,  smooth  wall,  turbulent  boundary 
layer.  Over  a  transitionally  rough  Reynolds  number  range,  ^<2000 
[12],  evidently  the  skin  friction  coefficient  is  reduced  by  the  ribs 
submerged  into  the  grooves.  Moreover,  note  that  for  ^=750-1200, 
the  coefficient  lies  below  the  curve  for  a  smooth  wall  boundary  layer, 
indicating  a  realization  of  smaller  wall  friction  over  non-smooth  surface. 
As  the  Reynolds  number  decreases,  at  around  /^-800,  the  skin  friction 
coefficient  cf  °f  the  d-type  rough  wall  flows  coincides  with  the 
corresponding  value  predicted  by  the  semi-empirical  formula  for  smooth 
wall  surface.  Whereas,  as  #  ->oo  the  ribs  cease  to  reduce  the  skin 
friction  and  drag  increases  caused  by  roughness  for  ^>2000.  Over 
such  a  high  Reynolds  number  range,  the  spanwise  spacing  Wr  is  too 


Figure  3:  Local  skin  friction  coefficient  obtained  by  direct  drag  balance 
measurement. 


122 


large  to  manage  the  streamwise  coherent  vortices:  for  example,  the  rib 
Reynolds  number  p^+isl50at  ^=5000. 

The  drag  reduction  rates  are  defined  as 

ACja  =  (Cjn  -C/lt)l Cfd  x  100  (%), 

ACjr,  =(Cjg  -Cfi)/ Cp  x  100  (%),  (1) 

for  the  original  d-type  roughness  and  the  smooth  surface,  respectively, 
and  are  plotted  against  the  relevant  Reynolds  numbers  in  Figs.4,  5  and  6. 
Here,  r  ,  r  »  and  r  are  the  local  skin  friction  coefficients  of  the 
managed  and  the  original  d-type  roughness  and  the  smooth  surface. 
The  dotted  area  covers  uncertainties  of  the  ratio  mostly  due  to  data 
scattering  in  skin  friction  measurement.  Figure  5  contains  results  for 
the  same  value  of  the  rib  Reynolds  number  ^+,  which  is  the  most 
relevant  parameter  to  describe  the  present  management,  but  at  two 
different  streamwise  locations,  that  is,  under  different  bulk  Reynolds 
numbers.  In  Fig.4  the  maximum  reduction  rate  reaches  about  10%  at 
around  ^=1000,  and  the  skin  friction  is  reduced  over  a  wide  Reynolds 
number  range,  ^=750-5000.  In  Fig.5  where  the  reduction  rate  is 
plotted  against  the  rib  Reynolds  number  ,  drag  reduction  is 
achieved  for  approximately  0/+<lOO;  this  evidently  shows  our  model 
for  momentum  exchange  to  be  reasonable.  However,  the  reduction 
rate  depends  on  the  bulk  Reynolds  number,  because  the  turbulent 
boundary  layer  is  in  a  transitionally  rough  regime  for  ^<2000. 

Figure  6  confirms  less  skin  friction;  the  maximum  reduction  rate  &C 

Is 

is  3%  over  the  d-type  roughness  modified  with  submerged  ribs 


5 


0 


XJ 

4- 

O 

<  -10 


-15 


-20 

500  1000  5000 

R9 

Figure  4:  Reduction  rate  in  local  skin  friction  coefficient  compared  with 
the  original  d-type  roughness. 

5 

0 


tj  -5 

XJ 

4- 

O 

<  -10 


-15 

-20 

0  50  100  150 

Wr+ 

Figure  5:  Reduction  rate  in  local  skin  friction  coefficient  compared  with 
the  original  d-type  roughness  as  a  function  of  rib  Reynolds  number. 


compared  with  the  smooth  surface. 


3.2  Mean  Velocity  and  Reynolds  Stresses 

Figure  7  shows  logarithmic  mean  velocity  profiles  which  were 
measured  over  a  groove  and  mid-span  of  two  ribs  at  225mm 
downstream  corresponding  to  2000  viscous  wall  length  units  of  the 
beginning  of  the  wall  modification.  The  virtual  origin  of  the  transverse 
coordinate  y-yt+s  in  the  velocity  plot  is  placed  at  a  downward 
location  shifted  from  the  top  of  the  surface  by  error  in  origin  8 ,  which 
is  properly  determined  with  the  friction  velocity  obtained  in  the  direct 
drag  balance  measurement  by  assuming  the  similarity  of  velocity  profile 
is  valid.  The  solid  lines  represent  the  standard  log  law  for  a  smooth 
wall  turbulent  boundary  layer  given  at  the  Stanford  Conference  in  1968. 
The  logarithmic  profile  in  mean  velocity  distribution  in  the  wall  layer  is 
fairly  reasonable  even  over  the  modified  d-type  rough  surface,  if  the 
virtual  origin  is  properly  considered.  At  /^=750  and  1210  where  the 


Figure  6:  Reduction  rate  in  local  skin  friction  coefficient  compared  with 
the  smooth  wall  turbulent  boundary  layer  under  zero-pressure-gradient. 


Figure  7:  Logarithmic  velocity  profile  in  the  flow  field  altered  by  the 
submerged  ribs. 


123 


smooth  and  the  modified  d-type  rough  wall  flows  take  the  same  value  of 
the  skin  friction  coefficient,  the  velocity  data  both  of  the  modified  and 
the  original  d-type  roughness  lie  on  the  standard  log  law  for  smooth 
surface.  Whereas,  at  ^=860  and  910  where  the  skin  friction 
coefficient  takes  a  smaller  value  compared  with  smooth  surface,  the 
logarithmic  velocity  profiles  are  slightly  shifted  upward,  as  often 
observed  in  drag  reduction  over  riblets  [5].  Otherwise,  at  ^=1570 
where  the  drag  increases  due  to  roughness  (see  Fig.3),  the  logarithmic 
profile  is  shifted  downward  by  the  roughness  function  which  is  normally 
a  positive  value. 

The  roughness  function  a U/ur  >  ordinarily  indicating  drag 
increase  over  rough  surfaces,  is  plotted  against  the  Reynolds  number 
based  on  error  in  origin  a ,  which  is  the  representative  length  scale  for  d- 
type  roughness.  By  assuming  the  Karman  constant  fC  in  the 
logarithmic  profile  to  be  0.41,  the  roughness  function  was  measured  as  a 
downward  shifting  value  from  the  standard  log  law.  The  results  in  a 
transitionally  rough  regime  urs/v  significantly  deviate  from  the 
empirical  formula  for  a  fully  rough  Reynolds  number  range  u^e/v^- 
Interestingly,  in  the  case  of  drag  reduction  by  the  submerged  ribs,  the 
roughness  function  and  the  Reynolds  number  M ^£/v  take  negative 


uTs/v 


Figure  8:  Roughness  function  plotted  against  the  Reynolds  number 
based  on  the  error  in  origin. 


Figure  9:  Turbulent  intensity  profiles  of  streamwise  fluctuating  velocity 
component. 


values  simultaneously.  When  requiring  a  continuous  representation 
going  through  the  origin  for  dependence  of  the  roughness  function  on 
the  Reynolds  number  from  drag  increase  through  drag  reduction,  we 
need  an  alternative  form,  for  example,  a  simple  linear  function. 

Turbulent  intensities,  u  ,  u  ,  and  w  ,  and  Reynolds  shear 
stress  profiles  are  given  in  Figs. 8,  9,  10,  and  11,  respectively.  To  see 
the  influence  of  the  ribs  on  the  activity  of  the  energy-containing 
turbulent  eddies,  these  profiles  are  normalized  with  the  outer  scales, 
boundary  layer  thickness  d  and  the  free  stream  velocity  jjx  •  Here, 
we  shall  look  at  typical  two  results  for  a  drag  reduction  case  at 
r  =1300  corresponding  to  ^+=35  and  for  a  no  drag  reduction  case  at 
^=5000  corresponding  to  lVr+=120.  Evidently,  the  streamwise 
turbulent  intensity  urms/Ul  *s  reduced  in  the  wall  layer  in  the  drag 
reduction  case  at  ^=1300,  and  the  maximum  reduction  rate  is  about 
45%,  although  all  the  flows  over  the  d-type  rough  wall  and  the  smooth 
wall  [13]  take  the  maximum  value  of  u^JU^  at  the  same  distance 
from  the  wall  y+  (=  yujv)  «  15-  Otherwise,  at  around  the  edge  of 
the  inner  layer  y(  /S  =0.2,  the  turbulent  intensity  is  slightly  enlarged  by 
the  turbulence  management.  This  suggests  that  the  influence  of  the 
wall  modification  spreads  into  the  outer  layer  and  alters  the  amount  of 
momentum  or  energy  entrainment  from  the  free  stream.  In  spite  of  no 
reduction  in  the  skin  friction  coefficient  at  /^=5000,  the  turbulent 
intensity  is  slightly  reduced  by  the  wall  modification.  When 
comparing  the  present  profiles  to  those  of  the  smooth  wall  flow  at 
7^=1300,  the  turbulent  intensity  takes  larger  values  throughout  the 
outer  layer  both  over  the  modified  and  the  original  d-type  rough 
surfaces. 

In  the  v^JU  profiles  (Fig.8),  this  turbulent  intensity 
component  is  reduced  by  12%  in  the  modified  d-type  rough  wall  flow. 
A  much  larger  reduction  in  this  component  was  observed  in  drag 
reduction  phenomenon  by  polymer  adding  turbulent  flow  (Tom’s  effect) 
[14]  .  Probably,  the  injected  polymer  solution  filled  into  a  whole  flow 
field  directly  alters  the  large  scale  energy  containing  eddies,  on  the  other 
hand,  the  submerged  ribs  in  the  present  method  indirectly  influence  the 
large  scale  eddies  through  the  turbulence  production  and  diffusion 
process.  This  difference  in  mechanisms  of  turbulence  management 
appears  in  the  reduction  rate  for  the  transverse  turbulent  intensity 
component.  In  the  profiles  of  the  wrms/Ul  component  (Fig.  10),  the 
magnitude  of  the  turbulent  intensity  is  slightly  reduced  in  the  wall  layer 
at  ^=1300.  In  Fig.  1 1,  obviously  the  Reynolds  shear  stress  is  reduced 
by  approximately  25%  in  the  drag  reduction  case  at  /^=I300.  It 
follows  that  the  ribs  submerged  into  transverse  grooves  suppress 


0.06  r 


0.04k 


0.02 


■ 1  rTTr 


"i - 1 - 1 — i — i  i  i  r  j 


o  o  o  o°° 


Re 

1300 

5000 

Wr+ 

35 

120 

4Q 

with  ribs 

o 

• 

•Q 

without  ribs 

A 

▲ 

- 1  I _ I _ 1  1  J  1  I 


-I _ I _ 1 _ I _ I  i-j-jj- 


**6 


0.02 


0.1 


V6 


1.0 


Figure  10:  Turbulent  intensity  profiles  of  the  fluctuating  velocity 
component  normal  to  the  wall. 


124 


momentum  transport  near  the  rough  wall.  However,  the  constant  stress 
layer  [15],  in  which  turbulence  scales  with  the  friction  velocity  and  the 
assumption  of  logarithmic  velocity  profile  are  supported,  can  be 
reasonably  recognized  in  the  wall  layer  even  when  the  ribs  alter  the 
structure  of  the  turbulence  near  the  wall. 


3.3  Conditional  Analysis 


Using  a  conditional  sampling  analysis  we  next  investigated  the 
coherent  structure  which  is  a  basis  for  proposing  the  present  turbulence 
management  technique.  Here,  the  VITA  technique  [16]  was  employed 
to  detect  bursting  events  producing  most  of  the  turbulent  energy  near  the 
wall.  When  the  turbulent  kinetic  energy  averaged  over  a  certain  time 
interval  T  exceeds  the  threshold  level,  it  is  considered  that  the  energetic 
turbulence  producing  process  has  taken  place.  A  preliminary 
experiment  gives  the  best  parameter  to  specify  the  detection  scheme: 
averaging  time  interval  T  was  adjusted  to  be  20  times  the  viscous  wall 
time  scale  v/w2  and  threshold  level  is  0.8  times  the  local  streamwise 
turbulent  energy  u 2  obtained  from  conventional  time  averaging. 

Figure  12  shows  ensemble  averaged  signals  of,  u,v  ,  and  uu 
components  obtained  at  y+(~  yur/v)~^  *n  the  drag  reduction  case  of 
^=1300.  The  averaged  signals  are  calculated  from  about  300 
samples  selected  with  an  additional  condition  of  acceleration  at 
detection  time  t=0.  In  cases  of  both  modified  and  original  d-type 
roughness,  we  can  see  typical  patterns  of  bursting;  the  ejection  of  low 
momentum  fluid  (u  <  0  and  £>0)  followed  by  a  high  speed  sweep 
( u  >  0  and  d  <  0),  in  the  ensemble  averaged  signals.  However,  the 
strength  (peak  value)  of  the  ejection  becomes  smaller  in  the  drag 
reduction  case.  Whereas,  in  the  sweep  process  no  influence  can  be 
seen  in  the  ensemble  averaged  signals.  These  results  reveal  that  as  we 
expected  when  designing  the  present  management  device,  momentum 
transport  induced  by  a  pair  of  streamwise  vortices  associated  with  the 
submerged  ribs  inside  the  transverse  grooves  suppress  the  ejection 
process.  Figure  13  shows  the  results  in  the  case  where  the  submerged 
ribs  have  no  influence  on  alternation  of  skin  friction  coefficient  at 
/^=5000  corresponding  to  0/+=15O.  In  this  case,  we  also  find 
suppression  of  the  peaks  in  the  ejection  process,  therefore,  the 
submerged  ribs  apparently  manage  momentum  transport  in  the  ejection 
process.  Low-Reynolds-number  effect  on  the  turbulent  structure  near 


l  1  1  1  1  1  r| 

aaaAaJ  a  . 

- 1 — 

Aaa 

— r 

"i — 1 — 1 — r  i  | - 

•*s 

id 

46 

•  Q 

- 

Re 

1300 

5000 

- 

Wr+ 

35 

120 

40 

r\  ”J 

with  ribs 

0 

• 

«p 

without  ribs 

A 

▲ 

1  1 

t  1  1  1  1  1 

1 

1  1 

— , - 

Ol 

.02 

0.1 

1.0 

yt/« 


Figure  11:  Turbulent  intensity  profiles  of  the  spanwise  fluctuating 
velocity  component. 


the  d-type  rough  wall  was  reported  [17];  dominant  motions  for  turbulent 
transport  near  the  d-type  rough  wall  are  ejection  at  a  transitionally  rough 
Reynolds  number  (^<2000),  but  are  replaced  by  sweeps  at  a  fully 
rough  Reynolds  number  (^>2000).  The  sweep  process  is  supposed 
to  be  closely  associated  with  large-scale  vortical  motion  scaling  with  the 
boundary  layer  thickness,  and  the  submerged  ribs  with  spanwise  spacing 
of  the  order  of  intermediate  length  scale  of  turbulence,  *  100  v/z/r  can 
not  alter  such  large  scale  eddies. 

We  should  describe  bursting  frequency  that  is  another  parameter 
indicating  activity  of  turbulence  production.  In  the  drag  reduction  case 
at  ^=1300,  the  normalized  bursting  frequency  fbS/Ul  is  reduced 
from  0.136  to  0.117  (by  14%)  under  management  with  the  submerged 
ribs.  Otherwise,  at  ^=5000  the  normalized  frequency  fbS/U]  is 
increased  from  0.097  to  0.120  (by  24%)  due  to  the  wall  modification. 
In  spite  of  reduction  in  the  strength  of  each  event  corresponding  to  the 
ejection  process,  increase  of  bursting  frequency  results  in  the  skin 
friction  coefficient  remaining  at  the  same  value  over  the  modified  d-type 
rough  wall  at  ^=5000. 

4.  CONCLUSIONS 


It  is  clear  that  the  management  device,  submerged  ribs  into  the 
transverse  grooves  with  suitable  spanwise  spacing,  is  effective  for 
reducing  the  drag  of  d-type  rough  wall  boundary  layer  over  a  certain 
Reynolds  number  range.  At  the  optimal  Reynolds  numbers,  the  skin 
friction  coefficient  is  reduced  by  10%  compared  to  the  original  d-type 
roughness.  We  should  note  that  with  the  present  device,  even  less  skin 
friction,  a  3%  drag  reduction  rate  compared  with  smooth  surface,  is 
possible.  The  turbulent  intensity  and  Reynolds  shear  stress 
measurements  reveal  that  the  submerged  ribs  suppress  the  turbulent 
production  and  dissipation  rate  near  the  rough  wall.  These 
experimental  results  prove  that  the  proposed  model  for  momentum 
exchange  based  on  observations  of  coherent  motions  near  the  roughness 
is  suitable. 

Based  on  the  mean  velocity  analysis  with  the  direct  drag  balance 
measurement  of  the  wall  shear  stress,  a  logarithmic  profile  with  a 
standard  value  of  Karman  constant  a:  =0.41  can  be  assumed  even  when 


2.5, 


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Figure  12:  Reynolds  shear  stress  profiles. 


125 


the  submerged  ribs  alter  the  turbulent  structure  in  the  wall  layer  over  d- 
type  roughness.  In  the  drag  reduction  case  the  logarithmic  profile  is 
shifted  downward  of  the  log  law  for  smooth  surface,  and  the  roughness 
function  and  the  representative  Reynolds  number  based  on  the  error  in 
the  origin  take  negative  values  simultaneously. 

In  conditional  sampling  analysis-giving  evidence  of  direct 
influence  of  the  present  management  system  on  ensemble  averages 
associated  with  coherent  motions,  it  is  seen  that  the  submerged  ribs 
suppress  the  ejection  process  during  a  bursting  both  in  drag  reduction 
and  in  no  drag  reduction  cases.  The  normalized  bursting  frequency 
f  S/U\  *s  educed  by  14%  in  a  drag  reduction  case  at  ^=1300,  but 
increased  by  24%  in  a  no  drag  reduction  case  at  ^=5000. 

AKNOWLEGEMENTS 

The  authors  acknowledge  the  financial  support  given  by  the 
Assistance  of  the  Mazda  Foundation  for  Research  in  Science  and 
Technology. 


REFERENCES 


1. M.Gad-el-Hak,“FIow  control”  ylppl.Mech.Rev.yol.42,26 1-293, 1989. 

2. M.Gad-el-Hak,  “Modem  developments  in  flow  control”, 

Appl.Mech.Rev .,  Vol.49,  365-379,  1996. 

3. M.J.Walsh,  “Riblets”,  Viscous  drag  reduction  boundary  layers ,  (Eds. 
D.M.Bushnell  and  J.N.Hefftier),  Progress  in  Astronautics  and 
Aeronautics,  Vol.123,  203-254,  1990. 

4. M.J.Walsh,  “Turbulent  boundary  layer  drag  reduction  using  riblets”, 
A1AA  Paper  82-0169,  1982. 

5. K.-S.Choi,  “Near-wall  structure  of  a  turbulent  boundary  layer  with 
riblets”,  J. Fluid  Mech.,  Vol.213,  419-442,  1989. 

6. H.Choi,  P.Moin  and  J.Kim,  “Direct  numerical  simulation  of  turbulent 
flow  over  riblets”,  J.Fluid Mech.,  Vol.255,  503-53,  1993. 


1.0 


0.5 


£ 

e 


-0.5 


1.5 
1.0 
*  0.5 
0 

-0.5 

-1.0 

-1.5 


\> 


-180  -120  -60  0 
tu  2/v 


60 


120 


180 


(a)  ^=1300  Of;=35) 


7.S.K.Robinson,  “Coherent  motions  in  the  turbulent  boundary  layer”, 
Annu.  Rev.  Fluid  Mech.,  Vol.23,  601-639,  1991. 

8.I.Tani,  “Drag  reduction  by  riblet  viewed  as  roughness  problem”,  Proc. 
Japan  Acad.,  B64,  21-24,  1988. 

9. L.Sirovich  and  S.Karlsson,  “Turbulent  drag  reduction  by  passive 
mechanisms”,  Nature ,  Vol.388,  753-755,  1997. 

10. H.Osaka,  T.Kameda,  and  S.Mochizuki,  “Re-examination  of  the 
Reynolds-number-effect  on  the  mean  flow  quantities  in  a  smooth  wall 
turbulent  boundary  layer”,  JSME  Int.J.,  Ser.B,  Vol.41,  No.l,  123-129, 
1998. 

11. H.Osaka  and  S.Mochizuki,  “Streamwise  vortical  structure  associated 
with  the  bursting  phenomenon  in  a  d-type  rough  wall  boundary  layer 
at  a  low  Reynolds  number”,  Proc.  the  6th  Symposium  on  Turbulent 
Shear  Flows,  Toulouse,  16.7.1-16.7.6,  1987. 

12. H.Osaka  and  S.Mochizuki,  “Turbulent  structure  of  a  d-type  rough 
wall  boundary  layer  in  a  transitionally  rough  regime”,  Proc.  the  Ist 
KSME-JSME  Thermal  and  Fluids  Conference ,  Seoul,  2.88-2.93, 1988. 

13. L.P.Purtell,  P.S.Klebanoff  and  F.T.Buckley,  “Turbulent  boundary 
layer  at  low  Reynolds  number”,  Phys.Fluids,  Vol.24,  802-811, 1971. 

H.H.Usui  and  Y.Sano,  “Effect  of  injected  polymer  thread  on  turbulence 
in  a  pipe  flow”,  Transport  Phenomena  in  Turbulent  Flow  (Eds. 
M.Hirata  and  N.Kasagi),  299-309,  Hemisphere,  1988. 

15. A.A.Townsend,  “The  structure  of  turbulent  shear  flow”,  Cambridge 
university  press,  1976. 

16. R.F.Blackwelder  and  R.E. Kaplan,  “On  the  structure  of  the  turbulent 
boundary  layer”,  J.Fluid  Mech.,  Vol.76,  89-1 12,  1984. 

17. H.Osaka  and  S.Mochizuki,  “Statistical  quantities  of  a  d-type  rough 
wall  boundary  layer  in  a  transitionally  rough  regime”,  Proc.  the  2nd 
KSME-JSME  Fluids  Engineering  Conference,  Seoul,  Vol.2,  202-207, 
1990. 


Figure  13:  Ensemble  averaged  signals  in  the  VITA  analysis. 


126 


A  NEW  APPROACH  TO  DRAG  REDUCTION 


Aline  J.  Cotel 

Department  of  Mechanical  Engineering 
University  of  Manitoba 
Winnipeg,  MB,  CA  R3T  5V6 
acotd@mail.cc.umanitoba.ca 


Robert  E.  Breidenthal 

Department  of  Aeronautics  and  Astronautics 
University  of  Washington 
Seattle,  WA  98195-2400 
breident@aa.washington.edu 


Abstract  -  A  novel  method  is  proposed  for  the  reduction  of  turbulent  skin  friction.  It  is  based  on  a  recent  model  of  vortex  persistence  on 
surface  fluxes  in  stratified  flows.  When  a  vortex  is  near  an  interface,  such  as  a  solid  wall,  the  fluxes  of  mass,  momentum,  and  energy  at  the 
wall  depend  on  the  stationarity,  or  persistence,  of  the  vortex  with  respect  to  the  wall.  For  a  stationary  vortex,  the  theory  predicts  that  the 
surface  fluxes  will  be  independent  of  the  small  scale  turbulence.  If  streamwise  vortices  are  introduced  into  a  turbulent  boundary  layer,  the 
theory  implies  that  the  skin  friction  can  be  dramatically  reduced,  provided  that  the  streamwise  vortices  can  be  held  sufficiently  stationary. 
Any  net  drag  reduction  also  requires  that  the  energy  invested  in  the  streamwise  vortices  is  largely  recovered  at  the  trailing  edge. 


I.  INTRODUCTION 

Conventional  approaches  to  reducing  skin  friction  usually 
involve  reducing  the  velocity  gradient  at  the  surface,  such  as  by 
displacing  the  vorticity  through  electromagnetic  torques  or  by  the 
inhibition  of  transition  to  turbulence.  Riblets  are  a  notable  exception, 
where  surface  grooves  are  intentionally  introduced. 

A  new  approach  for  the  potential  reduction  of  skin  friction  has 
been  deduced  from  observations  on  stratified  entrainment.  Before 
applying  the  concept  to  skin  friction,  it  is  instructive  to  consider  the 
physics  of  stratified  entrainment. 

In  experiments  on  entrainment  across  a  thin,  stratified  interface 
subjected  to  impinging  turbulence,  it  was  found  that  the  entrainment 
rate  normalized  by  the  impingement  velocity  could  have  widely 
different  values,  even  when  conventional  parameters  such  as 
Reynolds  and  Schmidt  numbers  were  held  constant.  For  example,  a 
vertical  jet  impinging  on  the  interface  yielded  an  entrainment  rate 
proportional  to  the  Richardson  number  to  the  -  1/2  power,  whereas 
tilting  that  same  jet  only  15  degrees  from  vertical  and  precessing  it 
yielded  an  exponent  of  -  3/2  [1].  At  a  Richardson  number  of  10,  the 
entrainment  rates  differ  by  a  factor  of  two  orders  of  magnitude.  The 
Reynolds  and  Schmidt  numbers  were  essentially  identical  in  the  two 
experiments.  The  differing  results  could  not  be  explained  by 
conventional  parameters. 

A  fundamental  difference  between  these  two  flows  is  the 
stationarity  of  the  impinging  turbulence.  The  vertical  jet  generated  a 
quasi-stationary  impingement  dome,  at  the  sides  of  which  fluid  was 
entrained  across  the  interface.  In  contrast,  the  precessing  jet 
impinged  on  the  interface  in  a  moving,  nonstationary  way,  such  that 
entrainment  appeared  to  be  achieved  by  the  rebound  of  the 
impingement  dome,  following  the  suggestion  of  Linden  [2]  for 
impinging  vortex  rings. 

H.  PERSISTENCE  THEORY 

If  stationarity  accounts  for  the  markedly  different  results,  then 
the  transition  between  the  two  regimes  must  depend  on  some 
quantitative  measure  of  the  stationarity.  We  have  defined  the  vortex 
persistence  T  to  be  the  number  of  rotations  a  vortex  makes  during  the 
time  it  moves  a  distance  equal  to  its  own  diameter  with  respect  to  the 
interface  [3].  Thus  the  persistence  is  %  times  the  eddy  velocity  ratio 
of  rotational  to  translational  speeds  (see  Figure  1).  Note  that  T  can 
only  be  defined  in  the  presence  of  an  interface  of  some  sort  in  the 
problem,  since  otherwise  the  translational  speed  is  arbitrary. 

Persistence  may  also  be  important  in  the  limit  of  large 
Richardson  number,  where  the  stratification  is  so  strong  that  the 
interface  remains  flat  for  all  eddies,  even  the  smallest.  Closely  related 
to  this  question  is  the  issue  of  surface  fluxes  at  flat,  solid  walls  under 
boundary  layers  in  unstratified  flow,  such  as  heat  transfer. 

According  to  surface  renewal  theory  [4],  the  heat  flux  is 
proportional  to  the  square  root  of  the  ratio  of  the  thermal 
difftisivity  and  the  rotation  period  of  the  appropriate  eddy.  In  high 
Reynolds  number  turbulence,  there  is  a  wide  spectrum  of  possible 
eddy  sizes,  ranging  from  the  largest  to  the  smallest,  the  latter  being 
the  Kolmogorov  microscale.  Which  eddy  is  the  correct  choice? 

In  the  absence  of  compressibility  or  stratification,  there  are 
only  are  two  special  eddy  sizes  in  high  Reynolds  number 


turbulence:  the  smallest  and  the  largest.  In  any  given  flow,  the 
wall  fluxes  can  depend  on  only  one  of  them.  There  are  also  two 
asymptotic  limits  of  the  persistence  parameter.  The  theory  asserts 
that  the  surface  fluxes  are  controlled  by  the  smallest  eddies  for 
T<T*,  and  by  the  largest  eddies  for  T>T*  (see  Figure  2).  The 
critical  value  T*  is  presumably  of  order  unity. 


Figure  1.  Persistence  parameter  T=itU  2/  Ui 


If  the  large  vortex  is  not  stationary,  then  the  statistics  are 
likewise  not  stationary,  so  that  the  scalar  transport  is  not  limited  by 
the  large  scale  eddies.  The  smallest  scale  eddies  control  the  flux. 
Only  when  the  boundary  layer  itself  becomes  turbulent  does  the  skin 
friction  depend  on  the  fine  scale  eddies,  since  the  strongest,  large 
vortices  are  now  moving  rapidly  with  respect  to  the  wall. 

Said  another  way,  the  surface  flux  of  heat  can  be  switched  from  its 
turbulent  value  to  its  laminar  value  if  large  eddies  are  sufficiently 
strong  and  stationary.  The  criterion  for  sufficient  strength  is  that  the 
eddy  in  question  possess  the  largest  induced  velocity.  The  criterion 
for  sufficient  stationarity  is  that  T>T*. 

The  theory  developed  from  these  stratified  flow  experiments  is 
in  accord  with  the  wall  heat  transfer  literature.  The  heat  transfer 
under  a  forced,  laminar  boundary  layer  was  measured  as  a  function  of 
the  level  of  freestream  turbulence  [5].  It  had  been  supposed  that  the 
heat  transfer  rate  would  increase  smoothly  with  increasing  freestream 
turbulence  in  a  wind  tunnel.  However,  the  surprising  result  is  that 
heat  transfer  is  completely  independent  of  freestream  turbulence,  at 
least  up  to  very  high  values  of  turbulence.  Of  course,  it  is  well 
known  that  once  the  boundary  layer  itself  became  turbulent,  the  heat 
transfer  coefficient  would  increase  markedly.  Thus  heat  transfer 
increases  for  some  kinds  of  turbulence,  but  not  for  others.  What  is 
different  about  the  two  types  of  turbulence? 


127 


7 - 7 - 7 - 7 - 7 - 7 - 7 - 7 

Figure  2.  Persistence  of  the  large  vortex  determines  which  eddy  size 
controls  the  surface  fluxes 

In  the  heat  transfer  experiments,  the  fine  scale  turbulence  in  the 
freestream  had  no  effect  on  heat  transfer  because  the  mean  flow  was 
sufficiently  steady,  corresponding  to  a  stationary  virtual  large  scale 
vortex.  However,  when  the  boundary  layer  itself  became  turbulent, 
the  large  eddies  within  it  moved  rapidly  downstream,  at  a  celerity  of 
about  80%  of  the  freestream  speed,  so  that  their  persistence  was 
small.  The  small  scale  turbulence  thus  controlled  the  surface  flux. 

This  can  also  be  viewed  from  a  statistical  viewpoint.  Suppose 
the  large  vortex  is  stationary.  Even  if  the  transport  by  the  smallest 
eddies  across  their  own  diameter  was  instantaneous,  the  heat  transfer 
would  still  be  rate-limited  by  the  relatively  slow  rotation  rate  of  the 
large  vortex.  It  is  the  bottleneck.  The  problem  is  statistically 
stationary. 

in.  SKIN  FRICTION 

According  to  Reynolds'  analogy,  heat  transfer  is  proportional  to 
skin  friction.  Consequently,  it  is  anticipated  that  with  sufficient 
vortex  stationarity,  the  skin  friction  will  also  be  reduced,  as  its 
dependence  suddenly  switches  from  the  smallest  to  the  largest  eddies, 
corresponding  to  the  change  from  turbulent  to  laminar  values.  Thus 
at  ship  Reynolds  numbers,  the  skin  friction  would  decrease  by  more 
than  an  order  of  magnitude.  This  hypothesis  has  not  yet  been  tested 
by  skin  friction  experiments. 

A  vortex  must  be  sufficiently  stationary  for  the  surface  flux  to 
decrease.  Consider  an  array  of  counter-rotating,  streamwise  vortices 
near  a  flat  wall.  If  the  vortex  core  diameter  is  comparable  to  the 
vortex  height  above  the  wall  and  to  the  vortex  spacing,  the  instability 
time  scale  is  comparable  to  the  vortex  rotational  period.  This  implies 
that  the  persistence  parameter  is  low,  of  order  unity.  If  seems  likely 
that  this  is  below  or  near  the  (T=T*)  transition.  Thus  the  vortices 
probably  require  some  means  of  artificial  stabilization  to  hold  them  in 
place,  through  either  passive  or  active  control,  to  raise  T  above  its 
critical  value.  Ironically,  while  the  momentum  transfer  at  the  wall 
would  be  reduced  by  the  addition  of  strong  vortices  in  the  boundary 
layer,  the  momentum  transport  throughout  the  rest  of  the  boundary 
layer  would  be  enhanced,  as  is  known  for  conventional  vortex 
generators.  So  any  tendency  for  boundary  layer  separation  would  be 
inhibited. 

If  these  streamwise  vortices  are  sufficiently  strong  in 
comparison  to  the  eddies  in  the  turbulent  boundary  layer,  the  value  of 
their  persistence  will  determine  the  skin  friction.  A  plausible 
estimate  for  the  required  strength  is  that  their  induced  velocity  is 
comparable  to  the  freestream  speed. 

Sufficiently  strong  vortices  may  be  able  to  resist  the 
deformations  of  the  background  turbulence  for  an  appreciable  time. 
However,  in  order  to  achieve  the  necessary  stationarity,  the  natural 
self-induced  inherent  in  the  streamwise  vortices  themselves  must 
somehow  be  inhibited. 

Balle  [6]  has  suggested  that  the  quasi-stability  of  the  vortices  in 
the  Karman  vortex  street  may  be  exploited  to  inhibit  two-dimensional 
instabilities.  Suppose  that  the  streamwise  vortices  are  all  co-rotating, 
and  the  wall  surface  is  corrugated,  with  the  axis  of  the  corrugations 


nominally  in  the  streamwise  direction.  Suppose  further  that  the 
surface  undulations  are  designed  such  that  they  correspond  to  the 
dividing  streamline  in  the  ideal  flow  model  of  a  Karman  street.  Such 
vortices  are  stable  to  two-dimensional,  phase-coherent  perturbations. 

The  question  of  three-dimensional  instability  remains.  From 
dimensional  considerations,  the  characteristic  growth  time  t  for  a 
Crow-type  instability  is 

x  =  82/T  (1) 

where  T  is  the  circulation  of  one  streamwise  vortex  and  5  is  its 
characteristic  height  from  the  wall,  comparable  to  the  boundary  layer 
thickness.  Because  of  the  relatively  large  magnitude  of  circulation 
required  to  dominate  the  background  turbulent  vortices  of  the 
boundary  layer,  the  characteristic  3-D  instability  time  scale  is 
relatively  short.  Consequently,  the  inhibition  of  3-D  instabilities  is 
probably  the  most  challenging  task  to  achieving  the  necessary  vortex 
persistence. 

IV.  ENERGY  RECOVERY 

Assuming  that  the  theory  is  correct  and  that  the  streamwise 
vortices  can  be  controlled,  the  third  requirement  for  drag  reduction  is 
that  the  energy  invested  in  the  vortices  is  largely  recovered  at  the 
trailing  edge  of  the  body.  Otherwise  it  is  only  a  Pyrrhic  victory,  since 
the  reduction  in  skin  friction  is  not  enough  to  compensate  for  the 
unrecovered  energy  lost  in  the  vortices. 

Anti-swirl  vanes  at  the  trailing  edge  should  be  able  to  extract 
most  of  the  rotational  energy  in  the  vortices,  especially  since  the 
latter  are  to  be  held  stationary  (see  Figure  3).  The  vanes  would  have 
their  own  parasitic  drag,  largely  from  laminar  skin  friction,  so  the 
overall  system  performance  must  account  for  this  cost  in  the  overall 
drag  budget. 


Figure  3.  Schematic  of  the  approach.  Streamwise  vortices  are  first 
introduced  with  vortex  generators,  held  stationary  with  active 
control,  and  finally  extracted  downstream  with  anti-swirl  vanes 


V.  CONCLUSIONS 

A  new  approach  to  drag  reduction  exploits  a  persistence  theory 
for  surface  fluxes  near  vortices.  If  the  nearby  vortex  is  sufficiently 
stationary,  the  surface  fluxes  are  independent  of  the  small  scale 
turbulence.  Applying  the  theory  to  the  problem  of  skin  friction,  it  is 
proposed  that  streamwise  vortices,  introduced  near  the  leading  edge 
and  held  stationary  by  active  or  passive  control,  would  yield  reduced 
skin  friction  underneath  them.  The  net  drag  reduction  depends  on  the 
ability  to  recover  the  rotational  energy  of  the  vortices,  as  well  as  any 
energy  expended  in  vortex  control.  The  next  step  is  a  laboratory  test 
of  the  underlying  theory  in  combination  with  passive  or  active  control 
of  streamwise  vortices  to  test  the  concept.  Heat  transfer  would  be 
measured,  as  it  is  much  easier  to  measure  than  skin  friction. 

VI.  REFERENCES 

1.  A.J.  Cotel,  J.A.  Gjestvang,  N.N.  Ramkhelawan  and  R.E. 
Breidenthal  “Laboratory  Experiments  of  a  Jet  Impinging  on  a 
Stratified  Interface”,  Experiments  in  Fluids,  23, 155-160,  1997. 

2.  P.F.  Linden  “The  Interaction  of  a  Vortex  Ring  with  a  Sharp 
Density  Interface:  A  Model  for  Turbulent  Entrainment”,  Journal  of 
Fluid  Mechanics ,  60, 467-480,  1973. 

3.  A.J.  Cotel  and  R.  E.  Breidenthal  “Persistence  Effects  on  Stratified 
Entrainment”,  Applied  Scientific  Research ,  57,  349-366,  1997. 


128 


4.  M.A.  Leveque  “Les  Lois  de  la  Transmission  de  Chaleur  par 
Convection”,  Ann.  Mines ,  13, 201-239,  1928. 

5.  A.  Edwards  and  B.N.  Furber  “The  Influence  of  Free  Stream 
Turbulence  on  Heat  Transfer  by  Convection  from  an  Isolated 
Region  of  a  Plane  Surface  in  Parallel  Flow”,  Proceedings  of  the 
Institute  of  Mechanical  Engineering,  170,941,  1956. 

6.  G.  Balle,  private  communication,  1998. 


130 


DIRECT  NUMERICAL  SIMULATIONS  OF  DRAG  MODIFICATION  USING 
RANDOMIZED  FORCE  FIELDS 


R.  B.  Dahlburg 

Laboratory  for  Computational  Physics  and  Fluid  Dynamics 
Naval  Research  Laboratory 
Washington,  DC  20375-5344 


R.  A.  Handler 
Remote  Sensing  Division 
Naval  Research  Laboratory 
Washington,  DC  20375 


W.  C.  Sandberg 

Laboratory  for  Computational  Physics  and  Fluid  Dynamics 
Naval  Research  Laboratory 
Washington,  DC  20375-5344 


L.  Sirovich 

Department  of  Mathematics 
Brown  University 
Providence,  RI 02912 


Abstract-  Recent  numerical1  and  physical2  experiments  of  channel  flow  have  clearly  shown  that  large  reductions  in  drag  can  be 
achieved  by  forcing  the  turbulence  at  appropriate  length  and  time  scales.  In  this  paper  we  present  new  results  from  direct 
numerical  simulations  of  turbulent  channel  flow  in  which  we  apply  internal  body  forces,  intended  to  model  Lorentz  forces,  to  the 
turbulence,  using  a  random  phasing.  In  all  cases  where  the  drag  is  modified  we  observe  an  increase,  suggesting  that  random 
phasing  alone  is  insufficient  to  achieve  drag  reduction.  Some  future  directions  for  the  research  are  discussed. 


L  INTRODUCTION 

Recent  numerical1  and  physical2  experiments  have  clearly  shown 
that  significant  reductions  in  drag  can  be  achieved  by  forcing  the 
turbulence  at  appropriate  length  and  time  scales.  In  fact,  the  above 
cited  numerical  experiments  show  that  a  reduction  on  the  order  of  58% 
can  be  achieved.  These  dramatic  reductions  in  drag  have  been 
achieved  by  a  novel  forcing  in  which  the  phases  of  the  energy 
containing  wave-like  modes  of  turbulence  are  periodically 
randomized.  It  is  further  noted  that  the  reduction  achieved  in  this  way 
rivals  that  pro-induced  drag  reduction.  A  remarkable  result  is  that  the 
drag  reduced  turbulence  achieved  in  this  way  is  almost 
indistinguishable  in  every  way  from  that  achieved  using  polymers.  This 
work  also  hints  at  a  fundamentally  new  view  of  turbulent  boundary 
layer  dynamics3.  The  physical  experiments2  noted  above  were 
designed  to  mimic  this  forcing  by  employing  a  randomized  array  of 
surface  roughness  and  were  also  successful  in  reducing  drag  by  more 
than  10%.  These  investigations  point  out  that  forcing  the  turbulence  at 
the  appropriate  length  and  time  scales  is  the  key  to  the  successful 
control  of  wall  bounded  turbulence.  It  is  also  clear  that  the  use  of  direct 
numerical  simulations  can  be  an  extremely  cost  effective  tool  in 
exploring  not  only  the  fundamental  physics  of  turbulence,  but  also  in 
testing  novel  ideas  and  rapidly  sorting  out  what  works,  what  does  not, 
and  why. 

In  this  paper  we  present  new  results  from  direct  numerical 
simulations  of  turbulent  channel  flow  in  which  we  apply  internal  body 
forces  to  the  turbulence,  using  a  random  phasing.  The  forcing  models 
that  which  can  be  achieved  using  Lorentz  forces.  Since  a  real  force  is 
applied  to  the  flow,  in  this  case  work  is  being  done.  In  this  respect  the 
present  calculations  differ  from  the  earlier  phase  randomization 
simulations  in  which  no  work  was  done  on  the  fluid1. 

II.  SETTING  UP  THE  PROBLEM 

We  have  performed  direct  numerical  simulations  of  turbulence  in 
a  periodic  channel  with  rigid  no-slip  walls.  Following  earlier 
treatments4, 5  a  fully  spectral  code  is  used,  in  which  the  velocity  field  is 
approximated  by  Fourier  modes  in  the  streamwise  (x)  and  spanwise  (z) 
directions  and  Chebyshev  polynomials  in  the  wall-normal  (y)  direction. 
In  the  present  instance  the  turbulent  flow  is  driven  by  a  constant 
streamwise  pressure  gradient.  For  all  simulations  reported  here  we 
have  used  65  x  64  x  68  grid  points  in  the  y,  z,  and  x  directions, 
respectively.  The  channel  dimensions  are  ly~  2hf  Z*  =  5h,  and  Z*  =  1  Oh 
where  h  is  the  channel  half  width.  Our  starting  point  is  the  Navier- 
Stokes  equations,  written  here  in  a  dimensionless  rotation  form: 

—  =  v  x  co  -  VII  +  lv2  v  +  AV,  (1) 

dt  R 

V  •  v  =  0,  (2) 


where  v(x,  t)  »  flow  velocity,  to  (x,  /)  =  V  x  v  *  vorticity,  II(x,  t)  ■ 
mechanical  pressure  +  kinetic  energy  density,  R  -  U„LJv  ■  Reynolds 
number  (with  the  viscosity  assumed  to  be  constant  and  uniform). 
Furthermore,  F(x,  z)  is  the  applied  Lorentz  force,  and  A(t)  is  the 


amplitude  of  this  force.  In  this  representation,  U  is  measured  in  units  of 
the  velocity  field  at  y  ~  0.  The  time  is  measured  in  units  of 
characteristic  flow  time,  4/t/0,  where  the  characteristic  distance,  Z*,,  is 
defined  by  the  half- width  of  the  channel. 

The  force  field  corresponding  to  the  wave-like  modes  is 

given  by: 

F(jc,z)  =  Rc{exp[/(k-x+(j>)]}  (3) 


where  is  a  random  phase.  This  gives 

Fx=  2  [cos(k,,x+kmz+fam)+cos(k^-kmz-fam)]  (4) 

n,ro 

and 

=  2  [cos(^+AMz+<^ff,)-cos(^-A:mz-(|)„ff,)]  (5) 

n,m 

The  time  dependence  is  a  square  wave  function  given  by: 


f  |,  if  mod  (ite)=100  and  it-its  <  10; 

(6) 

^  0,  otherwise; 

where  it  is  the  iteration  level  and  its  is  basically  every  hundredth 
iteration.  The  parameter  §  is  the  amplitude  of  the  forcing  function. 

Before  applying  random  forcing  with  the  Lorentz  force  we 
integrated  forward  in  time  until  a  steady  state  was  established.  This  was 
shown  to  satisfy  the  averaged  form  of  the  streamwise  momentum 
equation  for  statistically  steady  turbulence.  In  tins  flow  we  have  chosen 
a  pressure  gradient  such  that  R*  -  u*h/v  =  125  in  the  steady  state. 
Once  we  have  established  a  steady  state  turbulence  in  this  way  the 
fluctuating  force  field  is  turned  on. 

III.  LOW  WAVENUMBER  LORENTZ  FORCING 

The  particular  cases  that  we  have  chosen  rely  on  the  phase 
randomization  calculations  for  fixing  the  wavenumber  space.  For  the 
forcing  functions  defined  in  equations  4  and  5  we  have  0  s  n  s  1 1  and  I 
as  m  *  6.  The  forcing  function  is  turned  on  every  one  hundred  time  steps 
for  a  duration  of  ten  time  steps,  as  indicated  in  equation  6.  Some  results 
of  the  numerical  simulations  are  shown  in  Figures  1  and  2.  Figure  1 
shows  the  mass  flux  Reynolds  number,  Rbi  as  a  function  of  /*.  The 
quantity  t*  is  related  to  the  viscous  time  by  t*  =  (u*)2t/v.  The 
calculations  shown  in  Figures  1  and  2  are  run  for  approximately  40 
viscous  time  periods. 

We  define  the  mass  flux  Reynolds  number  as  Rb  =  Ubh/v,  where 
Ub  =  1/2  J02h  U(y)  dy.  A  decrease  in  drag  would  appear  in  Figure  1 
as  an  increase  in  Rb.  It  is  apparent  that  in  no  case  does  drag  reduction 
occur.  Rather,  above  a  threshold  value  of  £  ~0.1  Rb  is  seen  to  decrease 
strongly,  indicating  an  increase  in  drag.  For  £  -  0.25  the  decrease  in  Rb 
is  about  3%,  while  for  £  «  1.,  Rb  decreases  by  about  19%.  Figure  2 
shows  the  friction  Reynolds  number  R*(~  u*/hv)  as  a  function  of  it. 


131 


Here  the  friction  velocity  u*  =  (r  j>)1/2,  with  xw  being  the  wall  shear 
stress  and  pis  the  mass  density  of  the  fluid.  As  noted  above,  R*  must 
return  to  its  equilibrium  value  of  125  since  the  driving  pressure  was 
held  constant  throughout  the  simulations.  In  all  cases  we  see  that  R* 
returns  to  a  value  close  to  its  initial  value,  indicating  that  the  system  has 
settled  down  to  a  new  turbulent  state. 

IV.  CONCLUSIONS 

The  numerical  calculations  reported  in  this  paper  represent  a  first 
attempt  to  reduce  drag  in  turbulent  flows  by  the  application  of  spatially 
random  Lorentz  forces.  Unfortunately,  in  no  case  was  drag  reduction 
achieved.  Hence  random  phasing  of  the  Lorentz  force  is  apparently 
insufficient  for  producing  drag  reduction.  In  fact,  we  observed 
significant  drag  increases  for  several  cases.  To  achieve  this  increase  in 
drag  a  rather  large  force  had  to  applied.  This  force  was  on  the  order  of 
1000  times  the  driving  pressure  gradient.  A  key  difference  between 
these  simulations  and  earlier  ones  is  that  here  we  are  doing  work  on 
the  flow.  In  the  earlier  phase  randomization  calculations  no  work  was 
done.  It  is  intriguing  that  force  amplitudes  of  10  to  100  times  the  driving 
pressure  gradient  did  not  change  the  drag  significantly. 

Our  present  results  point  the  way  to  future  directions  for  this 
research.  As  was  performed  for  the  phase  randomization  calculations 
different  wavenumber  bands  should  be  investigated.  Different  phases 
and  forcing  frequencies  and  durations  also  should  be  tried.  Vertical 
tapering  of  the  force  would  confine  its  effect  to  the  buffer  layer,  and 
hence  this  feature  should  be  included.  Finally,  the  present  simulations 
utilize  a  spatially  random  but  temporally  constant  Lorentz  force  profile. 
The  effect  of  temporal  randomness  might  be  significant.  It  would  also 
be  of  interest  to  determine  the  relationship  between  the  applied  force 
and  the  turbulent  dynamics  that  underlie  the  apparent  insensitivity  to  a 
range  of  external  force  amplitudes. 

V.  ACKNOWLEDGMENTS 

This  work  was  supported  by  ONR.  The  numerical  simulations 
were  performed  on  the  Cray  C90  at  WPAFB  under  a  grant  of  time 
from  the  DoD  HPC  program. 


VI.  REFERENCES 

1.  Handler,  R.  A.,  E.  Levich  and  L.  Sirovich,  Drag  reduction  in 
turbulent  channel  flow  by  phase  randomization ,  Phys.  Fluids  A,  5 
686,(1993). 

2.  L.  Sirovich  and  S.  Karlsson  Turbulent  drag  reduction  by  passive 
means ,  Nature,  August,  753,  (1997). 

3.  P.  Carpenter,  The  right  sort  of  roughness ,  Nature,  August,  13, 
(1997). 

4.  J.  Kim,  P.  Moin,  and  R.  Moser,  Turbulence  statistics  in  fully 
developed  channel  flow ,  J.  Fluid  Mech.,  177, 133,  (1987). 

5.  R.A.  Handler,  E.W.  Hendricks,  and  R.I.  Leighton,  Low  Reynolds 
number  calculation  of  turbulent  channel  flow:  a  general 
discussion ,  Naval  Research  Laboratory  Memorandum  Report 
6410,  (1989). 


132 


1850 


Figure  1:  Mass  flux  Reynolds  numbers  versus  time. 


25  *  50  75  100 

t 


igure  2:  Friction  Reynolds  numbers  versus  time. 


ADAPTIVE  FEED-FORWARD  CONTROL  OF  TURBULENT  BOUNDARY  LAYERS 


K.S.  Breuer,  R.  Rathnasinghamf  K.  Amonlirdviman 
Department  of  Aeronautics  and  Astronautics 
Massachusetts  Institute  of  Technology 
Cambridge ,  MA  02139 
breuer@mit . edu 


We  discuss  recent  progress  in  active  control  of  the  near- wall  region  of  a  turbulent  boundary  layer  using  a  linear  adaptive 
feed-forward  control.  A  wall-based  detection  scheme  is  described  which  effectively  detects  coherent  structures  and 
predicts  downstream  flow  behavior.  The  detection  scheme  is  based  on  correlation  function  measured  experimentally 
between  adjacent  input  sensors  and  defined  control  points.  By  saving  only  the  portion  of  the  signal  that  is  correlated 
over  some  small  spanwise  distance,  large-scale  coherent  structures  can  be  effectively  identified  in  real  time.  The 
conditioned  input  signals  are  used  to  compute  optimal  linear  transfer  functions  between  the  sensors  and  the  control 
locations  and  these  transfer  functions  are  then  used  in  an  adaptive  feed-forward  control  system  to  minimize  turbulent 
fluctuations  at  the  control  points.  The  algorithm  is  demonstrated  to  work  surprisingly  well,  reducing  turbulent  velocity 
fluctuations  in  the  near  wall  region  by  over  30%  and  reducing  wall  pressure  fluctuations  by  17%. 


1  INTRODUCTION 

Recent  advances  in  the  understanding  of  near-wall  turbulent 
shear  flow  structure  have  resulted  in  several  suggestions  for 
active  control  including  schemes  based  on  qualitative  phys¬ 
ical  arguments  [5],  formal  optimal  control  [3],  neural  net¬ 
works  [9]  and  reduced-order  dynamical  representations  of  the 
near- wall  region  [7]  (A  review  of  the  main  approaches  was 
recently  presented  by  Moin  and  Bewley  [15]).  Several  prob¬ 
lems,  both  theoretical  and  practical  face  the  successful  im¬ 
plementation  of  a  real-time  turbulence  control  scheme.  From 
the  theoretical  side,  the  complexity  of  the  turbulent  bound¬ 
ary  layer  and  its  dynamics  make  the  choice  of  a  control  algo¬ 
rithm  far  from  intuitive.  From  the  practical  side,  the  spatial 
and  temporal  scales  at  which  the  control  must  be  executed 
make  the  design  of  sensors,  actuators  and  control  hardware 
very  challenging. 

This  paper  describes  some  of  the  recent  results  demon¬ 
strated  in  our  group  in  which  a  conceptually  simple  control 
algorithm  has  been  developed  for  near  wall  turbulence  con¬ 
trol  [19,  16].  The  algorithm  is  based  on  the  short-time  lin¬ 
ear  dynamics  of  the  coherent  structures  and  an  adaptive  feed¬ 
forward  algorithm  to  predict  and  inhibit  the  development  of 
turbulence-producing  events.  The  experiments  have  shown 
a  uniform  31%  reduction  in  turbulent  v! -fluctuations  in  the 
near- wall  region  as  well  as  a  17%  reduction  in  turbulent  wall- 
pressure  fluctuations. 

2  OVERVIEW  OF  CONTROL  STRATEGY 

The  control  approach  is  based  on  two  key  assumptions, 
namely:  (i)  that  the  majority  of  the  turbulence-producing 

*  Present  Address,  Schlumbeger  Research  Center.  Ridgefield  CT 


events  in  the  near- wall  region  of  the  flow  are  associated  with 
the  large-scale  “coherent  structures”  and  (ii)  that  these  co¬ 
herent  structures  may  be  modeled  (for  short  times)  by  dy¬ 
namical  equations  which  are  linear  with  respect  to  the  mean 
flow.  The  first  assertion  is  supported  by  a  large  body  of  re¬ 
search  on  coherent  structures  over  the  past  twenty  years,  and 
is  well-illustrated  by  Johansson,  Alfredsson  &  Kim’s  analysis 
of  numerically-generated  turbulence  [10]  in  which  they  report 
that  the  coherent  structures,  while  only  occupying  25%  of  the 
volume  in  the  near-wall  region,  are  responsible  for  50%  of 
the  total  turbulence  production.  The  assumption  of  linearity 
is  based  on  the  observation  that  the  strong  mean  shear  of  the 
near-wall  turbulent  flow  will  dominate  the  short-time  evolu¬ 
tion  of  small  perturbations.  This  is  consistent  with  the  frame¬ 
work  provided  by  the  Rapid  Distortion  Theory  of  turbulence 
[8]  and  other  models  for  near- wall  turbulence  [12].  In  addi¬ 
tion,  experiments  by  Johansson,  Her  &  Haritonidis  [11]  found 
that  conditionally-sampled  u ,  v  and  p  signals  scaled  linearly 
with  threshold  amplitude,  again  suggesting  an  amplitude- 
invariant  behavior  for  these  coherent  structures.  For  the  pur¬ 
poses  of  control,  this  linearity  assumption  need  only  hold  for 
the  short  time  it  takes  a  structure  to  advect  from  an  upstream 
sensor  to  an  actuator  and  does  not  imply  that  turbulence  pro¬ 
duction  as  a  whole  is  governed  by  a  linear  mechanism. 

Given  these  working  assumptions,  the  control  strategy  pur¬ 
sued  in  these  experiments  is  shown  schematically  in  figure  1. 
A  multiple-input,  multiple  output  (MIMO)  linear  filter  [2]  is 
constructed  as  an  estimate  of  the  transfer  function  between 
signals  from  a  spanwise  array  of  upstream  wall-based  sen¬ 
sors  (in  this  case  from  three  sensors:  52(f)  and  s3(£)) 

and  the  signals  from  sensors  located  at  downstream  control 
points  (again,  in  this  case,  three  sensors:  ci,C2  and  c3).  The 
estimated  transfer  function  is  represented  in  figure  1  as  Hi, 
while  the  physical  (true)  relationship  between  the  upstream 


135 


FLOW 


{+  other  inputs 


Figure  1 :  Schematic  diagram  showing  the  plant  -  the  turbulent 
boundary  layer  -  together  with  detection  sensors  (si,  S2,  S3), 
actuators  (ui ,  ®2 ,  s3 )  and  downstream  control  points  (cj ,  C2 
and  C3).  The  block  diagram  below  the  dotted  line  repre¬ 
sents  the  controller  including  the  adaptive  feedback  path.  Hi 
and  H2  are  actual  transfer  functions,  while  Hi  and  H2  are 
their  linear  estimates,  derived  from  cross-correlation  mea¬ 
surements. 

and  downstream  sensors  is  indicated  by  Hi .  in  general  Hi 
will  not  be  equal  to  Hi,  the  difference  resulting  from  both 
nonlinear  relationship  between  the  two  arrays  of  sensor  sig¬ 
nals  and  the  fact  that  the  signals  at  the  downstream  sensor 
array  will  also  be  affected  by  other  inputs  not  sensed  by  the 
upstream  sensor  array  (for  example,  outer-flow  effects,  etc). 

In  a  similar  manner,  we  construct  a  linear  transfer  function 
between  the  actuators  and  the  downstream  control  points  (in 
this  case,  a  3  x  3  matrix  of  transfer  functions).  This  is  repre¬ 
sented  by  i?2  and,  as  before,  the  “true”  relationship  between 
the  actuators  and  Cj  is  nonlinear  and  includes  additional  in¬ 
puts,  not  captured  by  this  representation. 

With  these  two  transfer  functions  (or,  more  correctly,  sys¬ 
tems  of  transfer  functions),  we  construct  a  feed-forward  con¬ 
trol  system  such  that  if  Hi  and  H2  were  completely  accurate 
descriptions  of  the  full  system,  the  fluctuating  signal  at  each 
control  point,  c,  would  be  zero.  In  reality,  small  variations, 
slow  changes  and  more-importantly,  nonlinearities  and  non¬ 
observed  inputs  will  result  in  an  error  at  the  control  points 
such  that  the  fluctuations  will  not  be  identically  zero.  How¬ 
ever,  the  error  can  be  further  minimized  by  perturbing  the  fil¬ 
ter  coefficients,  either  randomly  or  by  some  proscribed  adap¬ 
tive  optimization  scheme.  In  this  manner,  the  overall  control 
performance  can  be  optimized  or  adapted  to  suit  changing 
freestream  conditions. 

This  control  approach  is  quite  general  and  may  be  applied 
to  an  arbitrary  number  of  upstream  sensors,  actuators  and 
downstream  sensors  (control  points).  It  has  several  appeal¬ 
ing  features,  namely: 

1.  The  filters  are  pre-computed,  and  only  require  low- 
bandwidth  adaptation  to  maximize  their  performance. 
This  architecture  greatly  simplifies  the  implementation 
when  compared,  for  example,  with  neural  network  or 
“bang-bang”  control  schemes  which  typically  require 
large  computational  resources  for  real-time  operation 


and  extensive  training  periods. 

2.  In  the  current  implementation,  the  filters  are  linear  FIR 
filters  which  could  even  be  implemented  using  analog 
technology  for  high  speed  and  low  cost.  More  complex 
filter  implementations  (HR)  can  be  implemented  with  a 
moderate  increase  in  complexity  for  even  more  efficient 
hardware  implementation. 

3.  The  template  of  transfer  functions  is  finite  and  inde¬ 
pendent  of  what  goes  on  in  the  rest  of  the  flow.  This 
is  self-determined  by  the  fact  that  the  correlation  be¬ 
tween  the  sensors  systems  will  naturally  approach  zero 
as  their  separation  increases  and  thus  no  additional  con¬ 
tribution  to  the  transfer  function  is  achieved.  This  means 
that  control  is  local  and  can  be  implemented  as  an  over¬ 
lapping  network  of  local  controllers  with  only  moderate 
“supervisory”  attention  to  optimize  and  update  filter  co¬ 
efficients. 

4.  This  local  nature  of  the  control  allows  for  complete  seal- 
ability  to  larger  areas  of  control  authority.  The  local 
processing  power  need  not  become  more  powerful,  only 
more  dense. 

2.1  SENSOR  PRE-CONDITIONING 

Central  to  the  success  of  this  scheme  is  the  ability  to  accu¬ 
rately  predict  the  flow  state  at  the  downstream  sensors,  d,  us¬ 
ing  the  upstream  wall  sensors,  s*.  For  the  turbulent  boundary 
layer,  the  dominant  contribution  over  such  large  distances  is 
by  the  large-scale  coherent  structures,  and  thus  the  problem  of 
prediction  becomes  one  of  (i)  identification  of  the  large  scale 
structures  and  (ii)  prediction  of  their  evolution.  If  we  assume 
that  we  can  define  large  scale  structures  statistically,  i.e.  any 
signal  that  retains  finite  correlation  over  some  spanwise  dis¬ 
tance,  then  the  identification  can  be  efficiently  achieved  using 
a  conditioned  spectral  analysis  [2]  which  isolates  the  corre¬ 
lated  portion  of  (any)  two  signals.  This  is  best  expressed  in 
the  frequency  domain: 

c^-W)SM  (l) 

where  Gy  is  the  correlated  part  of  the  two  signals  St  and  Sj 
(Si(t)  and  s2(j)  expressed  in  the  frequency  domain),  Gy  and 
Gjj  are  the  cross-spectra  and  auto-spectra  respectively.  Note 
that  for  a  spatially  homogeneous  field  (such  as  the  spanwise 
direction  in  a  turbulent  boundary  layer),  Gy  is  identical  to 
Cji. 

The  conditioning  filter,  Gy /Gy,  is  nothing  more  than  a 
linear  filter  which  pre-conditions  the  input  signals  weighting 
them  to  favor  a  frequency  band  determined  to  be  most  highly 
correlated.  In  this  sense,  it  is  a  rather  simple  pre-conditioning 
and  many  more  complex  pre-conditioning  schemes  can  be  en¬ 
visaged,  particularly  if  a  dynamic  model  of  the  near-wall  re¬ 
gion  of  the  boundary  layer  were  available,  in  which  case  a 
Kalman  filter  could  be  constructed.  This  would  give  a  real¬ 
time  identification  of  large-scale  structures  and,  presumably, 
a  superior  performance  over  the  simple  case  presented  here. 


136 


Figure  2:  Cross-correlations  between  the  upstream  wall-shear 
sensors  and  the  downstream  velocity  sensor,  c2  (located  300/* 
downstream  and  at  y+  =  10).  The  three  curves  represent  (i) 
$2  aligned  in  the  cross-stream  direction  (sensitive  to  stream- 
wise  shear),  (ii)  s2  aligned  in  the  streamwise  direction  (more 
sensitive  to  spanwise  shear)  and  (iii)  The  correlated  portion 
of  si  and  s2  (ci2),  both  aligned  to  be  sensitive  to  spanwise 
shear. 

The  effectiveness  of  the  conditioned  spectral  analysis  is 
illustrated  in  figure  2  which  shows  the  measured  cross¬ 
correlation  between  the  shear  measured  by  the  upstream  sen¬ 
sor  (si)  and  a  velocity  sensor  placed  at  c2,  300/*  downstream 
of  the  middle  sensor  (s2).  All  of  the  experiments  reported 
here  were  conducted  in  a  fully-developed,  zero-pressure- 
gradient  turbulent  boundary  layer  with  Ree  =  I960.  For 
reference,  the  friction  velocity,  ur,  was  0.31  m/s,  the  viscous 
length  scale,  /*,  was  55  fim  and  the  viscous  time  scale,  £*, 
was  270  (is.  Each  wall  sensor  consisted  of  a  flush-mounted 
constant-temperature  hot  wire,  sensitive  to  wall  shear.  When 
the  wires  are  aligned  normal  to  the  flow  direction,  they  are 
most  sensitive  to  streamwise  shear.  However,  figure  2  indi¬ 
cates  that  in  this  orientation  the  correlation  between  the  wall 
shear  and  the  downstream  velocity  sensor  is  relatively  poor. 
However,  when  the  surface  wires  were  aligned  in  the  flow 
direction  (making  them  more  sensitive  to  spanwise  shear), 
a  marked  improvement  in  the  cross-correlation  is  observed. 
Furthermore,  after  adopting  the  signal  conditioning  technique 
(equation  1),  the  maximum  cross-correlation  (now  between 
C12  and  c2)  improves  by  an  additional  50%  to  0.6.  The  time 
delay  of  the  maximum  corresponds  to  the  transit  time  of  the 
large-scale  structures  from  one  sensor  to  the  other  and  repre¬ 
sents  a  lag  in  the  control  scheme. 

The  alignment  of  the  hot  wire  with  the  flow  is  some¬ 
what  counter-intuitive  and  care  must  be  taken  in  interpret¬ 
ing  its  results.  A  conventional  hot-wire  shear  sensor  (one 
aligned  perpendicular  to  the  primary  flow  direction)  is  pre¬ 
dominantly  sensitive  to  the  streamwise  shear  stress,  du/dy 
and  only  slightly  sensitive  to  the  magnitude  of  the  spanwise 
shear  stress,  \dw/dy\.  By  rotating  the  wire,  the  mean  sig¬ 
nal  of  the  sensor  remains  dominated  by  the  streamwise  shear 
(since  it  is  so  large).  However,  the  fluctuating  part  of  the 


signal  (which  is  the  only  part  of  interest  to  the  linear  con¬ 
troller)  is  now  dominated  by  the  magnitude  of  the  spanwise 
shear  fluctuations  and  only  slightly  sensitive  to  fluctuations 
in  streamwise  shear.  The  improved  performance  of  spanwise 
shear  as  a  control  input  has  also  been  noted  in  numerical  ex¬ 
periments  for  active  flow  control  [13]. 

A  second  practical  aspect  of  the  sensor  configuration  is 
also  worth  noting:  the  alignment  of  the  wire  gives  the  sensor 
extremely  good  spatial  resolution  in  the  spanwise  direction 
(limited  by  the  thickness  of  the  sensing  wire  which  for  these 
experiments  was  2.5  fjxa  -  less  than  Z*/20).  The  streamwise 
resolution  of  the  sensor  (dictated  by  the  length  of  the  sensing 
wire)  is  somewhat  worse  (in  our  case  about  10/*).  However, 
this  preferential  sensitivity  matches  the  shape  of  the  coherent 
structures  we  are  trying  to  detect  which  are  typically  greatly 
elongated  in  the  streamwise  direction.  This  geometric  factor 
might  be  one  reason  for  the  observed  improvement  in  control 
performance. 

2.2  FORWARD  PREDICTION  AND  THE 
WIENER  FILTER 

With  the  pre-conditioned  input  signals,  we  now  need  to  pre¬ 
dict  the  evolution  of  the  large-scale  structures  so  that  we  can 
schedule  the  actuators  to  minimize  the  error  signal  at  the 
downstream  control  points.  Again,  assuming  a  statistically 
linear  transfer  function,  we  derive  a  Wiener  filter  to  opti¬ 
mally  predict  the  downstream  flow  quantity,  c*,  from  the  con¬ 
ditioned  input  data.  The  Wiener  filter  is  the  linear  filter  which 
minimizes  the  mean-square  error  between  the  flow  field  pre¬ 
dicted  by  the  sensor  inputs  and  the  actual  flow  properties  at  a 
remote  location.  The  filter  is  expressed  as  a  set  of  weighting 
constants  which  multiply  the  input  signal  (collected  at  differ¬ 
ent  points  in  both  space  and  time)  and  thus  maps  the  input 
signal  onto  a  predicted  value  for  the  desired  flow  parame¬ 
ter.  The  weighting  constants  are  determined  by  solving  a  set 
of  simultaneous  equations  which  relate  the  auto-  and  cross¬ 
correlations  of  the  sensor  inputs  and  the  correlations  with  the 
desired  output.  These  equations  may  be  expressed  as  a  series 
of  linear  equations: 


$11  $12  • 

•  $1AT 

'  H i  ’ 

$21 

H2 

= 

$2  y 

$iVl 

&NN 

_  hn  _ 

where  $ij  is  the  auto- correlation  of  the  input  signals  taken 
from  different  time/space  slices,  and  <f>iy  is  the  cross¬ 
correlation  between  the  input  and  output  signals.  Solving  for 
Hi,  H2, .  --Hn  results  in  the  linear  filter  to  estimate  the  out¬ 
put  from  the  N  inputs.  The  inputs  can  be  located  anywhere 
in  space  and  time  and  can  even  be  comprised  of  multiple  flow 
quantities,  so  long  as  the  cross  correlations  between  each  of 
the  sensors  are  known.  As  described  here,  the  filter  is  derived 
as  a  Finite  Impulse  Response  (FIR)  filter.  This  can,  if  so  de¬ 
sired,  be  approximated  as  a  Infinite  Impulse  Response  (HR) 
filter  for  more  compact  representation  in  a  real-time  control 


137 


10’  10’  io''  io" 

r 


Figure  3:  Cross-spectra  between  the  detection  sensors  and 
the  streamwise  velocity  300/*  downstream;  (a)  with  a  single 
sensor,  (b)  with  a  pair  of  sensors  separated  by  40/*  in  the 
span  wise  direction,  (c)  with  three  sensors  separated  by  40/*, 
(d)  with  a  single  sensor  whose  signal  is  filtered  to  emphasize 
the  most  coherent  structures  in  the  flow  and  (e)  three  sen¬ 
sors  centered  about  the  downstream  measurement  point  and 
all  filtered  to  emphasize  the  large  scale  motion.  The  solid 
and  dashed  lines  represent  the  predicted  and  measured  spec¬ 
tra,  respectively.  The  dashed-dotted  line  represents  the  line 
that  passes  through  the  downstream  measurement  point. 

system.  However,  this  must  be  done  with  care  to  avoid  filter 
instabilities  and  causality  problems  in  the  control  system. 

2.3  ADDITIONAL  INPUT  WEIGHTING 
SCHEMES 

In  its  most  basic  form,  the  Wiener  filter  uses  the  raw  input 
signals  or  perhaps  the  pre-conditioned  signals,  as  described 


earlier.  However,  by  combining  the  input  signals  in  differ¬ 
ent  ways,  different  Wiener  filters  can  be  derived,  each  with 
different  forward  prediction  performance.  This  is  illustrated 
in  figure  3  which  shows  a  variety  of  different  combinations 
and  their  different  predictive  performance.  Here,  the  predic¬ 
tive  performance  is  measured  as  the  rms  difference  between 
the  predicted  signal  and  the  signal  actually  measured  (in  this 
case  the  streamwise  fluctuating  velocity  300  /‘downstream  of 
the  input  sensors).  Figure  3a  shows  that  a  single  in-line  sensor 
predicted  urms  with  an  error  of  7.1%.  Using  a  pair  of  sensors 
(figure  3b)  made  a  marked  improvement,  reducing  this  error 
to  4.4%.  The  increased  performance  of  the  second  configu¬ 
ration  suggests  that  the  flow  structures  that  contribute  to  the 
linear  relationship  between  the  upstream  and  downstream  sig¬ 
nals  possess  some  degree  of  spanwise  spatial  coherence.  An 
addition  of  a  third  sensor,  shown  in  figure  3c,  further  reduces 
the  prediction  error  to  3.8%,  indicating  that  the  coherence  of 
the  large  scale  flow  structures  extend  up  to  80/*  in  the  span- 
wise  direction  (agreeing  with  the  typically  quoted  value  of 
100/*) 

Figures  3d  and  e  represent  configurations  with  filters  in¬ 
corporated  to  emphasize  the  coherent  scales.  Each  FIR  filter, 
Lij,  has  32  poles  and  was  constructed  from  the  cross-spectra 
between  adjacent  sensors,  as  described  earlier.  The  configu¬ 
ration  shown  in  figure  3d  uses  a  filtered  signal  from  the  mid¬ 
dle  sensor  alone  to  estimate  the  signals  from  all  three  sensors. 
This  was  done  by  combining  the  signal  from  the  middle  sen¬ 
sor  with  the  filters  L2 1  and  L23  which  correspond  to  the  part 
of  the  adjacent  sensor  signals  that  are  correlated  with  the  mid¬ 
dle  sensor  signal.  The  prediction  error  for  this  configuration 
was  2.9%  and  corresponded  to  the  lowest  value  obtained.  The 
effect  of  the  filters  can  be  readily  observed  from  the  plots  of 
the  cross-spectra.  The  low  frequencies  were  more  accurately 
reproduced  than  in  the  unfiltered  cases  shown  in  Figures  3a. 
This  improvement  was  attributed  to  the  preferential  weighting 
of  these  lower  frequencies  imposed  by  the  conditioned  anal¬ 
ysis.  Finally,  an  attempt  to  combine  all  sensors  to  produce 
an  optimal  configuration  is  shown  in  figure  3e.  It  combines 
the  highly  effective  prediction  of  the  middle  sensor  with  the 
filtered  signals  of  the  adjacent  sensors  to  extract  the  most  co¬ 
herent  parts  from  all  signals.  The  prediction  error  of  2.9% 
was  identical  to  that  with  just  the  middle  sensor.  This  seems 
to  suggest  the  addition  of  adjacent  sensors  will  have  no  ef¬ 
fect  on  the  prediction  of  u.  However,  on  closer  examination 
of  the  cross-spectra,  the  lower  frequencies  is  seen  to  be  more 
accurately  predicted,  so  that  although  the  overall  error  is  un¬ 
changed  (over  the  entire  frequency  range),  the  improved  pre¬ 
diction  of  the  larger  scales  may  improve  controllability  of  the 
flow. 

The  phase  diagrams,  which  were  not  shown  in  the  figures, 
exhibited  a  constant  slope  (always  true  for  a  FIR  filter),  which 
corresponded  to  a  lag  that  matched  the  average  convection 
speed  of  the  large  scale  structures  (u+  =  10.7,  where  the  con¬ 
vection  speed  uc  has  been  normalized  by  the  friction  velocity, 
uT).  This  lag  was  seen  to  be  constant  for  all  cross-spectra  be¬ 
tween  the  upstream  and  downstream  sensors. 


138 


3  CONTROL  PERFORMANCE 


With  the  shear  sensors  aligned  with  the  flow  direction,  the 
forward  prediction,  Hi,  was  thus  computed  from  the  condi¬ 
tioned  signals  Cu  and  C23  and  then  approximated  by  a  linear 
32-pole  FIR  filter.  This  low-order  approximation  is  necessary 
for  efficient  implementation  in  our  real-time  digital  controller. 
The  final  form  of  the  filter  was  able  to  predict  v!  measured  at 
C2  from  shear  stress  measured  at  $i,  s2  and  S3,  (300  Z*apart) 
with  a  maximum  rms-error  of  less  than  3%.  Hi  was  then 
combined  (as  shown  in  figure  1)  with  H2  -  the  transfer  func¬ 
tion  between  each  actuator  control  voltage  and  a  -  to  provide 
the  appropriate  input  to  the  actuator  array  so  that  the  resul¬ 
tant  signal  at  the  downstream  sensors  would  be  (ideally)  zero. 
For  the  current  experiments,  the  adaptation  algorithm  simply 
minimized  the  rms  of  the  error  signal,  c2,  by  varying  the  gain 
and  lag  of  the  forward  predictive  filter.  More  sophisticated 
forms  of  adaptation  are  possible  and  will  be  explored  in  the 
future. 

For  the  current  results,  only  three  sensors  and  three  actu¬ 
ators  were  used  in  a  proof- of-concept  experiment.  The  actu¬ 
ators  chosen  were  resonant  membrane  “zero-net-mass-flux” 
devices,  similar  in  nature  to  those  described  by  Coe  et  al  [6], 
although  modified  so  that  the  control  jet  discharges  from  a 
streamwise-aligned  slit  measuring  10 /*  by  150 1 *.  The  phys¬ 
ical  parameters  of  the  actuators  were  chosen  so  as  to  optimize 
the  actuator’s  performance  [17],  The  resultant  devices  oper¬ 
ated  at  a  resonant  frequency  of  2  kHz  and  were  capable  of 
producing  exit  velocities  up  to  .4  m/s  (1.3  uT).  The  oscilla¬ 
tory  flow  through  the  streamwise  slit  was  measured  [14]  and 
found  to  produce  a  pair  of  counter-rotating  streamwise  vor¬ 
tices,  very  similar  to  that  observed  (in  a  laminar  boundary 
layer)  by  Jacobson  &  Reynolds  [9]  who  used  similar  devices 
and  who  also  successfully  demonstrated  control  of  stream- 
wise  vortical  structures  in  a  laminar  boundary  layer. 

As  discussed  above,  all  of  the  experiments  were  carried  out 
in  a  fully  developed,  zero-pressure-gradient  turbulent  bound¬ 
ary  layer  at  a  Reynolds  number  based  on  momentum  thick¬ 
ness  of  1960.  The  viscous  length  and  time  scales  at  this 
Reynolds  number  are  55^m  and  270/xs,  respectively.  To  en¬ 
sure  the  statistical  convergence  of  the  measured  data,  record 
lengths  were  based  on  a  95%  confidence  level  with  a  0.2% 
uncertainty  in  the  root-mean- squared  value.  This  resulted  in 
data  records  consisting  of  2  x  106  independent  sample  points. 

The  control  loop  was  implemented  using  a  60  MHz  DSP- 
based  real-time  signal-processing  board  and  operated  at  35 
kHZ  (9.5/*)  -  much  faster  than  was  actually  required.  For  the 
current  experiments,  the  downstream  sensor  was  a  traversable 
hot  wire,  located  downstream  of  the  actuator  array  and  the 
control  objective  was  thus  to  minimize  ul  fluctuations  at  the 
location  of  this  sensor.  A  more  technologically  relevant  ob¬ 
jective  might  be  to  use  a  wall-mounted  shear  or  pressure  sen¬ 
sor,  with  corresponding  objectives  of  minimizing  turbulent 
wall  shear  or  pressure  fluctuations.  The  convenience  of  a 
movable  sensor  for  diagnostics  and  optimization  dictated  the 
choice  of  uf  for  most  of  the  experiments,  although  we  also 
report  on  some  limited  experiments  aimed  at  the  control  of 


ior 
0  < 

%Aurms  -10 
-20 
-30 

-40L 


o  steady  forcing 
+  real  time  control 


0.2  0.4  0.6  0.8 

v+ 


Figure  4:  Percentage  change  in  urms  above  the  middle  actu¬ 
ator  (a2)  slit  as  a  function  of  the  (rms)  forcing  amplitude. 

25 

20 

15 
u+ 

10 
5 


10  20  30  40 

y+ 

Figure  5:  Near- wall  velocity  distribution  with  and  without 
active  control,  showing  the  reduction  in  velocity  gradient  near 
the  wall  resulting  in  a  7%  reduction  in  wall  shear  stress. 


+ forced 
°  unforced 


Prms- 

Figure  4  shows  the  performance  of  the  controller  as  func¬ 
tions  of  the  filter  gain  (i.e.  actuator  amplitude)  and  plots  the 
percentage  reduction  in  urrns  at  the  location  of  the  down¬ 
stream  sensor  which,  in  this  case  was  positioned  at  the  down¬ 
stream  end  of  middle  actuator  exit  slit  and  at  y+  =  10.  Al¬ 
though  the  identification  stage  predicted  that  the  control  jet 
amplitude  of  vControi  =  0.45ur  should  be  optimal,  the  adap¬ 
tation  indicates  that  a  higher  amplitude  of  vcontroi  =  0.55 ur 
yields  slightly  better  performance,  with  a  maximum  reduction 
in  Urms  of  approximately  31%.  Data  from  open-loop  forcing 
(i.e.  constant  amplitude  forcing,  with  the  upstream  sensors 
disconnected)  is  indicated  by  circles  and  also  indicate  some 
reduction  in  urms  although  the  net  result  is  only  about  one 
third  as  effective  as  the  active  control,  for  the  same  energy 
input.  As  the  actuator  gain  is  increased  beyond  the  optimal, 
the  energy  injected  by  the  actuators  overwhelms  the  control 
benefits  and  the  rms  signal  returns  to  its  undisturbed  value. 

The  reduction  in  urms  is  also  accompanied  by  a  reduction 
in  the  local  mean  velocity  at  the  control  location.  This  is 


139 


Figure  6:  Percentage  change  in  urms  above  the  actuator  array 
as  a  function  of  the  span  wise  coordinate  z+.  Circles  indicate 
results  using  one  actuator  while  plusses  indicate  results  ob¬ 
tained  using  three  actuators.  The  actuators  are  located  at  z+= 
0  and  40.  The  bold  symbols  represent  control  optimization 
points. 


shown  in  figure  5  which  shows  the  near-wall  velocity  pro¬ 
file.  The  controlled  and  non-controlled  mean  velocities  at 
each  y-location  were  obtained  by  switching  the  actuators  on 
and  off,  without  moving  the  hot  wire  probe.  By  this  means 
a  1%  reduction  in  the  near-wall  mean  velocity  gradient  was 
measured.  Although  the  inference  of  wall  shear  from  a  mea¬ 
sured  mean  velocity  profile  is  often  problematic  and  subject 
to  errors,  the  comparative  measurement  indicated  by  figure  5 
clearly  shows  a  reduction  in  wall  shear. 

The  spanwise  extent  of  the  controlled  flow  is  illustrated  in 
figure  6  which  shows  the  reduction  in  urms  at  y+of  12  and 
plotted  versus  z+ at  a  station  immediately  behind  the  actua¬ 
tor  array  (and  at  the  same  streamwise  station  as  the  control 
points).  Since  the  measurements  are  symmetric  with  respect 
to  z+-  0,  only  one  side  of  the  actuator  array  is  shown.  Two 
series  of  data  are  plotted  here,  control  achieved  using  one  ac¬ 
tuator  and  control  achieved  using  all  three  actuators.  The  sin¬ 
gle  actuator  result  indicates  that  the  maximum  reduction  is 
achieved  slightly  off-center  from  the  axis  of  the  actuator,  and 
the  controlled  region  relaxes  to  its  undisturbed  state  approxi¬ 
mately  50  z+on  either  side  of  the  actuator.  A  slight  overshoot 
is  also  observed  at  the  spanwise  edge  of  the  controlled  region. 
The  use  of  all  three  actuators  extends  the  spanwise  range  of 
the  controlled  field  and  slightly  decreases  the  overshoot. 

The  variation  in  the  streamwise  direction,  x,  and  the  wall- 
normal  direction,  y,  are  shown  in  figures  7  and  8  respectively. 
Here  we  see  that  the  relaxation  of  the  controlled  flow  takes 
place  over  a  streamwise  distance  of  approximately  1000  1* 
before  returning  to  the  uncontrolled  fluctuation  level.  With 
all  three  actuators  in  operation,  more  extensive  measurements 
[18]  reveal  that  a  wedge  of  controlled  flow  is  created  directly 
downstream  of  the  actuator  array  which  relaxes  back  to  the 
natural  boundary  layer  structure  with  a  half  angle  of  approxi¬ 
mately  15°as  fully  turbulent  fluid  mixes  back  in  with  the  con¬ 
trolled  fluid  at  the  edges  of  the  control  patch.  The  vertical 
extent  of  the  controlled  flow,  indicated  by  figure  8,  shows 


Figure  7:  Percentage  change  in  urms  above  the  actuator  array 
as  a  function  of  the  streamwise  coordinate  x+. 


0 

+  + 

-5 

+ 

-10 

+ 

-15 

+ 

-20 

+ 

-25 

-30 

+ 

•30 1 - - - 1 

0  50  100 

y' 


Figure  8:  Percentage  change  in  urms  above  the  actuator  array 
as  a  function  of  the  wall-normal  coordinate  y+ . 


maximal  control  is  achieved  at  y+  =  12  -  the  point  at  which 
the  transfer  functions  were  optimized  (indicated  by  the  bold 
plus  symbol)  and  that  the  region  of  control  is  limited  to  the 
near  wall  region  (y+  <  50)  -  perhaps  not  surprising  when  one 
realizes  that  the  coherent  structures  are  confined  to  the  near 
wall  region  and  so  one  the  control  of  these  near  wall  struc¬ 
tures  should  only  have  limited  spatial  influence. 

The  extensibility  of  the  control  region  by  using  additional 
spanwise  actuators  suggests  that  a  larger  spanwise  array  will 
enable  both  larger  spanwise  regions  of  controlled  flow  as  well 
as  more  extensive  regions  in  the  streamwise  direction  (due  to 
reduced  edge  contamination).  This  concept  is  currently  being 
tested. 

Figure  9  shows  the  velocity  power  spectrum  of  the  un¬ 
controlled  and  controlled  flows  (both  open-  and  closed-loop 
conditions).  The  frequency  at  which  the  actuator  operates  is 
clearly  seen  as  the  small  peak  at  high  frequency  representing 
the  energy  injected  by  the  actuator.  Note  that,  for  the  open- 
loop  condition,  this  peak  is  sharp,  while  for  the  closed-loop 
condition,  the  peak  is  broadened  due  to  the  amplitude  modu¬ 
lation  of  the  actuator  signal.  However,  this  energy  injection 
is  negligible  when  compared  to  the  broad  reduction  in  energy 
in  the  frequency  band  associated  with  the  coherent  structures 
which  occurs  at  lower  frequencies.  In  this  manner  we  clearly 


140 


Figure  9:  Spectrum  of  streamwise  velocity  fluctuations  for 
the  uncontrolled  (i)  ,  open-loop  (ii)  and  closed-loop  (iii) 
cases.  The  peak  at  high  frequency  is  the  actuator  resonant 
frequency. 

see  how  the  actuator  input  is  rectified  by  the  flow  and  results 
in  reduced  fluctuation  energy. 

Although  these  results  are  shown  for  the  control  of  urms, 
the  control  scheme  is  equally  applicable  to  the  control  of  any 
flow  quantity.  One  particularly  important  control  objective  is 
the  reduction  of  the  wall-pressure  fluctuations.  By  replacing 
the  downstream  velocity  sensor  with  a  wall-mounted  pres¬ 
sure  sensor,  the  described  procedure  (generation  of  the  linear 
predictive  filter  and  subsequent  linear  control)  was  repeated 
and  we  were  able  to  achieve  17%  reduction  in  prrns.  The 
decreased  efficiency  of  the  system  is  primarily  due  to  the  in¬ 
creased  distance  between  the  actuator  and  the  control  point 
(the  wall  pressure  sensor,  c2,  was  200  /^downstream  of  the 
actuator,  while,  in  the  case  of  the  control  of  u',  the  hot-wire 
was  directly  downstream  of  the  actuator).  This  increased  sep¬ 
aration  resulted  in  a  reduced  accuracy  of  both  the  forward 
prediction  filter,  Hi ,  and  the  actuator  transfer  function,  H2. 

4  DISCUSSION  AND  CONCLUSIONS 

The  experimental  results  clearly  indicate  that  the  feed¬ 
forward  control  algorithm  described  works  and  is  successful 
in  moderating  the  turbulence  intensity  in  the  near- wall  region 
of  a  fully  turbulent  boundary  layer.  The  performance  of  the 
system  is  enhanced  by  the  use  of  pre-conditioned  input  sig¬ 
nals  which  emphasize  the  lower  frequencies  that  are  associ¬ 
ated  with  large-scale  structures.  In  the  current  experiments, 
the  detection  of  large-scale  structures  is  achieved  using  a  con¬ 
ditioned  spectral  analysis  which  essentially  band-passes  the 
input  signals  with  a  filter  that  is  derived  by  maximizing  the 
coherence  between  two  adjacent  wall  sensors.  Although  we 
see  that  this  works  surprisingly  well,  there  is  no  doubt  that 
improvements  in  the  detection  of  the  large-scale  structures 
can  be  achieved  if  one  could  implement  a  dynamic  recogni¬ 
tion  algorithm  so  that  large-scale  structures  can  be  recognized 
and  isolated  in  real  time  (at  present  they  are  only  recognized 
in  a  statistical  sense).  This  improvement  requires  some  un¬ 


derstanding  of  the  dynamics  of  the  coherent  structures  in  the 
near  wall  region  and,  if  this  were  available,  then  an  adap¬ 
tive  (Kalman)  filter  could  be  implemented  which  should  im¬ 
prove  the  large-scale  detection  further.  Possible  candidates 
for  near  wall  models  include  the  low-order  system  proposed 
by  Waleffe  [20]  or  possibly  those  based  on  Karhunen-Loeve 
eigenmodes  [1].  Waleffe’s  approach  seems  at  present  more 
appealing  since  it  includes  streamwise  dependencies  which 
are  clearly  essential  for  this  application. 

Using  this  technique,  we  find  that  we  can  predict  the  flow 
using  a  purely  linear  system  with  surprisingly  good  accuracy 
over  300  /Mownstream.  The  accuracy  of  the  forward  predic¬ 
tion  supports  the  original  hypothesis  that  the  near  wall  dy¬ 
namics  are,  for  short  times,  dominated  by  linear  interactions 
with  the  mean  shear.  Given  the  success  of  the  forward  pre¬ 
diction,  the  overall  success  of  the  scheme,  which  currently 
realizes  over  30%  reduction  in  turbulent  fluctuation  intensity, 
is  perhaps  not  surprising. 

This  paper  represents  a  summary  of  research  results  some  of 
which  as  been  published  in  Physics  of  Fluids  [19]  and  pre¬ 
sented  at  1997  and  1998  AIAA  Conferences  [18,  4].  The 
work  was  supported  by  the  Office  of  Naval  Research,  grant 
N00014-92-J-1918  monitored  by  Dr.  L.  Patrick  Purtell. 

References 

1.  N.  Aubry,  P.  Holmes,  J.  L.  Lumley,  and  E.  Stone.  The 
dynamics  of  coherent  structures  in  the  wall  region  of  a 
turbulent  boundary  layer.  J.  Fluid  Mech.,  192:115-173, 
1988. 

2.  J.  S.  Bendat  and  A.  G.  Piersol.  Random  Data.  Wiley, 
1986. 

3.  T.  R.  Bewley  and  P.  Moin.  Optimal  control  of  turbu¬ 
lent  channel  flows.  In  K.  W.  Wang,  A.  H.  Von  Flotow, 
R.  Shoureshi,  E.  W.  Hendricks,  and  T.  M.  Farrabee,  ed¬ 
itors,  Active  Control  of  Vibration  and  Noise ,  volume  DE 
Vol.  75.  ASME,  1994. 

4.  K.  S.  Breuer,  K.  Amonlirdviman,  and  R.  Rathnasingham. 
Adaptive  free-forward  control  of  turbulent  boundary  lay¬ 
ers.  AIAA  Paper  98-1025, 1998. 

5.  H.  Choi,  P.  Moin,  and  J.  Kim.  Active  turbulence  control 
for  drag  reduction  in  wall-bounded  flows.  J.  Fluid  Mech. , 
262:75-110, 1994. 

6.  D.  J.  Coe,  M.  G.  Allen,  M.  A.  Trautman,  and  A.  Glezer. 
Micromachined  jets  for  manipulation  of  macro  flows. 
In  Proceedings  of  the  Solid-State  Sensor  and  Actuator 
Workshop ,  Hilton  Head,  SC,  June  1994. 

7.  B.  D.  Coller,  P.  Holmes,  and  J.  L.  Lumley.  Control  of 
bursting  in  boundary  layer  modes.  Applied  Mech.  Rev., 
47(6,  Part  2):  139-149,  June  1994. 

8.  J.  C.  R.  Hunt  and  D.  J.  Carruthers.  Rapid  distortion  the¬ 
ory  and  the  “problems”  of  turbulence.  J.  Fluid  Mech,, 
212:497-532, 1990. 


141 


9.  S.  Jacobson  and  W.  C.  Reynolds.  An  experimental  inves¬ 
tigation  towards  the  active  control  of  turbulent  boundary 
layers.  Technical  Report  TF-64,  Stanford  University,  De¬ 
partment  of  Mechanical  Engineering,  1995. 

10.  A.  V.  Johansson,  P.  H.  Alfredsson,  and  J.  Kim.  Evolu¬ 
tion  and  dynamics  of  shear  layer  structure  in  near  wall 
turbulence.  /.  Fluid  Mech.,  224:579-599, 1991. 

11.  A.  V.  Johansson,  J.  Her,  and  J.  H.  Haritonidis.  On 
the  generation  of  high  amplitude  wall-pressure  peaks  in 
turbulent  boundary  layers  and  spots.  J.  Fluid  Mech., 
175:119-142,1987. 

12.  M.  T.  Landahl.  On  sublayer  streaks.  J.  Fluid  Mech. , 
212:593-614,  1990. 

13.  C.  Lee,  J.  Kim,  D.  Babcock,  and  R.  Goodman.  Appli¬ 
cation  of  neural  networks  to  turbulence  control  for  drag 
reduction.  Phys.  Fluids ,  9(6):  1740 -1747,  1997. 

14.  T.  Lorkowkski.  Small-scale  forcing  of  a  turbulent  bound¬ 
ary  layer,  1996.  Fluid  Dynamics  Research  Laboratory 
Report  97-1. 

15.  P.  Moin  and  T.  Bewley.  Feedback  control  of  turbulence. 
Appl  Mech.  Rev.,  47(6): S3  -  S5,  June  1994.  (Part  of 
Mechnaics  USA  1994,  edited  by  A.S.  Kobayashi). 

16.  R.  Rathnasingham.  System  Identification  and  Active 
Control  of  a  Turbulent  Boundary  Layer.  PhD  thesis, 
MIT,  Department  of  Aeronautics  and  Astronautics,  1997. 
(MIT  FDRL  TR  97-6). 

17.  R.  Rathnasingham  and  K.  S.  Breuer.  Coupled  fluid- 
structural  characteristics  of  actuators  for  flow  control. 
AIAAJ.,  35:832-837, 1997. 

18.  R.  Rathnasingham  and  K.  S.  Breuer.  System  identifi¬ 
cation  and  active  control  of  a  turbulent  boundary  layer. 
AIAA  Paper  97-1793;  1997. 

19.  R.  Rathnasingham  and  K.  S.  Breuer.  System  identi¬ 
fication  and  control  of  turbulent  flows.  Phys.  Fluids, 
9(7):  1867-1 869, 1997. 

20.  F.  Waleffe.  On  a  self-sustaining  process  in  shear  flows. 
Phys.  Fluids,  9(4):883-900, 1997. 


142 


FLOW  MANAGEMENT 

USING  INHERENT  TRANSITION  AND  RECEPTIVITY  FEATURES 


Yurchenko,  N.F. 

Institute  of  Hydromechanics 
National  Academy  of  Sciences,  Kiev,  Ukraine 


Rivir,  R.B. 

Propulsion  Directorate,  AFRL/PRTT 
Wright-Patterson  Air  Force  Base,  Dayton,  OH,  USA 


Abstract  -  It  is  shown  that  the  effectiveness  of  the  motion  connected  with  a  flow  structure  in  a  near-wall  region  can  be  naturally 
improved  by  manipulation  with  stream  wise  vortices.  These  vorticies  represent  inherent  structural  elements  of  boundary  layer,  which 
are  strongly  affected  by  body  forces.  The  scales  of  vortices  in  boundary  layer  were  analytically  obtained  under  the  influence  of 
buoyancy/centrifugal  forces.  These  scales  and  their  location  were  used  for  the  analysis  of  the  vortex  dynamics  around  a  turbine  blade. 
The  numerical  calculations  revealed  non-similarity  between  the  shear  stress  and  heat  flux  and  suggested  recommendations  for  the 
generation  and  maintenance  of  vortical  boundary  layer  structures,  which  will  enhance  attached  flow  on  the  suction  surface. 


I.  INTRODUCTION 

Low-pressure  turbine  blades  for  both  air,  and  seawater  applications 
usually  represent  a  compromise  between  a  desire  to  highly  load  the  aft 
section,  to  reduce  the  number  of  components,  and  highly  loading  the  aft 
section  resulting  in  increased  sensitivity  to  separation  and  the  associated 
efficiency  penalties.  Low  Reynolds  number  operation  at  off  design 
conditions  or  for  very  small  blade  dimensions  results  in  enhanced 
separation  on  the  suction  surface  which  is  not  accurately  predicted. 
Separation  and  transition  typically  might  occur  at  a  nominal  60%  of  axial 
chord  (Ref.  1,  2).  Low  Reynolds  number  effects  become  especially 
important  for  the  separation  problem  at  chord  Reynolds  numbers, 
Red,<  100,000.  The  low-pressure  designs  currently  employed  therefore  are 
far  from  being  optimal  for  the  range  of  flow  conditions  encountered. 

Optimization  of  the  turbine  performance  and  work  should  be  based 
on  insight  into  the  dynamics  of  the  mechanisms  of  vortex  flows  which  takes 
into  account  the  blade  geometry  (curvature  effects)  and  the  operational 
regimes  (flow  temperature  stratification  affected  by  body  forces  and 
Reynolds  numbers  (centrifugal  forces  and  buoyancy).  Possibilities  to 
favorably  modify  the  near-wall  vortical  structure  for  given  flow  parameters 
are  formulated  in  the  frame  of  the  receptivity  problem,  i.e.  The  boundary 
layer’s  response  to  controlled  excitation  may  be  studied  in  terms  of  its 
receptivity  to  the  possibility  of  favorably  modifing  the  near  wall  vortical 
structures.  The  receptivity  formulation  provides  the  specification  of  the 
appropriate  boundary  layer  control  techniques. 

The  inherent  feature  of  flows  effected  by  body  forces  is  the 
development  of  secondary  flows  in  a  form  of  the  large-scale  boundary  layer 
structure,  or  stream  wise  counter-rotating  pairs  of  vortices.  The  vortex 
dynamics  of  these  flows  can  therefore  be  used  naturally  for  manipulation 
and  optimization  of  the  attachment  of  separated  flows. 

The  general  objective  of  the  present  work  consisted  of  fundamental 
studies  of  the  development  and  control  of  boundary  layers  under  body 
forces,  as  well  as  the  application  of  these  results  to  control  flows  on  the 
suction  surface  of  turbine  blading  at  low  Reynolds  numbers.  The  objective 
was  to  examine  the  boundary  layer  structure  over  a  turbine  blade  taking 
into  account  centrifugal  effects  and  then  application  of  this  information  to 
develop  recommendations  related  to  the  generation  and  maintenance  of  a 
stable  vortical  flow  structure  that  is  optimal  from  the  viewpoint  of 
hydraulic  losses. 

Generally,  these  recommendations  should  concern  both  the  suction, 
and  pressure  sides  of  the  blade.  They  should  include  the  possibilities  to 
modify  both  the  blade  shape  and  its  surface  using  special  techniques  (e.g. 
riblets  or  organized  surface  roughness).  These  techniques  should  stimulate 
and  maintain  a  favorable  boundary  layer  vortical  structure  to  delay  flow 
separation  on  the  suction  surface. 

II.  THEORETICAL  BACKGROUND 

The  flow  geometry  over  a  turbine  blade  surface  involves  both  signs 
of  curvature,  which  are  varying  with  axial  chord  location.  The 
computation  needs  to  address  boundary  layers  as  they  are  effected  by 
centrifugal  forces  or,  for  the  more  general  case,  by  body  forces  (centrifugal 
forces  and  buoyancy).  GSertler  stability  of  boundary  layers  over  concave 
surfaces  (e.g..  Ref.  4,  5)  along  with  the  stability  of  thermally  stratified 
flows  represents  the  state  of  the  art  of  the  problem  for  the  turbine  blade 
application  using  traditional  approaches. 


E.  Nikiforovich,  Ref.  7,  in  a  more  general  approach,  which  is 
different  from  the  known  stability  theories,  naturally  accounts  for  the 
combined  effect  of  all  body  forces  in  a  flow  (Ref.  6,  7).  Theoretically  this 
approach  is  based  on  the  asymptotic  analysis  of  the  full  Navier-Stokes 
equations  using  a  small  parameter  explicitly  depending  on  body  forces.  In 
case  of  centrifugal  forces  only  this  small  parameter  is 

e  =  ReR-1  (D 

where  ReR  is  the  Reynolds  number  (UJR/v  )  based  on  the  radius  of 
curvature,  R. 

Estimates  for  spatial-temporal  vortical  scales  in  a  boundary  layer  are 
given  from  this  analysis  in  terms  of  the  basic  flow  parameters.  The 
analysis  has  shown  that  the  longitudinal  vortices,  as  an  essential  flow 
structural  feature,  originate  from  the  interaction  of  two  vorticity  sources 
(one  due  to  viscous  and  one  due  to  centrifugal  forces)  when  their  intensities 
become  comparable  at  a  certain  downstream  distance 

Xo=  ARRen'1/3  (2) 

where  A  is  a  constant  The  minimum  spatial  scale  in  normal  and  spanwise 
directions  for  these  longitudinal  vorticies  is, 

U  =  RReR-w  (3) 

A  similar  analysis  was  carried  out  for  the  case  of  buoyancy,  with  the 
small  parameter,  s=p(T,-T0),  where  p  is  a  coefficient  of  volumetric  thermal 
expansion,  T,  and  T0  are  correspondingly  surface  and  mean  flow 
temperatures.  The  normal  spatial  scales  of  these  buoyancy  driven  vortices 
and  the  downstream  location  of  their  formation  are  again  expressed  in 
terms  of  the  basic  flow  parameters. 

Experimental  results  have  been  obtained  for  a  transitional  boundary 
layer  over  a  concave  surface  (Ref.  4)  which  matches  both  of  the  theoretical 
approaches  and  the  physical  mechanisms  as  interpreted  by  the  theoretically 
deduced  values  of  scale  (Ref.  6,  7). 

III.  RESULTS 

Preliminary  experiments  (Ref.  2)  on  riblets  applied  to  a  blade  in  a 
turbine  cascade  with  turbulence  levels  to  8%  showed  a  6-8%  decrease  in 
average  blade  heat  transfer  from  riblets  which  were  scaled  for  the 
maximum  curvature  location.  Although  skin  friction  was  not  measured 
directly,  it  was  assumed  to  follow  heat  transfer.  The  turbulence  scale  was 
much  larger  than  the  riblet  spacing.  It  would  normally  be  expected  that 
this  level  of  turbulence  would  dominate  any  effect  the  riblets  might  have. 
However  the  micro  surface  effects  of  riblets  appear  to  alter  macro  free- 
stream  flows  and  offer  the  possibility  of  passive  boundary  layer  control  due 
to  the  induced  longitudinal  vortices.  Therefore  the  problem  obviously 
needs  more  physically  deep  and  mathematically  rigorous  investigation. 

The  two-dimensional  equations  of  a  stratified  boundary  layer 
together  with  continuity  and  thermal  conductivity  equations  were  solved 
numerically  using  a  finite-difference  method.  The  calculations  showed  the 
important  role  of  body  forces  in  affecting  the  laminar-turbulent  transition 
process  and  the  boundary  layer  characteristics,  in  particular,  the  effects  on 
the  velocity  and  temperature  profiles.  It  was  found  that  buoyancy 


143 


essentially  influences  downstream  distributions  of  heat  flux,  Q(x),  and 
shear  stress,  F(x).  Figure  1,  where  T,  and  T0  are  correspondingly  the 
surface  and  the  free-stream  temperature,  shows  the  non-similarity  between 
these  distributions.  This  observation  can  be  used  for  heat  transfer 
optimization.  The  inherent  flow  structure  which  develops  under  body 
forces  appears  to  be  advantageous  from  the  viewpoint  of  heat  transfer 
enhancement:  heat  flux  grows  faster  downstream  than  does  the  shear  stress 
as  streamwise  vortices  appear  in  a  boundary  layer. 

However,  to  apply  this  basic  result  to  the  case  of  turbine  blade  flow 
optimization,  the  spatial  scales  of  naturally  developing  streamwise  vortices 
over  the  turbine  blade  should  be  measured  and  compared  against  the 
theoretical  model.  Comparison  of  the  boundary  layer’s  experimentally 
observed  receptivity  to  the  artificially  generated  disturbances  of  this  type 
also  needs  to  be  documented. 

Liquid  crystal  visualization  made  it  possible  to  observe  longitudinal 
vorticies  on  the  pressure  surface  of  a  Langston  2D  cascade  that  is  described 
in  Ref  8.  The  blade  shape  defines  the  geometry  for  the  flow.  The  pressure 
surface  had  a  radius  of  curvature  varying  from  the  leading  edge  of  R= 
1.59mm  -  6.35mm,  increasing  through  R~25.4mm.  The  aft  section 
increased  to  R=305mm.  The  chord  Reynolds  numbers  ranged  from 
Rec=5 0,000  to  300,000.  The  experimentally  observed  structure  had  a 
spatial  scale  of  Xz=0.8  mm  at  Rec=67500.  These  structures  were  initiated 
at  the  location  Xo/c«O.2-0.7  (chord,  c=  178mm). 

These  experimental  results  were  processed  and  analyzed  using  the 
relationships  of  equation  (2)  and  (3).  The  Xo/c  calculated  value  of  the  non- 
dimensional  downstream  distance  where  the  streamwise  vortices  should 
appear,  under  given  experimental  conditions,  was  checked  for  3  values  of 
curvature  radius,  R=17.8mm,  127mm  and  305mm,  for  Rec  =  100,000  and 
67500.  The  calculated  value  showed  good  agreement  between  the 
observed  experimental  values  (xo/c=0.2).  According  to  the  theory  (Ref. 
7),  Xz=8Lo  where  Lo  is  a  vortex  spatial  scale  normal  to  the  velocity  vector. 
The  scales,  Lo,  of  the  streamwise  vortical  structure  expressed  in  terms  of 
the  basic  flow  parameters  were  calculated  and  found  to  be  Lo=0.1mm  for 
R=  127mm,  Rec=67,500;  Lo=0.09  mm  for  R=127mm,  Rec=100,000; 
Lo=0.12  mm  for  R=254mm,  Rec=67,500.  These  calculations  of  Lo  all 
show  good  agreement  (calculated  X*  -8mm,  7.2mm,  9.6mm,)  with  the 
experimentally  observed  value  of  Xz=0.8  mm. 

Gdertler  theory  was  used  to  interpret  the  experimental  data  and  to 
establish  its  correlation  with  the  above  theoretical  approach.  The  well- 
known  centrifugal  stability  diagram  is  useful  to  interpret  the  amplification 
rates  of  streamwise  vortices  with  various  scales  which  evolve  in  boundary 
layers  as  a  function  of  the  G6ertler  number  G  =  Uo  §23/2  v  1  R  m.  Vortices 
described  by  the  non-dimensional  wavelength,  A  =  Xzin  U0  /  v  R,/2  «  39, 
are  neutral,  i.e.  have  a  zero  amplification  rate  for  a  wide  range  of  Gdertler 
numbers.  Larger  scale  vortices  are  described  in  the  Gdertler  diagram  by 
the  straight  lines  of  A  =  constant  >  39.  It  is  interesting  to  check  where  the 
experimentally  observed  vortices  are  located  on  the  diagram.  This 
estimation  was  made  for  the  8  mm  scale  vortices  from  the  expression  A  = 
X/2  Rec  /  c  Rin,  for  R=  127mm,  Rec=67,500  it  was  found  that  A  =  24, 
and  for  R=  127mm,  Rec=100,000,  A  =  36. 

This  means  that  the  streamwise  vortical  structure  which  appears  in 
the  boundary  layer  of  a  low  pressure  turbine  blade  cascade  is  of  a  neutral 
type,  i.e.  neither  amplifying,  nor  decaying  in  a  downstream  direction.  This 
flow  structural  feature  can  be  used  to  keep  a  thermodynamic  balance  in  the 
boundary  layer  using  different  methods  of  boundary  layer  control.  In  the 
controlled  case,  it  is  essential  to  maintain  the  favorable  vortical  structure  as 
long  as  possible.  This  mechanism  can  be  observed  and  exploited  in  the 
receptivity  problem. 

The  receptivity  investigation  of  a  boundary  layer  effected  by  body 
forces  was  carried  out  by  the  generation  of  regular  systems  of  longitudinal 
vortices  using  special  vortex-generator  arrays  mounted  transversely  on  the 
test  surface.  The  boundary  layer  response  was  analyzed  as  a  function  of 
the  spatial  scale  of  vortices,  Xz,  and  the  Reynolds  number  of  the  flow. 

Flows  with  buoyancy  were  also  investigated  in  a  closed  wind  tunnel 
with  a  test  section  of  2. 8 5x0. 30x0.3 0m  (Ref  9)  at  a  free-stream  velocity, 
U0=10  m/s  or  20  m/s.  The  test  section  plate  consisted  of  conducting  foil 
surface  which  was  heated  electrically  to  maintain  a  temperature  difference 
with  the  free-stream  of  TrTo=20°.  The  foil  was  insulated  on  the  backside 
to  provide  a  constant  heat  flux  surface  to  the  flow.  The  local  surface 
temperature  distribution  was  measured  using  flush  mounted 
thermocouples. 

The  detailed  description  of  these  experiments  in  boundary  layers 
effected  by  centrifugal  forces  is  given  in  (Ref.  4).  Figures  2  and  3  illustrate 


the  boundary  layers  reaction  to  the  longitudinal  vortices  induced  with 
different  X*  scales  at  different  downstream  Xo  locations.  The  preferable 
values  of  both  parameters  to  enhance  heat  transfer  may  be  obtained  from 
these  figures.  The  general  idea  of  utilization  of  natural  flow  dynamics  and 
boundary  layer  control  based  on  the  generation  of  inherent  vortical 
structure  is  seen  to  be  possible  and  the  validity  of  the  (Ref.  6,  7)  theory  has 
been  demonstrated  in  a  flow  under  the  influence  of  body  forces. 

Simple  calculations  of  the  scale  of  longitudinal  vortices  and  a 
downstream  position  of  their  natural  formation  can  be  made  for  given  flow 
conditions.  An  appropriate  tool  for  boundary  layer  control  (vortex 
generators,  riblets,  roughness  elements,  etc.)  may  then  be  employed  to 
generate  vortices  of  the  estimated  scale  and  location.  Figure  4  illustrates 
experimental  evidence  of  the  favorable  role  of  longitudinal  vortices  to 
delay  boundary  layer  separation  under  the  adverse  streamwise  pressure 
gradients. 

rv.  CONCLUSIONS 

Calculated  spatial  scales  of  the  vortical  flow  structure  over  a  turbine 
blade  for  the  given  test  conditions  using  the  theoretical  relationships  of 
(Ref.  9)  are  in  a  good  agreement  with  the  observed  experimental  data. 
Gfiertler  stability  analysis  showed  a  neutral  character  of  regular  vortices  in 
a  turbine  blade  boundary  layer.  The  non-similarity  between  heat  and 
momentum  fluxes  in  boundary  layers  effected  by  buoyancy  was 
numerically  shown.  This  mechanism  gives  the  basis  to  optimize  heat 
transfer  using  streamwise  vortices  as  naturally  occurring  flow  structures. 
The  effectiveness  of  boundary  layer  control,  in  a  form  of  heat  transfer 
enhancement,  depends  on  the  receptivity  of  a  boundary  layer  to  streamwise 
vortices,  that  its  selective  response  to  the  spatial  scale  of  the  generated 
vortices  and  the  downstream  location  of  their  formation.  Stimulation  and 
maintenance  of  streamwise  vortices  corresponding  to  the  requirements  of 
flow  optimization  can  result  in  the  delay  of  the  flow  separation  on  a  suction 
surface  of  a  turbine  blade. 

V.  REFERENCES 

1.  J.  W.  Baughn,  R.  J.  Butler,  A.  R.  Byerley,  R.  B.  Rivir  "An  Experimental 
Investigation  of  Heat  Transfer,  Transition  and  Separation  on  Turbine 
Blades  at  Low  Reynolds  Number  and  High  Turbulence  Intensity",  ASME 
International  Engineering  Congress  And  Exposition,  San  Francisco,  CA, 
Nov  1995. 

2.  R.  B.  Rivir,  P.  A.  Maciejewski  "The  Effects  of  Free  Stream 
Turbulence  and  Surface  Riblets  on  Heat  Transfer  in  a  Linear  Cascade", 
International  Gas  Turbine  Institute,  Hague,  Netherlands,  ASME  94-GT- 
245,  June  1994. 

3.  E.  I.  Nikiforovich,  N.  F.  Yurchenko  "Vortical  Flows  -  Properties  and 
Analogues”  (in  Russian),  Hydromechanics,  Kiev,  Ukraine,  70,  pp.  131- 
154,  1996. 

4.  N.  F.  Yurchenko,  V.  V.  Babenko,  L.  F.  Kozlov  "Development  of  Three- 
Dimensional  Disturbances  in  Transitional  Boundary  Layers",  Proceedings 
of  the  IUTAM  Symposium  on  Laminar-Tufbulent  Transition,  Novosibirsk, 
pp.  329-335,  1984. 

5.  W.  S.  Saric  "Goertler  Vortices",  Annual  Review  of  Fluid  Mechanics,  26, 
pp.  379-409,  1994. 

6.  E.  I.  Nikiforovich,  R.  B.  Rivir,  N.  F.  Yurchenko  "Kinematic  Similarity 
of  Flows  Developing  Under  Body  Forces",  8th  Taylor-Couette  Workshop, 
Boulder,  Colorado,  1995. 

7.  E.  I.  Nikiforovich,  N.  F.  Yurchenko  "Boundary-Layer  Flows  with 
Centrifugal  Forces",  ERCOFTAC  Bulletin,  32,  pp.  61-65,  March  1997. 

8.  S.  T.  Walsh,  D.  N.  Barlow,  R.  J.  Butler,  K.  W.  VanTreuren,  A  R. 
Byerley,  J.  W.  Baughn,  R.  B.  Rivir,  "Effect  of  Passive  and  Active  Air  Jet 
Turbulence  on  Turbine  Blade  Heat  Transfer,"  International  Gas  Turbine 
Institute,  Orlando,  Florida,  ASME  97-GT-131,  June  1997. 

9.  N.  F.  Yurchenko,  A.  A  Pedishius,  G.  P.  Zygmantas  "Boundary  Layer 
Receptivity  and  Heat  Transfer  Enhancement"  (in  Russian,  abstract  in 
English),  Engineering-Physical  J.,  56,  pp  916-924,  1989. 


144 


Q(x)/F(x) 


RexlO4 

Fig.  1.  Downstream  variations  of  a  heat  flux  related  to  the  shear  stress  Q(x)/F(x) 
in  flows  with  buoyancy  for  Ts>T0,  Pr=0.7  (1),  Pr=7.0  (2)  and  without  buoyancy  for  Pr=0.7  (3),  Pr=7.0  (4). 


2  4  6  8 

RexlO5 


Fig.  2.  Heat  transfer  variation  vs  Re  in  a  boundary  layer  disturbed  by  the  vortex  generators  of  different  shape: 

1  -  A,z=1.5  cm,  2  -  Xz=l,5  cm,  3  -  X,z=1.8  cm. 


145 


IHl 


Fig.  3.  Heat  transfer  variations  along  a  heated  flat  plate  depending  on  a  streamwise  position  xo  of  vortex  generators 
1,2  -  reference  measurements  for  the  natural  laminar-turbulent  transition  and  for  the  tripped  boundary  layer; 

3  -  a  single  vortex  generator;  4,  5,  6  -  vortex  generation  with  X.z=1.5  cm;  2,  5  -  tripped  boundary  layer; 

V  -  position  of  vortex  generators 


tj 


£ 


■V  \/ 

1  (tellurium  2  ^lfeurhjm  mttty 
probe) 


2.0  cm 


Fig.  4.  Influence  of  longitudinal  vortices  on  a  water  flow  with  unfavorable  streamwise  pressure  gradient 
(over  the  surface  with  a  concave  section:  R=lm,  Uo=4  cm/s,  x=0.6  m) 


146 


Seawater  Physics 


147 


IN-SITU  ESTIMATION  OF  THE  ABUNDANCE  AND  SIZES  OF  PARTICULATES 

IN  THE  SEA 


D.V.  Holliday 
Tracor  Aerospace 
4669  Murphy  Canyon  Road,  #102 
San  Diego,  CA  92123-4333 
holliday@galileo.tracor.com 


Abstract  -  The  speed  threshold  at  which  turbulent  flow  near  a  boundary  is  initiated  can  be  modified  by  the  presence  of  particulates  in  the  fluid.  In  sea 
water,  much  of  the  particulate  mass  is  due  to  either  living  organisms  or  detritus  with  a  biotic  origin.  Advances  in  acoustical  technology  have  resulted  in 
the  availability  of  new  information  on  the  abundance,  size  spectra,  patchiness  and  temporal  variability  of  distributions  of  zooplankton  and  micronekton  in 
the  open  sea  and  in  the  littoral  zones  of  the  world's  oceans.  This  contribution  includes  an  overview  of  this  measurement  technology,  the  instrumentation, 
and  descriptions  of  several  modes  in  which  such  sensors  have  been  deployed  to  estimate  particulate  abundances  by  size.  A  brief  description  is  provided 
of  the  mathematical  method  used  to  transform  acoustical  scattering  measurements  at  multiple,  high,  acoustical  frequencies,  i.e.,  frequencies  spanning  a 
range  from  one  hundred  kilohertz  to  ten  megahertz,  to  estimates  of  particulate  abundances,  their  sizes  and  their  physical  characteristics.  Recent  advances 
in  applying  inverse  theory  to  this  problem  allows  separation  of  particulates  into  different  types.  Data  illustrating  the  spatial  and  temporal  distributions  of 
zooplankton  abundance  and  its  variability  are  presented  for  a  variety  of  geographic  locations. 


I.  INTRODUCTION 

A  transition  from  laminar  to  turbulent  flow  near  a  boundary  can 
be  triggered  by  a  near-encounter  of  volume  inhomogeneities  in  the 
fluid  with  the  boundary.  In  specific  situations,  very  fine  airborne 
particles  with  a  terrestrial  origin  (dust  and  sand)  sometimes  contribute 
to  the  abiotic  part  of  the  marine  particle  field,  as  do  resuspended 
sediments  in  very  shallow  water,  turbidity  flows  across  the  shelf, 
sediment-laden  fresh  water  outflows  from  rivers  and  such  nearshore 
phenomena  as  rip  tides.  However,  in  general,  most  particulates  in  the 
marine  environment  have  a  local  biotic  origin.  Living  plants 
(phytoplankton)  and  animals  (zooplankton  and  micronekton)  are  major 
contributors  to  a  highly  variable  size-abundance  spectrum  of 
particulates  in  the  ocean.  Detritus  (dead  or  decaying  plants,  whole 
animals,  animal  parts,  and  fecal  pellets)  also  contribute  to  the  total 
spectrum  of  volume  inhomogeneities  in  the  marine  water  column. 

The  spatial  distribution  of  particulates  in  the  marine  environment 
is  heterogeneous  (patchy  and  layered)  in  both  horizontal  and  vertical 
dimensions.  In  the  horizontal,  scales  of  patchiness  range  from  less  than 
a  meter  to  hundreds  of  kilometers.  In  the  vertical  dimension,  scales  of 
heterogeneity  range  from  centimeters  to  hundreds  of  meters  (Figure  1). 

Particulates  in  the  ocean  are  also  characterized  by  a  widely 
variable  temporal  spectrum,  with  changes  in  local  abundances  and 
spatial  pattern  ranging  from  minutes,  through  daily,  seasonal  and 
annual  cycles,  to  decadal  or  longer.  The  correlations  and  coherences 
between  these  temporal  variations  and  possible  "driving"  phenomena  in 
ocean  physics,  such  as  the  depth  of  the  pycnocline,  fine-structure  in 
temperature  and  salinity,  mixing,  turbulence,  fronts,  gyres  and  internal 
waves  have  been  the  subject  of  numerous  studies  during  the  last 
decade. 

The  abundance  of  particulates  in  the  sea  also  varies  with  the 
sizes  of  the  particles.  Even  in  the  least  productive  parts  of  the  "blue 
water"  ocean,  millimeter  size  particulates  often  number  in  tens  to 
hundreds  per  cubic  meter.  Densities  can  reach  tens  of  millions  per 
cubic  meter,  or  more,  in  layers  and  patches.  There  is  often  a  trend 
towards  higher  abundances  in  the  biologically  productive  littoral  or 
coastal  zone. 

II.  PREDICTION,  REMOTE  AND  IN  SITU  ESTIMATES  OF 
PARTICLE  ABUNDANCE 

Measurements  of  the  spatial  and  temporal  distribution  of 
phytoplankton  from  satellites  with  ocean  color  capabilities  (e.g., 
SeaWifs)  are  now  common  for  the  upper  tens  of  meters,  but  much  of 
the  phytoplankton  biomass  is  subsurface  and  is  often  distributed  in  a 
complex  of  layers  near  or  below  the  thermocline.  Further,  the  standing 
stock  of  phytoplankton  (measured  by  satellites)  is  not  necessarily  a 
good  analog  for  the  standing  stock  of  zooplankton,  micronekton,  or 
larger  animals.  At  depths  of  50  or  100  m,  depending  on  the  local  optical 
extinction  depth,  particularly  in  the  littoral  zone,  satellite  estimates  of 
phytoplankton  abundance  can  often  be  problematic. 

Attempts  to  model  and  predict  the  distribution  and  dynamics  of 
marine  life  at  levels  in  the  food  web  above  the  primary  producers 


(phytoplankton)  will,  at  best,  currently  provide  only  strategic  (long 
term,  large  scale)  information  about  the  particulate  field  in  the  sea. 


Biovolume  (mm3  /  m3) 


Figure  1:  Vertical  distribution  of  zooplankton  at  a  station  15  km  off 
southern  California  in  June  1996.  Seventy  eight  percent  of  the  biomass 
was  in  a  complex  of  thin  layers  above  9  m.  Calanus  pacificus  adults 
were  the  dominant  zooplankters  in  the  upper  10  m. 


149 


Existing  models,  whether  based  on  first  principles  (e.g.,  upwelling, 
nutrients,  phytoplankton  blooms,  zooplankton  growth  and  reproduction) 
or  on  correlations  or  coherences  with  readily  observed  parameters, 
such  as  sea  surface  temperature  or  ocean  color,  do  not  yet  provide 
reliable  information  at  tactical  (short  term,  local  area)  scales.  There 
has  been  progress  during  the  last  decade  in  the  prediction  of  changes  in 
vertical  distribution  and  in  overall  abundance  on  seasonal  time  scales  at 
larger  spatial  scales.  However,  in  a  wide  sense,  small  scale  and  short 
term  prediction  of  pattern  and  change  at  secondary  and  higher  levels  in 
the  food  web  are  not  yet  ready  for  application  at  tactically  useful 
scales  of  time  or  space.  Because  animals,  from  sub-millimeter  size 
zooplankton  to  large  nekton,  have  the  option  to  make  choices  in 
response  to  their  physical  and  food  environment,  one  can  not  count  on 
much  small-to-medium  scale  coherence  between  phytoplankton 
distributions  and  the  spatial  or  temporal  pattern  of  the  higher  trophic 
levels.  Plankton  actively  react  to  their  local  environment,  changing 
their  locations  in  the  water  column  to  optimize  growth  and  reproductive 
strategies  in  response  to  a  variety  of  stimuli  and  conditions,  many  of 
which  have  not  yet  been  identified.  The  word  ’’plankton",  derived  from 
the  Greek  word  for  "drifter",  should  be  taken  rather  lightly,  at  least  in 
the  vertical  dimension.  Even  millimeter-sized  zooplankton  often 
migrate  vertically  tens  of  meters  in  response  to  light  or  food  cues. 
Larger  "plankton",  a  few  centimeters  in  length,  which  we  sometimes 
categorize  as  micronekton  (e.g.,  euphausiids)  routinely  migrate 
hundreds  of  meters  in  the  vertical. 

We  presently  have  no  reliable  means  to  measure  or  infer  the 
distribution  of  zooplankton  or  micronekton  with  remote  satellite 
sensing.  If  one  wishes  to  know  the  sizes,  abundances  and  distributions 
of  particles  in  the  marine  environment  on  small  scales,  at  a  specific 
time  and  place,  there  are  currently  only  two  viable  approaches.  Both 
involve  direct  measurement.  One  is  optical,  the  other  is  acoustical. 
Optical  particle  counting  (OPC)  is  a  field  in  transition  from 
experimental  to  routine  application.  Holography,  another  optical 
method,  remains  experimental,  but  holds  promise  for  examining  small 
(cm  scale)  fields  in  great  detail.  In  the  epipelagic  zone,  many  animals 
are  transparent,  giving  them  a  significant  advantage  in  survival  in  an 
environment  that  provides  few  places  to  hide.  While  this  does  not 
eliminate  optical  methods,  this  transparency  does  often  limit  their 
effectiveness.  Acoustical  methods  are  based  on  the  contrasts  between 
the  density  and  compressibility  of  the  animal’s  bodies  and  the 
surrounding  sea  water.  Even  nearly  neutrally  buoyant  organisms,  such 
as  chaetognaths  and  jellies  (e.g.,  doliolids,  medusae)  have  sufficient 
compressibility  contrast  with  the  water  around  them  to  allow  their 
detection.  In  addition,  many  such  "soft  bodied"  animals  eat  crustaceans, 
which  can  be  acoustically  detected  as  gut  contents.  At  this  particular 
point  in  the  development  of  sensing  methods,  an  acoustical 
methodology  seems  to  have  some  advantage  over  optical  methods, 
especially  for  remote  sensing  at  distances  of  several  meters. 
Therefore,  the  following  discussion  focuses  on  the  relevant  acoustical 
methods. 

III.  ACOUSTICAL  DETECTION  AND  CHARACTERIZATION 
OF  PARTICLES 

During  the  last  decade  there  have  been  substantial  technology- 
based  advances  related  to  acoustical  observations  of  millimeter-sized 
marine  particulates,  especially  for  zooplankton.  Laboratory  and  in  situ 
measurements  of  scattering  from  a  variety  of  marine  taxa  (Greenlaw, 
1977;  Pieper  and  Holliday,  1980;  Holliday  and  Pieper,  1984;  Medwin 
and  Clay,  1998,  pp.  391-402;  Stanton,  et  al  1998)  have  led  to  the 
development  of  a  variety  of  mathematical  models  for  acoustical 
scattering  with  frequency,  particle  size  and  shape  as  parameters 
(Greenlaw,  1977;  Pieper  and  Holliday,  1984;  Holliday,  1987;  Holliday, 
1992;  Stanton  etal,  1998a;  Stanton  et  al,  1998b;  Stanton  et  al,  1998c). 
Both  measurement  and  modeling  reveal  a  consistent,  non-monotonic 
dependence  of  acoustical  scattering  on  both  particle  size  and  the 
frequency  of  ensonification. 

This  complexity  in  scattering  from  small  marine  zooplankton  has 
major  implications  in  the  quantitative  acoustical  assessment  of  their 
size-abundance  spectra  as  well  as  of  the  total  biomass.  Measurements 
of  acoustical  scattering  at  a  single,  discrete  frequency  can  lead  to 
major  errors  in  estimation  of  the  abundance  and  size  of  particles.  An 
increase  in  scattering  can  occur  under  reasonably  common 
circumstances  as  a  result  of  lower  numbers  of  smaller  particles. 
Likewise,  a  decrease  in  scattering  can  result  from  the  presence  of 
larger  numbers  of  larger  particles.  Thus,  spatial  distributions  and 


temporal  changes  in  acoustical  scattering  at  a  single,  discrete 
frequency  can  not  be  reliably  interpreted  in  terms  of  parallel  changes  in 
abundance  or  sizes  of  small  zooplankton  or  micronekton.  Similar 
models,  and  conclusions,  apply  to  detrital  particles  with  biotic  origins 
and  to  abiotic  scatterers  such  as  sand  or  resuspended  sediments.  On  the 
other  hand,  the  same  characteristics  that  prevent  us  from  easily 
interpreting  volume  scattering  at  single  frequencies  allow  us  to  extract 
both  size  and  abundance  estimates  from  multi-frequency  scattering 
measurements. 

IV.  MULTI-FREQUENCY  METHODS 

Though  it  is  more  complex  in  practice,  for  reasons  discussed  in 
Holliday  (1977),  the  successful  transformation  of  acoustical  volume 
scattering  strength  measurements  to  estimates  of  the  size-abundance 
spectra  or  biomass  spectra  for  marine  particulates  is  in  principle  very 
straightforward.  There  are  several  basic  assumptions  (Holliday  and 
Pieper,  1995),  which  must  be  met,  the  most  important  of  which  are  that 
the  frequencies  used  must  span  the  transition  from  Rayleigh  to 
geometric  scattering  for  all  of  the  sizes  of  particles  that  are 
contributing  to  the  scattering  and  that  we  be  able  to  quantitatively 
describe  the  dependence  of  the  backscattered  sound  on  the  acoustical 
frequencies  used  and  on  the  morphology  (size,  shape  and  physical 
characteristics,  such  as  the  density  and  compressibility  contrasts 
between  the  water  and  the  particles  that  cause  the  scattering. 

While  one  can  easily  generalize  to  several  kinds  of  scatterers, 
e.g.,  bubbles,  small  crustaceans,  elastic  particles  such  as  sand  grains,  or 
zooplankton  with  shells  or  exoskeletons  (e.g.,  some  gastropods  and 
pteropods),  elongate  scatterers  such  as  euphausiids  or  shrimps,  and 
perhaps  even  larval  fish,  for  simplicity,  we  will  restrict  our  discussion 
in  this  overview  to  just  two  kinds  of  particles,  say  small  crustaceans  and 
resuspended  sand.  Models  that,  at  least  to  first  order,  describe  the 
reflectivity  (target  strengths)  from  each  of  these  kinds  of  particles  can 
be  found  in  the  literature  (Holliday,  1992;  Holliday  1987).  While  more 
complex  models  are  available  for  some  taxa,  in  the  absence  of  good 
a  priori  information  on  their  presence,  small  crustaceans  (e.g., 
copepods)  tend  to  dominate  high  frequency  sound  scattering  in  most 
locations  and  are  generically  relatively  well  described  by  the  truncated 
fluid  sphere  model  (Pieper  and  Holliday,  1984;  Holliday,  1992).  If 
a  priori  information  is  available  regarding  the  taxa  which  are  present, 
and  if  more  precise  or  better  models  are  available  for  those  taxa,  then 
those  can  and  should  be  used.  It  should  be  stressed  that  one  must 
consider  all  of  the  species  or  taxa  that  contribute  to  the  scattering,  not 
just  the  ones  of  specific  interest  in  the  study  being  undertaken. 

The  acoustical  volume  scattering  strengths  (Svj)  at  each 

frequency,  indexed  by  i,  from  a  mix  of  two  kinds  of  particles  can  be 
written  as: 

SVi=£  (Ty  n’j  +  2  <*ip"  n"p> .  0) 

where  j  and  p  are  size  indices  for  each  scatterer  type.  The  first  sum  is 
over  j  and  the  second  over  p.  The  terms  n'j  and  n"p  are  the  respective 
particle  abundances  for  the  two  scatterer  types  at  each  size.  The  terms 

0y  and  ajp"  represent  the  mathematical  models  that  describe  and 
quantify  the  acoustical  backscattering  dependence  on  frequency  and 
size  for  each  type  of  scatterer. 

Equation  1  represents  a  set  of  linear  equations  whose  solution  is: 

[n1  n"]T  =  [cxTa]  1  aT  [Sv],  (2) 

where  a  =  [a’  a"].  [Sv]  represents  a  column  vector  whose  elements 
are  the  volume  scattering  strengths  at  each  frequency. 

In  practice,  because  one  cannot  make  completely  noise  free 
estimates  of  volume  scattering  strengths,  one  must  constrain  the 
individual  elements  of  the  abundance  vector  to  non-negative  values. 
Application  of  these  constraints  and  additional  examples  of  the  use  of 
multi-frequency  acoustical  methods  in  bioacoustics,  along  with  a 
discussion  of  many  of  the  assumptions  employed,  can  be  found  in 
Holliday  and  Pieper  (1995)  and  in  Medwin  and  Clay  (1998),  Figures  4a 
and  4b,  and  pp.  462-465.  An  overview  of  the  inverse  method  used  to 
transform  acoustical  volume  scattering  strengths  at  multiple 


150 


frequencies  to  estimates  of  zooplankton  biomass  size  spectra  is  also 
described  in  Medwin  and  Clay  (1998),  pp.  461-462.  Additional  details 
can  be  found  in  Holliday  (1977)  and  in  Greenlaw  (1979). 

V.  INSTRUMENTATION  AND  MODES  OF  DEPLOYMENT 


Advances  have  also  been  made  in  both  the  mechanics  and  the 
methodology  used  to  transform  acoustical  scattering  data  to  estimates 
of  crustacean  biomass  and  elastic  scatterers.  These  calculations  are 
usually  termed  "inverse"  calculations,  to  distinguish  them  from  the 
"forward"  calculations  in  which  volume  scattering  is  calculated  from 


In  plankton  bioacoustics,  the  1990's  have  been  characterized  by 
a  transition  from  experimental,  prototype  zooplankton  acoustics  sensors 
such  as  the  Multi-frequency  Acoustical  Profiling  System  (MAPS™)  to 
the  less  complex,  more  "user-friendly"  Tracor  Acoustic  Profiling 
System  (TAPS™).  The  twenty  one  frequency  MAPS™  was  designed 
for  research  into  the  details  and  character  of  acoustical  scattering  at 
high  frequencies  (100  kHz  to  10  MHz)  and  allowed  description  of  the 
scattering  in  sufficient  detail  to  quantify  the  processes  which  define 
scattering  from  many  kinds  of  small  zooplankton  at  high  frequencies. 
The  TAPS™  series  of  instruments  was  evolved  from  this  detailed 
understanding  of  the  multi-frequency  scattering  process  for  small 
zooplankton.  Although  the  smallest  sizes  are  not  as  well  quantified  and 
less  size  resolution  is  available  than  was  the  case  with  21  frequencies, 
the  current  generation  of  TAPS™  systems  are  more  affordable  and 
much  more  easily  deployed  and  operated  by  the  interested  user 
community.  As  a  consequence,  they  are  much  more  widely  used  than 
the  technically  more  capable,  much  more  complex  MAPS™  could 
have  ever  been. 

With  the  introduction  of  the  TAPS™,  which  operate  in  a  band 
extending  from  265  kHz  to  3  MHz  at  four,  six  or  eight  frequencies, 
depending  on  the  size  resolution  desired,  the  available  modes  of 
deployment  have  been  greatly  expanded  from  the  original  "cast  mode 
only"  methods  used  widely  in  the  1980's  (e.g.,  along  with  a  CTD  from  a 
ship).  Additional  operating  modes  now  include  towing  on  various  net 
frames  (e.g.,  MOCNESS  and  large  trawls);  underway  to-yo  profiling 
(e.g.,  the  SeaSoar™  data  of  Figures  2  and  3),  use  as  a  downlooking 
multi-frequency  echo  sounder;  deployment  in  an  inverted  echo  sounder 
mode  at  a  fixed  location  on  the  bottom  (Barans,  et  al ,  1997);  and  long 
term  use  at  discrete  depths  on  a  mooring,  with  telemetry  to  shore  or 
internal  data  recording,  depending  on  the  location.  In  some  bottom 
mooring,  profiling  modes,  vertical  resolutions  of  the  water  column  can 
be  as  fine  as  ca  12.5  cm  in  depth,  with  complete  multi-frequency 
profiles  every  two  minutes  (Greenlaw,  et  al,  1998).  The  data  rate  is 
largely  limited  by  communication  bandwidths  and  could  be  substantially 
increased  (e.g.,  to  a  few  seconds). 


Northern  Arabian  Sea 


Degrees  Longitude  (E) 


Figure  2:  Cruise  track  for  the  TAPS™  SeaSoar™  deployment 
during  the  ONR  ARI  on  Upper  Ocean  Atmospheric  Forcing 
(TN-048)  in  the  Arabian  Sea  during  the  southwest  monsoon  in 
July  1995. 


Figure  3:  Horizontal  distributions  at  several  discrete  depth  strata  (12.5  m,  25  m  and  37.5  m)  for  zooplankton  biomass  of  animals  with  sizes 
between  0.50  and  0.75  mm  Equivalent  Spherical  Radii  (ESR).  The  ESR  is  the  radius  of  the  sphere  which  would  contain  the  actual  volume  of 
the  individual  zooplankters.  The  size  range  displayed  here  includes  several  species  of  adult  copepods,  e.g.,  Eucalanus,  Rhincalanus, 
Euclirella  and  Euchaeta.  The  data  were  derived  from  volume  backscattering  at  six  frequencies  (265,  420,  700,  1100,  1850  and  3000  kHz). 
Numerical  abundance  was  estimated,  by  size,  for  the  volumes  ensonified  by  the  TAPS™  and  biovolumes  were  computed.  The  gray  scale 
represents  biovolume  (mm3/m3),  an  analog  of  displacement  volume,  and  is  directly  related  to  the  zooplankton  biomass  in  the  indicated  size 
range. 


151 


estimates  of  the  sizes  and  abundances  of  animals  present.  MATLAB™ 
m-file  code  is  available  to  make  the  inverse  transformations  and  to 
display  the  results.  This  code  can  be  executed  on  a  number  of  widely 
available  computers. 

VI.  DATA  AND  EXAMPLES 

Targe  scale  measurements  with  TAPS™  on  a  SeaSoar™ 

As  a  part  of  the  ONR  ARI  on  Upper  Ocean  Atmospheric 
Forcing,  a  TAPS-6™  was  deployed  on  several  SeaSoar™  cruises  in  the 
Arabian  Sea,  including  one  during  the  southwest  monsoon  (TN-048)  in 
July  1995.  This  program  was  a  part  of  a  coordinated  effort  to  study  the 
effects  of  monsoons  on  the  biological  productivity  of  the  northern 
Indian  Ocean  and  involved  scientists  working  within  the  context  of  the 
ONR  study,  US  JGOFS  and  US  GLOBEC.  The  cruise  track  involved 
several  transects  and  "radiator  grid"  patterns  as  illustrated  in  Figure  2. 
The  TAPS™  was  to-yo'ed  repetitively  to  depths  of  several  hundred 
meters  at  intervals  of  about  10  minutes.  Volume  scattering 
measurements  at  six  frequencies  were  binned  into  12.5  m  bins  in  the 
vertical.  The  transformation  of  these  measurements  to  zooplankton 
biovolume  revealed  a  complex  horizontal  and  vertical  distribution  of 
biomass  (Figure  3).  For  clarity  of  presentation,  data  from  only  three 
depth  bins  are  illustrated.  In  some,  but  not  all  locations,  there  were 
correlations  of  varying  strengths  at  larger  scales  with  the  local  physical 
oceanography,  as  observed  with  satellite  and  shipboard  sensors. 

Small  scale  measurements  in  a  cast  mode 

Six  frequency  TAPS™  data  were  collected  at  the  BITS  pilot 
mooring  site  about  15  km  off  the  southern  California  coast  in  June 
1996.  A  close  examination  of  the  total  biomass  profile  (Figure  1) 
reveals  the  presence  of  at  least  four  thin  layers  above  the  seasonal 
thermocline.  The  thermocline  at  this  station  was  between  about  18  and 
20  m.  Fluorescence,  an  indication  of  chlorophyll  A  in  phytoplankton, 
exhibited  a  broad  peak  starting  near  18  m  and  extending  to  about  50  m. 
The  chlorophyll  maximum  was  near  30  m.  These  data  were  originally 
processed  with  one  quarter  meter  depth  resolution.  Additional  data 
from  this  profile,  including  the  detailed  temperature  and  fluorescence 
profiles  can  be  examined  in  Holliday,  et  al  (in  press,  1998).  The 
shallowest  layer,  which  peaked  at  ca  3.25  m,  contained  63.5%  of  the 
total  water  column  biomass  above  50  m.  Two  very  thin  layers,  which 
were  not  resolved  and  appeared  to  be  a  single  layer  with  0.25  m  depth 
resolution,  occurred  near  4.5  m  and  encompassed  6.5%  of  the  biomass 
at  this  location.  A  fourth  layer,  between  6.5  and  7.5  m  contained 
another  8.4%  of  the  biomass.  Together,  these  four  structures  accounted 
for  over  78%  of  the  zooplankton  biomass  at  this  station.  Direct, 
conventional  net  sampling,  with  a  MOCNESS,  revealed  that  various 
stages  of  a  small  copepod,  Calanus  pacificus,  were  the  dominant 
scatterers  in  these  layers.  The  size-abundance  spectrum  for  each  of 
these  layers  differed.  An  assemblage  of  small  copepods  (0.050  to 
0.500  mm  ESR)  were  distributed  over  a  wider  range  of  sizes  at  2.6  m 
than  in  the  layer  near  7  m,  where  a  single  size  dominated  in  the  small 
size  classes.  Animals  with  sizes  between  3.019  and  3.653  mm  ESR 
occurred  in  the  7  m  layer,  but  did  not  appear  in  the  2.6  m  layer 
(Figure  4).  While  there  were  similarities  in  size  structure,  differences 
were  also  evident  in  the  size-abundance  compositions  of  the  two  thin 
layers  near  4.5  m  (Figure  5)  and  at  depths  near  the  top  and  bottom  of 
the  chlorophyll  maximum  layer  (Figure  6). 

Separating  multiple  scattering  types  into  size-abundance  spectra 

In  November  1995,  TAPS™  data  were  collected  at  five 
frequencies  near  the  crest  of  Georges  Bank,  where  the  water  is  about 
40  m  deep.  Nearby,  underwater  sand  dunes  contribute  sand  to  the 
water  column  during  periods  of  high  tidal  currents.  The  size- 
abundance  spectra  at  5.5  m  were  extracted  from  the  volume  scattering 
data  at  this  location  for  small  Crustacea  (left  panel,  Figure  7)  and 
elastic  scatterers  (middle  panel,  Figure  7).  The  acoustical  scattering 
spectrum  for  each  of  these  two  scattering  types  and  the  dashed  line  in 
the  rightmost  panel  illustrates  the  contribution  of  the  sand  to  the 
acoustical  scattering  spectrum. 


Figure  4:  Acoustically  estimated  size-abundance  spectra  for 
two  thin  layers  detected  with  the  TAPS™  off  southern 
California  in  June  1996.  The  station  was  located  just  inshore  of 
the  shelf-slope  break  about  15  km  SSE  of  the  Los  Angeles  - 
Long  Beach  harbor  entrance. 


Figure  5:  Size-abundance  spectra  for  zooplankters  in  two  very 
thin  layers  separated  by  only  0.25  m,  near  4.5  m  depth. 


800 

700 

000 
®500 

a 

S400 

i 

fs  00 

1 

SB 

200 

100 

0, 

Equivalent  Spherical  Radius  (mm) 


X9fi06ltl941 
Depth  bin:  20.19; 


-i - t — r 


Figure  6:  Size-abundance  spectra  from  two  locations  in  a 
relatively  broad  layer  centered  on  the  chlorophyll 
(fluorescence)  maximum.  The  data  in  the  left  panel  is  from  a 
depth  near  the  top  of  the  layer  of  phytoplankton,  while  the  right 
panel  illustrates  the  size-abundance  spectrum  from  a  depth 
near  the  bottom  of  this  layer. 


152 


Crustacean 
Abundance  Spectra 


TP9511021222d1 
Depth  bin:  5.5  m 


Elastic  Scatterer 
Abundance  Spectra 
xIO5 


Measured  Data 
and  NNLS  Fit 


100 


jlx 

0  1  2 
ESR  (mm) 


10  10  10 
Frequency  (Hz) 


Figure  7:  Abundance  spectra  vs  size,  expressed  as  the 
equivalent  spherical  radius  (ESR),  for  crustaceans  and  elastic 
scatterers  (sand)  at  5.5  m  near  the  crest  of  Georges  Bank. 
Total  scattering  was  computed  from  the  results  of  a  Non- 
Negative  Least  Squares  (NNLS)  inverse  calculation  and  are 
displayed,  along  with  the  measured  data  in  the  rightmost  panel. 


VII.  DISCUSSION  AND  CONCLUSIONS 


In  most  marine  environments,  including  the  littoral  zone, 
particulate  fields  Often  occur  in  vertically  layered,  horizontally  patchy 
structures.  Within  these  layers  particulate  densities  can  be  thousands 
of  times  those  just  below  and  just  above  the  structure.  Differences  in 
the  size-abundance  spectra  within  different  layers  often  reflects  the 
presence  of  different  assemblages  of  zooplankters  in  those  layers. 
While  the  physical  environment  may  dynamically  modulate  these 
layers  in  depth  (e  g.,  by  mechanisms  such  as  internal  waves),  it  is  worth 
considering  whether  or  not  one  might  take  advantage  of  an  in  situ 
measurement  of  the  particle  size-abundance  spectrum  to  adjust  the 
operating  depth  of  high  speed  underwater  vehicles,  avoiding  depths  at 
which  particulates  are  most  abundant,  thereby  minimizing  encounter 
rates  with  particles  which  are  likely  to  trigger  the  onset  of  turbulent 
flow  on  or  near  the  vehicle's  surface.  At  times,  adjustment  of  vehicle 
depth  by  as  little  as  a  meter  could  lower  the  encounter  rate  with 
zooplankton  by  several  orders  of  magnitude. 

If  we  wish  to  know,  and  perhaps  adaptively  respond  to,  the  local 
abundance  of  particles  in  the  sea,  we  are  presently  left  with  no 
alternative  but  to  measure  those  distributions  in  situ.  During  the  last 
decade  there  have  been  major  advances  in  acoustical  methods  for 
studying  the  distribution  of  small  particulates  in  aquatic  environments. 
During  the  next  decade,  it  is  likely  that  technology  would  allow  direct 
in  situ ,  real-time  measurements  of  the  size-abundance  spectrum  of 
particles  several  meters  ahead  of  a  high  speed  vehicle.  The  principal 
barrier  to  doing  this  today  is  simply  the  speed  with  which  the  necessary 
acoustical  measurements  can  be  transformed  to  size-abundance 
spectra.  This  barrier  is  unlikely  to  persist  for  more  than  a  few  years 
and  is,  even  today,  more  a  question  of  cost  than  of  available 
technology. 


Greenlaw's  long  and  short  term  contributions  to  the  development  of  this 
technology  have  been  invaluable.  I  also  thank  Duncan  McGehee  for 
processing  the  Arabian  Sea  data  and  for  a  critical  reading  of  the 
manuscript. 

IX.  REFERENCES 

D.V.  Holliday,  "Extracting  Bio-Physical  Information  from  the  Acoustic 
Signatures  of  Marine  Organisms",  in  Ocean  Sound  Scattering 
Prediction,  pp.  619-624,  (1977). 

C. F.  Greenlaw,  "Acoustical  estimation  of  zooplankton  populations", 
Limnol.  Oceanogr.  24:  226-242  (1979). 

D. V.  Holliday  and  R.E.  Pieper,  "Volume  scattering  strengths  and 
zooplankton  distributions  at  acoustic  frequencies  between  0.5  and 
3  MHz,  J.  Acoust.  Soc.  Am.  67:  135  -1  46  (1980). 

R.E.  Pieper  and  D.V.  Holliday,  "Acoustic  measurements  of 
zooplankton  distributions  in  the  sea",  J.  Cons.  Int.  Explor.  Mer  41:  226- 
238  (1984). 

D.V.  Holliday,  "Acoustic  determination  of  suspended  particle  size"  in 
"Coastal  Sediments  '87".  M.C.  Kraus,  ed.,  American  Society  of  Civil 
Engineers,  New  Orleans,  LA,  May  12-14,  1987,  ASCE,  New  York, 
NY,  pp.  260-272  (1987). 

J.H.  Costello,  R.E.  Pieper,  and  D.V.  Holliday,  "Comparison  of  acoustic 
and  pump  sampling  techniques  for  the  analysis  of  zooplankton 
distributions",  J.  Plankton  Res.  11(4):  703-709(1989). 

D.V.  Holliday,  "Zooplankton  acoustics"  in  Oceanography  of  the  Indian 
Ocean.  B.N.  Desai,  ed.,  pp.  733  -  740  (1992). 

D.V.  Holliday  and  R.E.  Pieper,  "Bioacoustical  oceanography  at  high 
frequencies",  ICES  J.  mar  Sci.  52:  279-296  (1995). 

D.V.  Holliday,  R.E.  Pieper,  C.F.  Greenlaw  and  J.K.  Dawson, 
"Acoustical  sensing  of  small-scale  vertical  structures  in  zooplankton", 
Oceanography  [in  press,  1998]. 

C.A.  Barans,  B.W.  Stender,  D.V.  Holliday  and  C.F.  Greenlaw, 
Variations  in  the  vertical  distribution  of  zooplankton  and  fine  particles 
in  an  estuarine  inlet  in  South  Carolina",  Estuaries  20(3):  467-482 
(1997). 

M.S.  Berman,  J.R.  Green,  D.V.  Holliday  and  C.F.  Greenlaw,  "Acoustic 
determination  of  the  fine-scale  distribution  of  zooplankton  on  Georges 
Bank",  Mar.  Ecol.  Prog.  Ser.  (submitted). 

H.  Medwin  and  C.S.  Clay,  Fundamentals  of  Acoustical  Oceanography. 
Academic  Press,  NY,  709  pp.  (1998). 

T.K.  Stanton,  D.  Chu,  P.H.  Wiebe,  L.V.  Martin  and  R.L.  Eastwood, 
"Sound  scattering  by  several  zooplankton  groups.  I.  Experimental 
determination  of  dominant  scattering  mechanisms",  J.  Acoust.  Soc.  Am. 
103:  225-235  (1998a). 

T.K.  Stanton,  D.  Chu  and  P.H.  Wiebe,  "Sound  scattering  by  several 
zooplankton  groups.  II.  Scattering  models",  J.  Acoust.  Soc.  Am.  103: 
236-253  (1998b). 


VIII.  ACKNOWLEDGMENTS 

The  basic  research  underlying  the  multi-frequency  acoustical 
technology  discussed  in  this  contribution  was  sponsored  by  ONR's 
Biological  Oceanography  Program,  with  contributions  from  Tracor,  the 
Ocean  Technology  and  Biological  Oceanography  programs  at  the 
National  Science  Foundation,  NOAA/AOML  and  NOAA/NMFS.  The 
assistance  of  K.  Brink's  team  (WHOI)  in  collecting  the  SeaSoar™  data 
from  the  northern  Indian  Ocean  is  gratefully  acknowledged.  We  are 
also  indebted  to  Richard  Pieper  and  John  Dawson  (both  USC),  Anne 
Lebourges  (ORSTOM),  R.S.  Player  and  Paul  Jarrett  for  their  assistance 
in  collecting  the  TAPS™  data  at  the  BITS  site  off  Los  Angeles.  The 
development  of  the  TAPS™  was  funded  by  Tracor.  Charles 


T.K.  Stanton,  P.H.  Wiebe  and  D.  Chu,  "Differences  between  sound 
scattering  by  weakly  scattering  spheres  and  finite-length  cylinders  with 
applications  to  sound  scattering  by  zooplankton",  J.  Acoust.  Soc.  Am. 
103:  254-264  (1998c). 

C. F.  Greenlaw,  D.V.  Holliday,  C.A.  Barans  and  B.W.  Stender,  "Long¬ 
term,  high-resolution  acoustical  monitoring  of  plankton  in  an  estuary", 
Eos,  Transactions  of  the  American  Geophysical  Union,  79:  OS31A-15 
(1998). 

D. V.  Holliday  and  C.F.  Greenlaw,  "Resolving  zooplankton  on  sub¬ 
meter  scales  at  intervals  of  minutes",  Eos,  Transactions  of  the 
American  Geophysical  Union,  79:  OS51H-8  (1998). 


153 


BIOFOULING  CONTROL:  A  CRITICAL  COMPONENT  OF  DRAG  REDUCTION 


Dr.  Geoffrey  Swain 
Ocean  Engineering 
Florida  Institute  of  Technology 
Melbourne,  FL  32901 
Tel  407  674  7129,  Fax  407  984  8461 
Email:  swain@fit.edu 


Abstract-  Biofouling  control  is  a  critical  component  of  drag  reduction  in  marine  environments.  The  most  effective  antifouling  coatings  are 
the  self-polishing  copolymer  organotin  (SPC/TBT)  based  paints.  However,  due  to  adverse  environmental  impacts  of  the  organotin  biocides, 
regulations  are  in  place  to  restrict  their  use.  There  is  now  a  requirement  to  develop  environmentally  friendly  alternatives.  What  are  the 
antifouling  and  hydrodynamic  characteristics  that  made  the  SPC  coatings  so  successful,  and  what  new  technologies  are  being  explored  to  provide 
a  viable  alternative?  This  paper  provides  a  baseline  of  performance  characteristics  necessary  for  biofouling  control  and  then  presents  alternative 
technologies  that  have  been  tried  or  proposed  as  antifouling  methods.  At  present,  the  most  promising  environmentally  friendly  systems  are  based 
on  non-toxic  silicone  foul-release  technology.  These  surfaces  will  become  fouled,  however,  the  organisms  are  easily  removed.  The  goal  is  to 
engineer  surfaces  that  are  durable,  have  a  five  plus  year  working  life,  and  self-clean  by  hydrodynamic  forces  generated  when  a  ship  is  underway. 


L  INTRODUCTON 

Biofouling  control  is  a  prerequisite  for  drag  reduction  in  marine 
environments.  Modem  day  antifouling  (AF)  paints  are  extremely 
effective  at  preventing  the  accumulation  and  growth  of  fouling 
organisms.  Environmental  issues  and  regulations  are,  however, 
requiring  the  development  of  systems  that  are  based  on  non-toxic  or 
non-polluting  antifouling  strategies. 

The  most  effective  systems  are  the  self-polishing  organotin 
(TBT/SPC)  paints  (See  Figure  1).  These  are  able  to  provide  in  excess  of 
five  years  protection,  a  roughness  not  exceeding  100  microns  average 
hull  roughness  (AHR),  and  complete  protection  against  biofouling  [1]. 
A  cost  benefit  analyses  made  by  Milne  and  Abel  [2]  comparing  the 
TBT/SPC  to  the  next  best  non-tin  alternative  (1980s)  estimated  that 
these  coatings  saved  the  world  commercial  fleet  some  $2.4  billion 
dollars  in  direct  fuel  savings,  extended  drydocking,  improved  ship 
availability  and  capital  savings.  The  problem  with  the  TBT/SPC 
systems  is  that  the  tributyl  tin  (TBT)  has  been  shown  to  adversely  affect 
the  environment.  TBT  has  become  one  of  the  most  studied 
anthropogenic  inputs  into  the  marine  environment.  It  was  shown  that 
extremely  low  concentrations  will  cause  defective  shell  growth  in  the 
oyster,  Crassostrea  gigas  (20ng  l'1)  [3]  and  imposex  in  the  dog-welk, 
Nucella  sp .  (Ing  l*1)  [4].  These  findings  led  to  regulations  that  prohibit 
the  use  of  TBT,  in  most  industrial  nations,  on  boats  less  than  25m  in 
length  [5].  In  December  1985,  the  US  Congress  passed  the  Fiscal  Year 
1986  Appropriation  Bill  with  the  rider  that  prohibited  the  US  Navy  from 
the  purchase  or  application  of  any  organotin  AF  coatings  until  certain 
conditions  were  met.  Although  this  ban  was  lifted  in  1989,  the  US  Navy 
has  chosen  not  to  implement  their  use  [6].  Further-more  the  Office  of 
the  Chief  of  Naval  Operations  has  formulated  a  vision  for  the 
environmentally  sound  ship  of  the  21st  century,  which  will  ensure 
compliance  with  environmental  requirements  while  maintaining  fleet 
effectiveness  and  readiness  [7].  More  recently  TBT  has  been  implicated 
in  the  deaths  of  bottle  nosed  dolphins  ( Tursiops  truncatus)  [8],  and  the 
International  Maritime  Organization  (IMO)  are  looking  at  how  to  further 
reduce  harmful  effects  of  organotin  by  more  restrictions  or  a  total  ban 

[91 

Ships,  boats  and  structures  coated  with  AF  paints  act  as  a  point 
source  input  of  the  biocide  used  to  control  fouling.  For  example,  a 
65,000  Gross  Registered  Tons  container  ship  (260m  long)  has  an 
approximate  wetted  surface  area  of  13,000m2.  If  it  is  coated  with  a 
TBT/SPC  based  system  with  a  biocide  output  of  4|ig/cm2/day  then  the 
TBT  input  into  the  environment  would  be  about  190  kg/year.  If  a 
copper  based  AF  system  was  used  with  a  minimum  biocide  output  of 
20pg/cm2/day  then  the  copper  input  into  the  environment  would  be 
about  950  kg/year.  The  environmental  impacts  of  such  outputs  are  being 
questioned,  and  it  is  apparent  that  non-toxic  technologies  are  required  to 
control  biofouling  while  maintaining  the  drag  reduction  performance 
achieved  by  the  biocide  based  systems.  This  paper  will  discuss  the 
hydrodynamic  penalties  associated  with  biofouling,  identify  the 
characteristics  that  make  TBT/SPC  systems  so  effective  and  investigate 
alternative  technologies  that  may  provide  an  environmentally  acceptable 
solution. 


Figure  1.  Performance  and  environmental  criteria  of  the  TBT/SPC 
systems  and  the  development  of  environmentally  friendly 
antifouling  technology 


II.  BIOFOULING  AND  DRAG 

The  effects  of  biofouling  on  drag  are  hard  to  predict  due  to  the 
complexity  and  variability  of  fouling  community  structure  [10].  Marine 
growth  accumulations  vary  according  to  geographical  area,  season, 
operating  schedule,  hull  zonation,  and  the  effectiveness  of  the 
antifouling  system.  An  example  of  biofouling  community  structure  for  a 
ship  moored  in  Honolulu,  Hawaii  for  three  months  is  shown  in  Figure  2 
[11].  This  vertical  profile  demonstrates  differences  in  the  fouling 
community  structure  with  depth.  Horizontal  variations  in  the  fouling 
communities  were  also  observed. 

One  of  the  earliest  scientific  investigations  of  the  effect  of 
biofouling  on  drag  was  by  McEntee  in  1915  [12].  He  exposed  3.0m  x 
0.6m  coated  steel  plates  to  fouling  in  the  Chesapeake  Bay  for  twelve 
months  and  conducted  monthly  towing  tank  resistance  measurements  at 
velocities  between  1.0  to  4.5  m/s.  The  fouling  layer  consisted  of  slimes 
and  small  barnacles  and  was  found  to  cause  about  a  four-fold  increase  in 


155 


resistance.  A  summary  of  the  early  research  related  to  the  effects  of 
marine  fouling  on  ship  resistance  is  documented  in  Marine  Fouling  and 
Its  Prevention  [13].  Power  trials  on  the  US  destroyer  Putnam  and  the 
US  battleship  Tennessee  and  towing  trials  on  the  Japanese  ex-destroyer 
Yudachi  demonstrated  that  coating  breakdown  and  biofouling  could 
double  the  ship  resistance  within  one  year. 


%  Cover 

Figure  2.  Vertical  profile  of  biofouling  on  a  ship  hull  moored  at 
Honolulu  HI 

Modem  day  AF  coatings  prevent  the  type  of  fouling  and  increase 
in  drag  observed  above.  However,  it  is  well  known  that  biological 
slimes  are  able  to  colonize  toxic  surfaces  and  under  certain  operating 
conditions  may  grow  on  AF  coatings  [14].  The  contribution  of  these 
films  to  ship  hull  drag  should  not  be  overlooked.  One  demonstration  of 
this  effect  is  described  in  ship  trials  of  the  Knox  class  frigate,  USS 
Brewton  [15,  16].  The  ship  was  coated  with  an  ablative  antifouling  paint 
containing  both  cuprous  oxide  and  tributyltin  oxide.  She  had  been 
subject  to  fouling  in  Pearl  Harbor,  Hawaii  for  22  months.  An  initial  hull 
inspection  by  divers  indicated  the  presence  of  a  microbial  biofilm  but 
little  hard  fouling.  Hull  roughness  measurements  gave  a  mode,  median 
and  mean  of  180,190  and  272  microns  respectively.  The  ship  was 
instrumented  to  measure  shaft  horsepower  and  speed  and  power  trials 
were  made  over  a  mile  course.  The  ship  then  returned  to  port  to  undergo 
hull  cleaning  before  running  a  second  ship  power  trial.  Post  hull 
cleaning  roughness  measurements  showed  only  a  slight  decrease  in 
roughness,  the  mode,  median  and  mean  being  160,  182  and  264 
respectively.  It  was  found,  however,  that  there  was  as  much  as  an  18% 
decrease  in  the  required  shaft  horsepower  to  propel  the  ship  at  same 
speed  after  cleaning.  This  was  associated  with  the  removal  of  the 
microbial  biofilm. 

Lewthwaite  et  al.  [17]  used  a  small  pitot  type  tube  to  make  detailed 
boundary  layer  velocity  distribution  measurements  on  a  23m  Admiralty 
fleet  tender.  Over  a  two  year  period  they  measured  an  increase  in  skin 
friction  of  about  80%  which  was  associated  with  a  dense  slime  estimated 
to  be  about  1mm  thick,  but  virtually  free  of  weed  and  shell  growth.  In  a 
more  detailed  study,  which  included  identification  of  the  fouling 
organisms  present  in  the  slime  film,  Schultz  [1 8]  used  a  water  tunnel  and 
laser  Doppler  velocimeter  to  measure  the  effects  of  biofilms  (74  to 
319pm  thick)  on  boundary  layer  structure  at  momentum  thickness 
Reynolds  numbers  from  5,500  to  19,000.  He  measured  increases  in  wall 


shear  stress  on  fouled  plates  of  33  to  187%  compared  to  the  smooth  plate 
conditions. 

Several  other  studies  [19,20,21]  have  also  demonstrated  the 
significance  of  low  form  and  slime  fouling  on  hydrodynamic  drag. 
These  findings  show  that  even  modem  day  antifouling  systems  may 
become  colonized  by  bacteria,  diatoms  and  algal  communities.  Control 
is  typically  achieved  by  the  use  of  co-biocides.  However,  these  are  also 
coming  under  scrutiny  for  environmental  effects. 

III.  ANTIFOULING  METHODS 

There  are  an  abundance  of  patents  and  ideas  relating  to  biofouling 
control,  although,  few  are  practical,  economic  or  effective  [22,23,24,25]. 
Most  present  day  systems  still  rely  on  a  coating  with  active  biocides  to 
protect  a  surface.  However,  environmental  concerns  over  the  effects 
these  compounds  may  have  on  non-target  species,  has  led  to  the  call  for 
“environmentally  friendly  antifouling”  systems.  The  term 
“environmentally  friendly  antifouling”  remains  to  be  fully  defined.  In 
its  purest  sense,  it  can  be  interpreted  as  meaning  a  system  that  has  no 
toxic  components.  In  its  broadest  sense  it  may  be  defined  as  lessening 
the  impact  of  the  TBT/SPC  coatings  (Figure  1). 

Tributyltin  Self-Polishing  Copolymer  Systems 

The  introduction  of  the  TBT/SPC  coatings  in  the  early  seventies 
revolutionized  biofouling  control  on  ships  [26,27,28].  An  understanding 
of  the  mechanisms  that  made  these  coatings  so  successful  helps  to 
identify  the  properties  that  are  required  of  replacement  technology.  TBT 
is  an  extremely  active  biocide  with  chronic  effects  being  observed  on 
many  common  invertebrates  at  levels  below  1  pg  l'1  [29].  It  is  bonded  to 
the  acrylic  polymer  backbone  as  the  TBT  ester  of  methacrylic  acid, 
tributlytin  methacrylate.  This  is  then  copolymerized  with  methyl 
methacrylate  to  form  a  copolymer  [30].  On  immersion  to  seawater,  the 
coploymer  at  the  paint  surface  reacts  to  release  the  TBT.  This  causes  the 
copolymer  to  become  brittle  and  hydrophilic  which  removes  the 
copolymer  chain  providing  both  self-polishing  action  and  a  new  supply 
of  biocide.  The  coating  remains  stable  because  the  reaction  is  confined 
to  an  extremely  narrow  surface  layer  due  to  the  hydrophobic  properties 
of  the  unreacted  paint  film. 

TBT/SPC  paints  are  usually  formulated  with  cuprous  oxide 
pigments  and  other  organic  co-biocides.  These  combinations  enable 
paint  manufacturers  to  formulate  coatings  that  comply  with  the 
maximum  release  rate  of  4pg/cm2/day  TBT,  provide  in  excess  of  five 
years  fouling-free  performance  and  maintain  excellent  hull  roughness 
properties  (about  100  microns).  They  are  considered  the  benchmark 
from  which  to  judge  new  systems. 

Tin-free  Antifouling  Coatings 

The  most  common  alternative  biocide  to  organotin  is  copper.  It  is 
about  ten  times  less  toxic  than  TBT  [31],  and  therefore  on  its  own  it  is 
less  effective.  For  this  reason  there  is  much  interest  in  co-biocides 
which  act  synergistically  to  enhance  the  performance  of  copper  based 
coatings.  The  most  commonly  found  additions  are;  diuron,  triazine, 
isothiazolin  and  zinc  omidine.  Diuron  and  triazine  have  been  shown  to 
be  persistent  in  the  environment  [32,  33,  34].  Isothiazolin  shows  less 
accumulation.  These  biocides  may  be  included  in  conventional  matrix 
paints  (soluble  matrix,  continuous  contact,  diffusion)  or  in  ablative  type 
systems  (self-polishing  polymers,  saponifying  polymers)  [27].  The 
conventional  matrix  paints  typically  provide  a  12  to  18  month  active  life 
and  the  ablative  saponifying  types  up  to  3  years.  More  recently  self¬ 
polishing  tin  free  coatings  have  been  developed  [35,36,37]  with  claims 
of  five  years  protection.  However,  these  compounds  are  already  under 
scrutiny.  Triazine  has  been  detected  at  excessively  high  levels  close  to 
marinas  and  high  boating  activity  [34]  and  even  copper  has  come  under 
scrutiny  [38,39].  Such  findings,  the  high  cost  of  biocide  registration, 
and  the  history  of  regulation,  increases  the  need  to  find  a  non-toxic 
alternative. 

Copper  Alloys 

It  is  well  known  that  the  90:10  copper-nickel  alloys  provide 
excellent  mechanical,  corrosion  and  AF  properties  [40].  They  have  been 
successfully  used  as  the  hull  plate  material  on  several  boats  [41]  and 
more  recently  as  cladding  material.  With  the  use  of  modem  adhesives 
and  polymers,  copper  alloys  can  be  applied  to  steel  hulls  and  structures 
without  creating  bimetallic  corrosion  problems.  In  unpolluted  seawater 
this  alloy  exhibits  relatively  low  homogeneous  corrosion  rates,  which 


156 


prevent  fouling,  and  yet  maintains  a  relatively  smooth  surface.  It  is 
interesting  to  note  that  a  1mm  thick  copper  foil  homogeneously 
corroding  at  20pg/cm2/day  would  theoretically  last  for  about  120  years. 
In  some  ways  it  is  surprising  that  these  materials  have  not  received 
wider  use,  however,  higher  capital  cost  compared  to  AF  paints,  the 
possibility  of  galvanic  interactions  with  other  metal  components  and 
cathodic  protection  systems,  and  unpredictable  performance  in  polluted 
waters  has  prevented  their  widespread  adoption. 

Natural  Antifouling  Mechanisms 

One  possible  source  of  new  technology  is  from  the  understanding 
of  natural  antifouling  processes.  In  recent  years  there  has  been  an 
explosion  of  research  in  this  area,  mainly  focused  on  chemical 
inhibition.  It  has  long  been  known  that  the  settling  phases  of  marine 
organisms  respond  to  a  diversity  of  chemical  cues  [42,  43].  This  has 
generated  interest  in  identifying  compounds  that  might  repel  or  inhibit 
fouling  organisms  [23,44].  For  a  compound  to  be  considered  effective, 
it  must  satisfy  certain  conditions.  These  include: 

•  Non-toxic  mode  of  action. 

•  Active  at  low  concentrations. 

•  Rapid  breakdown  to  non-polluting  substances. 

•  Effective  over  a  broad  spectrum  of  biofouling  organisms. 

•  Compatible  with  coating  systems. 

Much  of  the  research  has  investigated  substances  derived  from 
organisms  that  are  known  to  remain  free  from  fouling.  For  example, 
extracts  from  bacteria  [45,46],  algae  [47,48,],  sea  grasses  [49],  corals 
[50],  sponges  [51,52]  and  even  terrestrial  plants  [53]  have  been 
identified  as  active  antifouling  agents.  The  identification  of  active 
compounds  is  just  one  of  the  steps  required  before  they  transition  to 
become  active  ingredients  of  AF  coatings.  A  mechanism  must  be  found 
from  which  they  can  be  incorporated  into  the  coating  matrix  and  be 
supplied  to  the  surface  at  a  rate  sufficient  to  prevent  fouling  and  yet  not 
wasteful  of  the  compound  [54].  Natural  sources  or  synthetic  analogues 
must  be  identified  to  ensure  supply  at  reasonable  cost.  The  compounds 
must  also  pass  rigorous  scrutiny  from  environmental  regulation  agencies 
[55].  For  these  reasons  no  natural  products  have  been  commercialized 
for  antifouling.  However,  researchers  are  still  hopeful  that  they  may 
identify  compounds  that  can  deter  fouling  without  compromising  the 
environment. 

Physiological  responses  that  lead  to  a  reduction  in  biofouling  are 
also  known.  All  arthropods  undergo  periodic  moults,  which  will 
inevitably  shed  old  fouled  surfaces  [56].  Tissue  sloughing  in  the  sponge 
Halichondria  panicea  has  also  been  associated  with  antifouling  activity 
[57].  A  deep  layer  sloughing  in  the  coralline  algae,  Spongites  yendoi, 
however,  was  shown  not  to  have  any  antifouling  function  [58]. 
Antifouling  systems  comprising  a  multi-layered  surface  from  which  the 
top  layer  could  periodically  be  peeled  have  been  proposed,  but,  to  date, 
no  practical  system  has  successfiilly  been  engineered. 

There  have  been  several  studies  that  have  investigated  the  surface 
properties  of  marine  organisms  with  respect  to  biofouling  control. 
Dogfish  egg  cases  [59]  and  the  epidermis  of  sea  urchins  [60]  were 
investigated  under  funding  from  MAST  II  Project  [61].  These  studies 
identified  a  variety  of  interesting  mechanisms,  but  none,  as  yet,  have 
been  transferred  to  practical  solutions.  From  a  hydrodynamic 
standpoint,  the  three  groups  that  are  of  greatest  interest  are  the  cetaceans 
(whales  and  porpoises),  teleosts  (bony  fish)  and  elasmobranchs 
(cartilaginous  fish).  The  no-foul  condition  of  porpoise  and  killer  whale 
skin  has  been  attributed  to  the  outermost  aspect  being  composed  of  a 
glycoproteinaceous  material  with  low  surface  free  energy  [62,63]. 

The  application  of  natural  control  in  terms  of  disease  [64]  and 
predation  [65]  has  also  been  suggested.  For  many  reasons,  the 
introduction  of  disease  into  marine  ecosystems  is  unacceptable  and 
unlikely  to  work.  The  use  of  predation  has  been  tried  on  offshore  oil 
platforms  where  starfish  were  introduced  to  control  mussels.  The 
experiment  failed  due  to  wave  action  removing  the  starfish  and  for 
simple  reasons  relating  to  the  dynamics  of  ecosystems. 

Finally,  it  should  be  remembered  that  behavioral  activities 
frequently  associated  with  biofouling  control  include  spending  extended 
periods  of  time  out  of  the  water  (seals,  sea  lions,  sea  otters  etc.), 
migrating  into  fresh  water,  or  attending  cleaning  stations  (shrimp  on 
coral  reefs).  Similar  behaviors  are  often  used  to  control  bio  fouling  on 
ships  and  boats. 


Novel  Technology 


There  are  several  review  papers  that  discuss  novel  ideas  for  the 
prevention  of  biofouling  [22,23,24,25].  As  yet  none  of  these  methods 
have  surpassed  the  performance  of  the  conventional  AF  coatings.  For 
this  reason,  only  a  brief  summary  is  provided  for  completeness. 

A  classification  of  novel  antifouling  technology  is  shown  in  Figure 
3.  There  have  been  several  ideas  to  provide  chemical  control  via  air 
bubble  curtains  [66,67]  or  chemical  production  at  the  surface  [68,69]. 
The  most  obvious  problem  with  these  sorts  of  treatments  is  that  they  act 
as  point  source  inputs  of  unwanted  chemicals  into  the  environment.  One 
possible  exception  maybe  found  in  the  control  of  pH.  Mor  [70] 
demonstrated  that  if  the  pH  could  be  maintained  below  4  or  above  10 
then  fouling  was  prevented.  A  high  pH  surface,  with  biocidal  properties, 
was  recently  created  by  formulating  paints  that  contain  lime  [71].  To 
date,  however,  none  have  been  made  to  work  in  a  marine  environment. 


Chemical 


Halogenation 
Ozonation 
Organic  Biocides 
PH 


Electrical 


Calcium  Carbonate  Exfoliation 
Electrochemical  Control 
HighCurrent 
High  Voltage 


Radiation  J 


Acoustics 
Magnetic 
Radiation 
Ultra  Violet 


Contours 

Fibers 

Roughness 

Texture 


Freezing 

Heating 


Figure  3.  Novel  Antifouling  Technology 

The  use  of  high  voltage  or  current  has  also  been  tried  [72,73]. 
These  do  not  work  due  to  low  seawater  resistance,  cathodic  chalk 
formation,  and  possible  corrosion  related  problems  [74]. 

Several  forms  of  radiation  have  been  investigated.  Ultraviolet 
radiation  is  routinely  used  to  sterilize  seawater  in  pipe  systems  [75]  but 
is  not  considered  practical  for  external  surfaces  due  to  rapid  attenuation. 
Radioactive  surfaces  using  thallium  204  have  been  shown  to  be 
extremely  effective  against  fouling  at  intensities  of  20  rad/hr,  but  not  at 
all  at  2  rad/hr  [76,77].  Such  levels  are  considered  too  high  for  safe 
handling  and  therefore  such  methods  are  considered  unacceptable. 
Magnetic  fields  have  been  shown  to  have  temporary  effects  on  some 
organisms  [78],  however,  there  are  no  published  demonstrations  of  any 
antifouling  effect.  The  most  commonly  tried  form  of  radiation  for 
biofouling  control  is  acoustics.  This  has  been  tried  using  external 
vibration  sources  and  by  the  use  of  piezoelectric  coatings.  There  have 
been  several  reports  of  success  [79,80,81].  The  power  requirements, 
however,  are  relatively  high,  and  the  effect  may  be  restricted  to  one 
fouling  type  [81].  Furthermore,  the  presence  of  bulkheads  and  other 
material  properties  impacts  the  distribution  of  energy. 

It  is  well  known  that  the  physical  condition  of  a  surface  will  affect 
the  settlement  of  biofouling  [83].  Smooth  surfaces  generally  foul  less 
than  rough  surfaces,  however,  no  topographical  surface  condition  has 
been  identified  that  will  prevent  biofouling.  One  recent  idea  has  been 
the  use  of  microfibers  [84],  but  this  has  yet  to  be  verified  by  long  term 
field-testing. 


157 


Thermal  control  of  biofouling  is  well  known  and  practiced  at  some 
power  utilities  [85].  However,  heat  or  cryogenic  treatment  of  ship  hulls 
and  structures  are  impractical. 

Mechanical  Cleaning 

The  mechanical  removal  of  biofouling  must  be  one  of  the  oldest 
methods  of  control  and  is  still  routinely  applied  to  modem  day  ships 
[86].  Cleaning  is  often  accomplished  in  water  by  large  rotating  brushes 
and  it  is  generally  used  to  supplement  failed  antifouling  coatings. 
Underwater  ship  hull  cleaning  extends  the  operational  period  of  a  ship 
by  cleaning  the  hull  and  activating  what  remains  of  an  antifouling 
coating.  Such  practice  has  recently  come  under  critism  due  to  the  large 
release  of  antifouling  coating  and  associated  biocides.  This  further 
emphasizes  the  need  to  develop  non-toxic  coating  systems. 

Non-Stick  and  Foul-Release  Surfaces 

From  an  environmental  perspective  the  non-stick  and  foul-release 
technologies  offer  the  most  attractive  option  for  biofouling  control. 
Unfortunately,  the  present  coating  formulations  are  still  not  as  effective 
as  the  existing  SPC/TBT  systems,  and  further  development,  perhaps  in 
combination  with  a  change  in  ship  hull  husbandry,  is  required. 

Interest  in  the  use  of  non-stick  surfaces  for  biofouling  control  was 
stimulated  by  the  synthesis  of  the  polytetrafluoroethylene  and  other 
hydrophobic  plastics.  In  1958,  Bruner  [87]  issued  a  patent  claiming  that 
such  surfaces  prevent  adhesion  and  growth  of  barnacles,  however,  we 
now  know  this  claim  to  have  been  erroneous.  It  took  the  scientific 
studies  of  Baier  [88,  89]  and  Dexter  [90]  to  explain  the  mechanism  for 
the  non-stick  phenomena.  They  demonstrated  that  settlement  and 
attachment  by  microorganisms  could  be  related  to  the  surface  free 
energy  of  the  substrate.  They  further  identified  a  surface  free  energy  of 
between  22-24  dynes/cm  that  produced  a  minimum  in  biological 
adhesive  strength.  These  observations  increased  interest  in  the 
development  of  non-stick  surfaces  and  a  number  of  fluorinated  coatings 
were  developed  with  superior  non-stick  characteristics  [91,92].  They 
were,  however,  unable  to  provide  sufficient  non-stick  characteristics  to 
prevent  attachment  by  macrofouling  organisms,  and  they  exhibit 
disappointing  foul-release  properties.  The  only  alternative  to  fluorinated 
compounds  identified  as  having  non-stick  and  foul-release  properties  are 
the  silicones.  In  addition  to  having  low  surface  energies  and  low  micro¬ 
roughness  for  non-stick,  these  materials  posses  other  properties  that 
confer  foul-release.  Silicones  possess  low  glass  transition  temperatures, 
Tg,  and  it  is  suggested  that  these  minimize  mechanical  locking  of 
biological  glues  and  increases  slippage  and  foul-release  [93,94]. 
Furthermore,  most  commercial  poly(dimethylsiloxane)  based  coatings 
contain  fluid  additives  and  it  is  suggested  that  these  create  weak  surface 
layers  and  macromosaic  surfaces  that  further  promote  foul-release  [95]. 


Figure  3  Requirements  for  a  Non-Toxic  Foul-Release  Coating 


Silicone  was  first  reported  as  a  foul  release  coating  in  1972  in  a 
patent  registered  to  the  Battelle  Institution  [96].  During  the  seventies 
and  eighties  there  was  only  limited  interest  in  these  coatings,  partly  due 
to  the  success  of  the  TBT/SPC  systems  and  also  due  to  some  of  the 
practical  limitations  of  existing  silicone  formulations  [97,98].  It  was 


only  when  the  biocide  containing  coatings  came  under  pressure  from 
environmental  regulations  that  a  concerted  effort  was  made  to  better 
understand  the  mechanisms  by  which  silicone  formulations  function  and 
to  improve  their  performance. 

The  Office  of  Naval  Research  (ONR)  has  funded  research  that  has 
made  significant  contributions  to  the  understanding  and  development  of 
silicone  foul-release  coatings.  During  the  1994  ONR  Biofouling 
Contractors  Workshop,  a  list  of  criteria  considered  important  for  the 
evaluation  and  understanding  of  such  coatings  was  developed  [99]  (See 
Figure  3).  These  were  categorized  under  four  main  headings:  biofouling 
properties,  operational  requirements,  physical  properties,  and  chemical 
properties. 

The  biofouling  properties  that  determines  the  effectiveness  of  these 
coatings  is  different  from  traditional  AF  systems.  Traditional 
antifouling  coatings  use  a  biocide  to  prevent  settlement  and  to  poison  the 
organisms.  Therefore  an  active  surface  will  remain  totally  free  of 
fouling  (See  Figure  4).  A  non-toxic  surface,  however,  may  become 
totally  covered  by  fouling  organisms.  Its  effectiveness  is  determined  by 
the  ease  with  which  the  organisms  become  detached. 


Figure  4  Settlement  matrix  for  toxic  and  non-toxic  surfaces. 

A  variety  of  techniques  have  been  used  to  measure  the  adhesion 
strengths  of  organisms  (diatoms  [100],  Enteromorpha  sp.  [97],  mussels, 
[101,102],  limpets  [103],  tubeworms  [104],  '  and  barnacles 
[104,105,106,107,108,109,110,])  to  different  substrates.  The  ONR 
Biofouling  Control  Program  has  adopted  an  ASTM  standard  for  the 
measurement  of  barnacle  adhesion  strength  in  sheer  [109].  There  is  now 
a  significant  database  of  barnacle  adhesion  strength  measurements  for 
different  species  and  for  different  substrates.  Some  examples  of 
barnacle  adhesion  strength  (Balanus  eburneus)  on  different  materials 
exposed  to  biofouling  at  the  Florida  Institute  of  Technology  static 
immersion  site  are  shown  in  Figure  5. 


Figure  5  Barnacle  Adhesion  Strength  in  Shear 

The  differences  between  non-stick  surfaces  such  as  FEP  Teflon 
(0.59  MPa)  and  the  best  foul-release  silicone  (0.02  Mpa)  can  be  seen. 

The  operational  requirements  for  a  foul-release  coating  are  that  it 
self-cleans  when  the  vessel  is  underway.  It  is  possible  to  predict  the 
velocity  for  foul  release  by  relating  barnacle  adhesion  strength  to 


158 


hydrodynamic  drag  forces  (Figure  6).  Theoretical  drag  and  lift  forces 
may  be  calculated  from  the  basic  equations: 

Fd  =  Vi  CD  p  V2  Af 
Fl  =  V*  Cl  P  V2  Ap 

where:  Fd  =  Drag  Force,  N;  FL  =  Lift  Force,  N;  C  =  Coefficient  of 
Drag;  Cl  =  Coefficient  of  Lift;  V  =  Average  Velocity,  m/s;  Ap 
Frontal  Area,  m,  Ap=  Projected  Area,  m;  p  -  Density,  kg/m3. 

The  drag  and  lift  coefficients  for  typical  acorn  barnacles  have  been 
measured  at  about  0.5  and  0.45  respectively  [104,  112]  and  remain 
reasonably  constant  at  high  Reynolds  number.  It  has  also  been  shown 
that  the  shear  adhesion  strength  of  a  barnacle  is  between  2.5  to  3.0  times 
as  great  as  the  tensile  strength  [105,109].  Assuming  free  stream  velocity 
and  no  boundary  layer,  we  would  predict  that  barnacles  on  the  best 
performing  silicone  shown  in  Figure  5  would  self-clean  at  about  10 
knots.  The  validity  of  such  a  prediction  was  confirmed  during  speed 
trials  on  a  41’  US  Coast  Guard  utility  boat  that  was  coated  with  a 
silicone  formulation  under  the  Environmental  Security  Certification 
Program.  It  was  found  that  the  boat  velocity  required  for  barnacle  foul- 
release  in  the  bow  section  closely  corresponded  to  the  velocity  predicted 
using  barnacle  adhesion  data  obtained  for  the  coating  and  the 
assumptions  made  above  [113].  In  contrast,  we  would  predict  that  a  ship 
would  have  to  travel  in  excess  of  50  knots  to  cause  foul-release  from  an 
FEP  Teflon  surface. 


Figure  6.  Theoretical  Foul-Release  Velocities  for  the  Barnacle 
Balanus  eburneus  from  the  Best  Silicone 

Although  the  theoretical  hydrodynamic  forces  experienced  by 
individual  barnacles  are  easily  calculated,  there  are  several  factors  that 
complicate  the  real  life  situation.  Barnacles  are  gregarious  and  tend  to 
live  in  clusters  surrounded  by  other  fouling  organisms.  This  will 
complicate  the  flow  patterns  and  the  resulting  force  vectors  experienced 
by  individual  organisms.  It  has  also  been  shown  that  barnacle  adhesion 
strength  differ  among  species  [109],  There  are  also  variations  in  the 
adhesion  strengths  and  drag  and  lift  coefficients  of  fouling  types  [103]. 
These  factors,  in  conjunction  with  the  variable  hydrodynamic 
characteristics  of  boundary  layer  thickness  and  flow  patterns  along  a 
ship  hull  make  it  difficult  to  predict  foul-release  with  any  certainty.  It  is 
conceivable  that  the  hydrodynamic  lift  and  drag  forces  on  certain  low 
form  soft  and  hard  foulers  will  never  be  sufficient  to  cause  foul-release. 
In  this  case,  some  sort  of  in-water  hull  cleaning  would  be  required  [1 14]. 

The  foul-release  performance  of  the  silicone  coatings  is  getting 
close  to  satisfying  the  requirements  for  successful  biofouling  control. 
Their  surfaces  also  appear  to  perform  as  hydrodynamically  smooth 
surfaces.  This  would  provide  a  drag  reduction  advantage  over  the  best 
average  hull  roughness  obtained  with  the  SPC7TBT  coatings. 

The  current  disadvantages  with  the  silicones  are  their  poor 
mechanical  properties,  difficulties  with  adhesion  to  tie  coats,  and  their 
relatively  high  costs.  Further  investment  in  advancing  the  technology  is 
required  before  they  can  be  considered  a  replacement  for  the  SPC/TBT 
systems. 

IV.  SUMMARY 

Biofouling  control  must  be  considered  a  part  of  any  drag  reduction 
program.  The  challenge  is  to  find  an  environmentally  acceptable 
method  that  will  provide  equal  or  better  performance  to  the  SPC/TBT 
systems.  The  tin-free  ablative  type  paints  will  provide  an  interim 


solution,  however,  their  reliance  on  copper  and  other  biocides  make 
them  a  target  for  future  environmental  regulations.  It  is  possible  that 
new  ideas  may  be  found  from  studying  natural  AF  mechanisms,  and 
from  a  better  understanding  of  the  cues  that  determine  the  settlement  of 
the  dispersal  phases.  The  idea  of  discovering  a  non-toxic  compound  that 
deters  settlement  is  indeed  attractive. 

Many  novel  ideas  have  been  proposed  for  biofouling  control. 
Several  are  not  considered  environmentally  acceptable,  others  are  not 
feasible  with  present  technology,  and  many  do  not  work.  However,  it  is 
important  that  new  ideas  continue  to  be  promoted  and  evaluated  through 
peer  review  and  trial  and  error. 

The  technology  that  shows  the  greatest  promise  is  non-stick  foul- 
release  surfaces.  Over  the  last  few  years  significant  improvements  in 
coating  performance  have  been  achieved.  Non-toxic  hydrodynamically 
self-cleaning  coatings  are  now  a  reality.  The  remaining  challenge  is  to 
improve  application  and  durability  issues.  One  solution  may  be  to 
combine  foul-release  coatings  with  frequent  hull  cleaning  programs. 

The  final  note  is  to  remember  that  the  development  of  new  AF 
technology  requires  a  multidisciplinary  approach.  Knowledge  of  the 
biological,  chemical,  and  physical  properties  are  required  as  well  as  an 
understanding  of  operational  requirements  of  the  system. 

V.  ACKNOWLEDGEMENTS 

The  information  and  ideas  presented  in  this  paper  are  the  result  of 
meetings,  discussions  and  collaboration  with  a  large  number  of  persons 
involved  in  marine  operations  and  biofouling  control.  I  am  particularly 
indebted  to  the  Office  of  Naval  Research  (Grant  No.  N00014-91-J-1465) 
the  Environmental  Security  Certification  Program,  the  Defense 
Advanced  Research  Project  Agency,  and  to  other  organizations 
(Conoco,  Dow  Coming,  DuPont,  General  Electric)  who  have  funded  our 
research  program.  I  would  also  like  to  acknowledge  all  my  students  and 
colleagues  who  have,  and  continue  to  work  towards  a  solution. 

VI.  REFERENCES 

1.  A.  Milne  “Roughness  and  Drag  from  a  Marine  Paint  Chemist's 
Viewpoint”,  Int.  Workshop  on  Marine  Roughness  and  Drag,  The  Royal 
Institution  of  Naval  Architects,  London,  Paper  12,  March  1990. 

2.  A.  Milne  and  P.D.  Able  “Cost  Benefit  Analyses  of  Remediation  of 
TBX  Contamination”,  Environmental  Impact  of Tributyl  Tin  (TBT)  and 
Development  of  Methods  for  the  Treatment  of  Contaminants  by 
Biotechnological  Means,  MEDSAP  91-1/UK/002/INT06, 1995. 

3.  C.  Alzieu  “TBT  Detrimental  Effects  on  Oyster  Culture  in  France  - 
Evolution  Since  Antifouling  Paint  Regulation.  Proceedings  Oceans’  86 
Organotin  Symposium.  Marine  Technology  Society.  Washington,  DC. 
V.4: 1130-1 134, 1986. 

4.  P.E.  Gibbs  and  G.W.  Bryan  “Reproductive  Failure  in  Populations 
of  Dog-Whelk  Nucella  lapillus.  Caused  by  Imposex  Induced  by 
Tributyltin  from  Antifouling  Paints”,  J.  Mar.  Biol.  Ass.  U.K.  V.67:507- 
523,  1986. 

5.  Anon  “The  Legislative  Position  of  TBT-Containing  Antifoulings”, 
Propeller,  VI  Issue  1,  Courtaulds  Coatings,  Jly/Aug  1994. 

6.  R.  Alberte  et  al.  “Biofouling  Research  Needs  for  the  United  States 
Navy:  Program  History  and  Goals”,  Biofouling,  Vol.6,  pp.  91-95, 1992. 

7.  A.D.  Nickens,  J.F.  Pizzino  and  C.H.  Crane,  “Environmental 
Compliance:  Requirements  and  Technology  Opportunities  for  Future 
Ships”,  Naval  Engineers  Journal,  pp.  349-371,  May  1997. 

8.  K.  Kannan  et  al.  “Elevated  Accumulation  of  Tributyltin  and  Its 
Breakdown  Products  in  Bottlenose  Dolphins  (Tursiops  truncatus)  Found 
Stranded  along  the  U.S.  Atlantic  and  Gulf  Coasts”,  Environ.  Sci. 
Technol.,  31, 296-301,  1997. 

9.  Anon.  “Harmful  Effects  of  the  Use  of  Antifouling  Paint  with  TBT 
Discussed”,  Marine  Environment  Protection  Committee  Session, 
International  Maritime  Organization,  40th  Session,  September  1997. 

10.  J.B.  Ricketts  “Naval  Ship  Self-Assessment  of  Hull  Powering 
Performance  Using  Propulsion  Shaft  Torsionmeters  and  GPS”,  Naval 
Engineers  Journal,  pp.  181- 193,  May  1997. 

11.  G.W.  Swain  and  M.  Schultz  “SLICE  Inspection  Report”, 
Environmental  Security  Certification  Program,  August  1997. 

12.  W.  McEntee  “Variation  of  Frictional  Rsesistance  of  Ships  with 
Condition  of  Wetted  Surface”,  Trans.  Soc.  Nav.  Arch.  And  Mar.  Eng., 
24,  p  85, 1915. 


159 


13.  L.W  Redfield  and  A.C.  Hutchins,  “Ship  Resistance”  in  Marine 
Fouling  and  Its  Prevention ,  Ch.  2,  U.S.  Naval  Institute  Press,  Annapolis, 
MD,  1952. 

14.  R.L.  Townsin  “Ship  Design  for  Fuel  Economy  -  Bottom  Condition 
and  Fuel  Conservation”,  West  European  Graduate  Education  in  Marine 
technology,  8th  School,  Gothenburg,  1983. 

15.  E.G.  Haslbeck  and  G.  Bohlander  Microbial  Biofilm  Effects  on 
Drag  -  Lab  and  Field”,  Proceedings  1992  S.N.A.M.E.  Ship  Production 
Symposium ,  1992. 

16.  E.G.  Haslbeck  and  G.  Bohlander  “Hydrodynamic  Drag  Evakuation 
of  Antifouling  Coatings  -  Laboratory  and  Field”,  Proceedings  of 
Emerging  Nonmetallic  Materials  for  the  Marine  Environment,  Honolulu, 
HI,  18 -20  March,  1997. 

17.  J.C.  Lewthwaite,  A.F.  Molland,  and  K.W.  Thomas  “An 
Investigation  into  the  Variation  of  Ship  Skin  Frictional  Resistance  with 
Fouling”,  Transactions  Royal  Institute  of  Naval  Architects ,  Vol.  127, 
1985  pp.  269-284. 

18.  M.  P.  Schultz  “The  Effect  of  Biofilms  on  Turbulent  Boundary 
Layer  Structure”’  PhD  Dissertation,  Ocean  Engineering,  Florida  Institute 
of  Technology,  Melbourne,  FL,  1998. 

19.  G.I.  Loeb,  D.  Laster,  and  T.  Gracik  “The  Influence  of  Microbial 
Fouling  Films  on  Hydrodynamic  Drag  of  Rotating  Discs”,  in  Marine 
Biodeterioration,  An  Interdisciplinary  Study,  edited  by  Costlow,  J.D. 
and  Tipper,  R.,  Naval  Institute  Press,  Annapolis,  MD,  1984,  pp.  88-94. 

20.  B.F.  Picologlou,  N.  Zelver,  and  W.G.  Characklis  “Biofilm  Growth 
and  Hydraulic  Performance”,  A.S.C.E.  Journal  of  the  Hydraulics 
Division ,  HY5, 1980,  pp.  733-746. 

21.  A.K.  Lewkowicz  and  D.K.  Das  “Turbulent  Boundary  Layers  on 

Rough  Surfaces  With  and  Without  a  Pliable  Overlayer:  A  Simulation  of 
Marine  Fouling”,  Proceedings  of  the  A.S.M.E/A.S.C.E.  Bioengineering, 
Fluid  Engineering,  and  Applied  Mechanics  Conference ,  1981, 

pp.  174-186. 

22.  “Marine  Fouling  and  Its  Prevention”,  Woods  Hole  Oceanographic 
Institution,  1952. 

23.  E.C.  Fischer  et  al.  “Technology  for  Control  of  Marine  Biofouling  - 
A  Review”,  Marine  Biodeterioration:  An  Interdisciplinary  Study,  Naval 
Institute  Press,  1981. 

24.  R  Mitchell  and  P  Benson  “Micro-  and  Macrofouling  in  the  OTEC 
Program:  An  Overview”,  US  Department  of  Energy,  ANL/OTEC-BCM- 
011. 

25.  G.  Swain,  “Antifouling  Practice:  The  Present  and  the  Future,  A 
European  Perspective”,  Technical  Report  to  the  Office  of  Naval 
Research,  February  1996. 

26.  A.  Milne  and  G.  Hails,  Patent  GB  1  457  590,  International  Paint 
Pic,  3  April  1974. 

27.  A.  Milne  “Ablation  and  After:  the  Law  and  the  Profits”,  Polymers 
in  a  Marine  Environment,  Paper  17, 23-24  October  1991. 

28.  R.L.  Townsin  et  al.  “Speed,  Power  and  Roughness:  The 
Economics  of  Outer  Bottom  Maintenance”  In:  Trans.  RINA.  123,  1981. 

29.  M.  Rexrode  “Ecotoxicology  of  tributyltin”,  Oceans  87 
Proceedings,  Volume  4,  International  Organotin  Symposium  pp  1443- 
1455,  1987. 

30.  C.D.  Anderson  “Tin  vs.  Tin-Free  Antifoulings”,  Conference 
Proceedings,  Protecting  the  Ship  While  Safeguarding  the  Environment, 
London,  5-6  April  1995. 

31.  D.  Anderson  and  R.  Dailey,  “Use  of  Organotins  in  Antifouling 
Paints”,  Proceedings  Oceans  86,  V.  4,  Washington  DC,  September  1986. 

32.  Anon  “Review  of  Current  and  Future  Marine  Anti-Fouling 
Coatings”,  Marine  Safety  Agency,  UK,  Report  93/TIPEE/4787, 1993 

33.  M.  Callow  and  G.  L.  Willingham,  “Degredation  of  Antifouling 
Biocides”,  Biofouling,  V.10,  pp  239-249,  1996. 

34.  F.  Pearce  “Alternative  Antifouling  Widespread  in  Europe”  New 
Scientist,  p  7, 14  January  1995. 

35.  Yoshihiro  Honda  “Quantum  Leap  Technology  After  Ban  of  TBT 
in  Japan”,  Proceedings  of  Emerging  Nonmetallic  Materials  for  the 
Marine  Environment,  Honolulu,  HI,  18-20  March,  1997. 

36.  Ping-Lin  Kuo  et  al.  “Interface-Crashed  Self-Polishing  Type  of  Tin- 
Free  Antifouling  Coating”,  Proceedings  of  Emerging  Nonmetallic 
Materials  for  the  Marine  Environment,  Honolulu,  HI,  March,  1997. 

37.  Anon.  “Five-year  Japanese  TBT-free  SPC  system  -  but  at  a 
price!”.  Ship  Repair  and  Corrosion  Technology,  1st  Quarter,  pp  24-31, 
1997. 


38.  Claisse  and  C.  Alzieu  “Copper  Contamination  as  a  Result  of 
Antifouling  Paint  Regulation?”,  Mar.  Pollut.  Bull.,  V  26,  No.  7,  pp  395- 
397,  1993. 

39.  J.J.  Molnar  “Copper  Storage  in  the  Liver  of  the  Wild  Mute  Swan 
(Cygnus  olor).  Its  Possible  Relation  to  Pollution  of  Harbor  Waters  by 
Antifouling  Paints”,  Arch.  Pathol.  Lab.  Med.  V.107,  No.  12,  pp.629-632, 
1983. 

40.  “Marine  Engineering  with  Copper-Nickel”,  The  Institute  of 
Metals,  London,  19-20  April  1988. 

41.  D.W,  Czimmek  and  L.W.  Saundor,  “Economic  and  Technical 
Feasibility  of  Copper-Nickel  Sheathing  of  Ship  Hulls”,  Marine 
Technology,  Vol.  22,  No.  2,  pp.  142-154,  April  1995. 

42.  J.R.  Pawlik  “Chemical  Ecology  of  the  Settlement  of  Benthic 
Marine  Invertebrates”,  Oceanogr  Mar  Biol  Annu  Rev  30:  273-335, 
1992. 

43.  M.G.  Hadfield  “Research  on  Settlement  and  Metamorphosis  of 
Marine  Invertebrate  Larvae:  Past,  Present  and  Future”,  Biofouling  Vol. 
12,  Vol.  1-3,  pp  9-30,  1998. 

44.  A.S.  Clare  “Marine  Natural  Product  Antifoulants:  Status  and 
Potential”,  Biofouling  Vol.  9,  pp  211-229,  1996. 

45.  Holmstrom  et  al..  “Regulation  of  Activity  and  Settlement  of 
Marine  Organisms  by  Bacterial  Extracellular  Components”,  Proceedings 
of  Emerging  Nonmetallic  Materials  for  the  Marine  Environment, 
Honolulu,  HI,  18  -  20  March,  1997. 

46.  S.  James  et  al.  “Marine  Bacteria  Immobilized  in  Hydrogel  Prevent 
Settlement  of  Larvae”  3rd  International  Marine  Biotechnolgy 
Conference,  Tromsoe,  Norway,  1994. 

47.  N.G.M.  Nadal  “Process  for  producing  antibiotic,  antifungal  and 
antifoulant  substances  by  solvent  extraction  of  Sargassum  natane, 
Chondria  littoralis  and  Cympolis  barhata  and  the  resulting  products”, 
US  Patent  No.  3,415,928,  10  Dec  1968. 

48.  P.D.  Steinberg,  R.  de  Nys,  S.  Kjelleberg  “Chemical  Inhibition  of 
Epibiota  by  Australian  Seaweeds”,  Biofouling,  Vol.  12(1-3),  pp227-244, 
1998. 

49.  J.S.  Todd  et  al.  “The  antifouling  activity  of  natural  and  synthetic 
phenolic  acid  sulfate  esters”.  Phytochemistry,  Vol.  34,  No.  2,  pp  401- 
404,  1993. 

50.  Rittschoff  et  al.  “Barnacle  In  Vitro  Assays  for  biologically  Active 
Substances:  Toxicity  and  Settlement  Inhibition  Assays  using  Mass 
Cultured  Balanus  amphitrite  amphitrite  Darwin”,  Biofouling,  Vol.  6  (2), 
ppl 15-123,  1992. 

51.  C.  Unabia  and  M.  Hadfield  “Bioactive  Marine  Isonitrile 
Compounds  form  Hawaiia  Sponges  as  Models  for  Synthetic  Nontoxic 
Antifoulant  and  Antibiotic  Agents”,  Proceedings  of  Emerging 
Nonmetallic  Materials  for  the  Marine  Environment,  Honolulu,  HI,  18  - 
20  March,  1997. 

52.  P.R.  Willemsen  “The  screening  of  Sponge  Extracts  for  Antifouling 
Activity  using  a  Bioassay  with  Laboratory  Reared  Cyprid  Larvae  of  the 
Barnacle  Balanus  amphitrite ”  Int  Biodeterior  Biodegrad  *-9:  361-373, 
1995. 

53.  S.S  Sawant  and  A.  Wagh  “  Terrestrial  Plants:  A  Potential  Source 
for  Isolation  of  Eco-Friendly  Antifouling  Compounds”,  Proceedings  of 
Emerging  Nonmetallic  Materials  for  the  Marine  Environment,  Honolulu, 
HI,  18 -20  March,  1997. 

54.  G.R.  Weisman  et  al.  “Controlled  Release  Antifouling  Coatings.  1. 
Approaches  for  Controlled  Release  of  2,4-Dinitrophenolate  and 
Benzoate  into  Seawater”,  Biofouling  Vol.  6  (2)  pp!23-147.  1992. 

55.  Environmental  Protection  Agency,  USA. 

56.  K.  Becker  and  M.  Whal  “Behaviour  Patterns  as  Natural 
Antifouling  Mechanisms  of  Tropical  Marine  Crabs”,  J.Exp.  Mar.  Biol. 
Ecol.  Vol.  203,  No.  2,  pp  245-258. 

57.  D.  Barthel  and  B.  Wolfrath  “Tissue  Sloughing  in  the  Sponge 
Halichondria  panicea :  A  Fouling  Organism  Prevents  Being  Fouled”, 
Oecologia  Vol.  78  No.  3,  pp.  357-360,  1989. 

58.  D.W.  Keats,  P.  Wilton,  G.  Maneveldt  “Ecological  Significance  of 
Deep-Layer  Sloughing  in  the  Eulittoral  Zone  Coralline  Alga,  Spongites 
yendoi  (Foslie)  Chamberlain  (Corallinaceae,  Rhodophyta)  in  South 
Africa”,  J.  Exp.  Mar.  Biol.  Ecol.  Vol.  175,  No.2,  ppl45-154,  1994. 

59.  J.C.  Thompson  et  al.  “Antifouling  Performance  of  the  Embryo  and 
Eggcase  of  the  Dogfish  Scyliorhinus  caniculd J.  mar.  biol.  Assoc. 
U.K.,  Vol.  74,  pp  823-836,  1994. 

60.  J.D.  McKenzie  and  I.V.  Grigolava  “How  do  Marine  Invertebrates 
Keep  their  Surfaces  Free  from  Microfouling”,  9  International  Congress 
on  Marine  Corrosion  and  Fouling,  Portsmouth,  U.K.,  17-21  July  1995. 


160 


61.  M.J.  Cowling  and  T.  Hodgkiess  “High  Technology  Antifouling 
Coatings  for  Submarine  Sensors  Based  on  Modelling  and  Synthesis  of 
Natural  Antifouling  Processes”  Contract  No:  MAS2-CT9 1-0009, 
European  Commision,  1991. 

62.  R.  Baier  et  al.  “Porpoise  and  Killer  Whale  Skin  as  Natural 
Examples  of  Low-Drag,  Low  Adhesion  Biomaterial  Surfaces”, 
Transactions  of  the  2nd  World  Congress  on  Biomaterials,  10th  Annual 
Meeting  for  the  Society  for  Biomaterials,  Minneapolis,  MN,  p.190, 
1984. 

63.  H.  Gucinski  and  R.  Baier  “Surface  Properties  of  Poroise  and  Killer 
Whale  Skin  In  Vivo”,  Amer.  Zoologist,  Vol.  23,  No.4,  p506, 1983. 

64.  W.D.P.  Stewart  “Preventing  Formation  of  Marine  Growth  by  the 
Use  of  Predatory  Bacteria”,  BSRA  Report 

65.  Anon  “Report  of  the  Marine  Fouling  Working  Party  for  the 
Director  of  Petroleum  Engineering”,  Department  of  Energy,  UK,  OT-R- 
8001,  Feb.  1980. 

66.  F.G.W.  Smith  “Mechanical  Control  of  Ship-Bottom  Fouling  by 
Means  of  Air  Bubbles”,  Fla.  Acad.  Sci.  Quarterly  Journal,  Vol.  9  pp. 
153-161, 1946. 

67.  G.W.  Swain  “The  Use  of  Ozone  Air  Bubble  Curtains  for  the 
Protection  of  Fixed  Structures  from  Marine  Fouling”,  Internal  Report. 
Dept,  of  Mech.  Eng.,  University  of  Southampton  ME/80/3. 

68.  T.  Matsunaga  “Electrochemical  Prevention  of  Biofouling”, 
Proceedings  of  Emerging  Nonmetallic  Materials  for  the  Marine 
Environment,  Honolulu,  HI,  18-20  March,  1997. 

69.  J.  Shibata  et  al.  “Ship  Hull  Anti-Fouling  System  Utilizing 
Electrolyzed  Sea  Water”’  Proc  3rd  International  Congress  on  Marine 
Corrosion  and  Fouling,  1972. 

70.  E.  Mor,  “  Influence  du  pH  du  Substratum  sur  la  Fixation  des 
Organismes  du  Fouling”, 

71.  Anon,  “Development  of  Lime  Paint  Offers  New  Weapon  in 
Antimicrobial  Arsenal”,  Paint  &  Coatings  Industry,  pp  216-217,  October 
1997. 

72.  E.S.  Castle  “Electrochemical  Control  of  Marine  Fouling”,  Ind. 
Eng.  Chem.  Vol .  43  No.  4,  pp.90 1  -904, 1951. 

73.  R.K.  Nazirov  et  al.  “Fouling  of  Structures  in  Marine  Oil  Fieldsand 
its  Prevention”,  In  Protection  Against  Marine  Growth,  Trans,  of  the 
Oceanographic  Committee,  ACSIL  transl.  #1560,  pp.  21-27,  USSR 
Academy  of  Sciences,  1960. 

74.  P.  Czerski  “Experimental  Models  for  the  Evaluation  of  Microwave 
Biological  Effects”,  Proc  IEEE  Vol  63,  No.  11,  PP.  1540-1544,  1975. 

75.  R.  Plotner  “Sensor  Fouling  on  Deep  Submergence  Vehicles”,  In: 
Marine  Sciences  Instrumentation,  Proc.  4th  National  ISA  Marine 
Sciences  Symposium,  Vol.  4,  pp.  267-295,  1968. 

76.  Morley  et  al.  “The  Use  of  Radioactivity  Against  Marine  Fouling”, 
J.  Oil.  Col.  Chem.  Assoc.,  Vol.  41,  pp.  445-452,  1958. 

77.  C.B.  Wootten  “Method  for  Prevention  of  Fouling  and  Corrosion 
Utilizing  Technecium-99”,  U.S.  Patent  No.  4,123,338,  31  Oct  1978. 

78.  V.F.  Gerencser  et  al.  “Inhibition  of  Bacterial  Growth  by  Magnetic 
Fields”,  Nature,  196  (4854),  pp.  539-541,  1962. 

79.  A.M.  Aksel’band  “Ultrasonic  Protection  of  Ships  from  Fouling”, 
In  Transactions  of  the  Oceanographic  Commision,  The  Academy  of 
Sciences,  U.S.S.R.,  Vol.  13, 1960. 

80.  R.  Giordano  et  al.  “Effects  of  Ultrasound  on  Unicellular  Algae”,  J. 
Acoust.  Soc.  Am.  Vol  60,  No.  1,  pp.  275-278, 1976. 

81.  P.V.  Murphy  and  M.J.  Latour  “Preventing  Marine  Fouling”,  U.S. 
Patent  No  4,170,185, 9  Oct.  1997. 

82.  D.  Rittschof  et  al  “Cues  and  Context:  Larval  Responses  to  Physical 
and  Chemical  Cues”,  Biofouling,  Vol.  12,  Nos.  1-3,  PP.  31-44,  1998. 

83.  J.M.  Hills  and  J.C,  Thomason  .’’The  Effect  of  Scales  of  Surface 
Roughness  on  the  Settlement  of  Barnacle  (Semibalanus  balanoides) 
Cyprids.  Biofouling,  Vol.  12,  No.  1-3,  PP.  57-70,  1996. 

84.  G.  Forsberg  “Fiberflock  -  A  Biomimicking  Nonfouling  Concept”. 
Proceedings  of  an  International  Workshop,  Biofouling:  Problems  and 
Solutions,  University  of  New  South  Wales,  Eds.  S  Kjelleberg  and  P. 
Steinberg,  p77,  April  1994. 

85.  D.C.  Sommerville  “Heat  Treatment  Optimization  Studies  at  the 
Diablo  Canyon  Power  Plant”,  Proceedings:  Condenser  Biofouling 
Control  -  State-of-the-Art  Symposium,  EPRO  CS-4339,  Nov.  1985. 

86.  NAVSEA  “Waterborne  Underwater  Hull  Cleaning  of  Navy  Ships”, 
Naval  Ships’  Technical  Manual  S9086-CQ-STM-010,  Chapter  081,  Oct. 
1989. 

87.  W.M.  Bruner  “Method  for  Preventing  Adhesion  and  Growth  of 
Barnacles”,  U.S.  Patent  2,865,702, 23  Dec.  1958. 


88.  R.E.  Baier  “Surface  Properties  Influencing  Biological  Adhesion”, 
in  R.S.  Manly,  Ed.  Adhesion  in  Biological  Systems,  Academic,  New 
York,  1970. 

89.  R.E.  Baier  “Influence  of  the  Initial  Surface  Condition  of  Materials 
on  Bioadhesion”  Proceedings  of  the  3rd  International  Congress  on 
Marine  Corrosion  and  Fouling,  pp  633-639,  October  1972. 

90.  S.C.  Dexter  “Influence  of  Substrate  Wetability  on  the  Formation  of 
Bacterial  Slime  Films  on  Solid  Surfaces  Immersed  in  Natural  Sea 
Water”,  Proceedings  of  the  4th  International  Congress  on  Marine 
Corrosion  and  Fouling,  pp  137-144,  June  1976. 

91.  J.R.  Griffith  and  J.D.  Bultman  “Fouling  Release  Coatings”,  Naval 
Engineers  Journal,  pp.  129-132,  April  1980. 

92.  R.F.  Brady  et  al.  “Nontoxic  Alternatives  to  Antifouling  Paints”,  J. 
Coatings  Technology  Vol  59,  pp  1 13-1 19,  1987. 

93.  B.Z.  Newby,  M.K.  Chaudhury,  H.R.  Brown  “Macroscopic 
Evidence  of  the  Effect  of  Interfacial  Slippage  on  Adhesion”,  Science 
Vol.  269,  pp  1407-1409,  8  Sept.  1995. 

94.  A.E.  Mera  et  al  “Toward  Minimally  Adhesive  Surfaces  Utilizing 
Siloxanes”,  Naval  Resrach  Reviews,  Vol  XLIX,  pp.  4-8, 1997. 

95.  W.A.  Finzel  and  H.L.  Vincent  “Silicones  in  Coatings”,  Federation 
Series  on  Coating  Technology,  March  1996. 

96.  K.  Kroyer,  Great  Britain  Patent  1,397,001,  1973. 

97.  A.  Milne  and  M.  Callow,  “Non-Biocidal  Antifouling  Processes”, 
Trans  I  MarE,  Conf.  2,  Paper  37,  1984. 

98.  A.  Milne,  M.  Callow  and  R.  Pitchers,  “The  Control  of  Marine 
Fouling  by  Non-Biocidal  Systems”,  Stud.  Environmental  Scxiences,  28 
(Algal  Biofouling),  145,  1986. 

99.  G.W.  Swain  Field  Evaluation  of  Non-Toxic  Antifouling  Coatings: 
New  Field  Technologies  and  Performance  Criteria”,  Naval  Resrach 
Reviews,  Vol  XLIX,  pp.  46-50, 1997. 

100.  M.A.  Harper  and  J.F.  Harper  “Measurements  of  Diatom  Adhesion 
and  their  Relationship  with  Movement”,  Br.  Phycol.  Bull.  Vol.  3  No.  2, 
ppl95-207, 1967. 

101.  H.A.  Price  “Seasonal  Variation  in  the  Strength  of  Byssal 
Attachment  of  the  Common  Mussel,  Mytilus  edulish .”,  J.  Mar.  Biol. 
Assoc.  U.K.,  Vol  60,  pp.  1035-1037. 

102.  J.H.  Waite  “Nature’s  Underwater  Adhesive  Specialist”,  Int.  J. 
Adhesion  and  Adhesives,  Vol.  7,  no.  1,  pp  9-14, 1987. 

103.  M.W.  Denny  “Biology  and  the  Mechanics  of  the  Wave-Swept 
Environment”,  Princeton  University  Press,  1988. 

104.  K.  Becker  “Attachment  Strength  and  Colonization  Patterns  of  Two 
Macrofoul ing  Species  on  Substrata  with  Different  Surface  Tension  (in 
situ  studies)”,  Marine  Biology,  Vol.  117,  pp30 1-309, 1993. 

105.  G.W.  Swain  and  M.P.  Schultz  “The  Testing  and  Evaluation  of 
Non-Toxic  Antifouling  Coatings”,  Biofouling  Vol.  10,  p  187-197, 1996. 

106.  A.  Becka  and  G.  Loeb  “Ease  of  removal  of  barnacles  from  various 
polymeric  materials”,  Biotechnology  and  Bioengineering,  XXVI,  pp. 
1245-1251, 1984. 

107.  J.D.  Bultman,  J.R.  Griffith  and  D.E.  Field  “Fluoropolymer 
Coatings  for  the  Marine  Environment”,  In  Proc.  Symp.  on  Marine 
Biodeterioration,  eds.  J.D.  Costlow  and  R.C.  Tipper,  pp  237-249,  Naval 
Institute  Press,  Annapolis,  MD,  1981. 

108.  J.F.  Grenon,  J.Elias,  J.Moorcroft,  D.J.  Crisp.  “A  New  Apparatus 
for  Force  Measurement  in  Marine  Bioadhesion”.  Marine  Biology,  53, 
381-388, 1979 

109.  G.W.  Swain,  J.R.  Griffith,  J.D.  Bultman,  H.L.  Vincent,  “The  Use 
of  Barnacle  Adhesion  Measurements  for  the  Field  Evaluation  of  Non- 
Toxic  Foul  Release  Surfaces”  Biofoul ingVol.  6,  pp.105-114. 1992. 

110.  A.B.  Yule,  G.  Walker,  “The  Adhesion  of  the  Barnacle,  Balanus 
balanoides ,  to  Slate  Surfaces”,  J.mar.biol.Ass.  U.K.,  64,  147-156, 1984. 

111.  ASTM  D5618  “Standard  Test  Method  for  Measurement  of 
Barnacle  Adhesion  Strength  in  Shear”,  American  Standard  for  Testing 
and  Materials,  1994. 

112.  M.  Schultz  “The  Measurement  of  Hydrodynamic  Forces  on  Fouling 
Organisms”,  MS  Thesis,  Ocean  Engineering,  Florida  Institute  of 
Technology,  Melbourne,  FL.,  August  1992. 

113.  G.  Swain  and  M.  Schultz  “Advanced  Non-Toxic  Antifouling 
Coatings  Technology  Demonstration,  NRL  /  GE  Duplex  Coating 
Systems,  41’  Utility  Boat.  U.S.  Coast  Guard  Reserve  Training  Center, 
Yorktown,  VA.’”  Environmental  Security  Technology  Certification 
Program.  Second  Inspection  Report.  October  1996. 

114.  K.  Schumacher  “An  Instrumented  Rotating  Brush  Device  to 
Evaluate  the  Removal  of  Biofouling  from  Non-Toxic  Antifouling 
Coatings.  MS  Thesis,  Florida  Institute  of  Technology,  1996. 


161 


ENVIRONMENTAL  FACTORS  FOR  OCEAN  BUBBLES 


Jeffrey  L.  Hanson 
The  Johns  Hopkins  University 
Applied  Physics  Laboratory 
Laurel,  Maryland  20723-6099 
jeffrey.hanson@jhuapl.edu 

Abstract  -  Acoustic  reverberation  experiments  conducted  during  the  extensive  Critical  Sea  Test  (CST)  Program  led  to  the  conclusion  that  near-sur¬ 
face  microbubble  clouds  are  the  primary  source  of  low  frequency  (0-1000  Hz)  acoustic  surface  backscatter  during  elevated  winds.  Crucial  issues 
remaining  from  CST,  however,  were  (1)  explanation  of  large  site-to-site  differences,  at  similar  wind  speeds,  in  surface  scattering  strength;  and  (2) 
understanding  how  to  extend  the  CST  deep  water  results  to  coastal  areas.  It  is  demonstrated  here  that  the  CST  observation  disparities  can  mostly  be 
attributed  to  physical  and  biological  processes  related  to  the  supply,  mixing,  and  removal  of  bubbles  in  the  upper  ocean.  Using  the  extensive  CST 
environmental  and  acoustic  observation  set,  as  well  as  satellite  remote  sensing  products  available  over  the  World  Wide  Web,  it  is  empirically 
shown  that  site-to-site  differences  in  acoustic  bubble  scatter  are  related  to  the  mean  ocean  temperature,  biological  productivity,  and  wave  condi¬ 
tions  at  each  site.  As  these  are  all  readily  available  environmental  parameters  from  satellites  and  operational  models,  they  may  ultimately  be 
employed  to  routinely  estimate  the  temporal  and  geographic  variability  in  near-surface  bubble  characteristics. 


1.  Introduction 

As  an  important  element  of  underwater  sonar  performance,  Iow-fre- 
quency  (0-1000  Hz)  acoustic  surface  scattering  strength  (SSS)  measure¬ 
ments  have  been  made  in  a  variety  of  oceanographic  conditions  by 
numerous  investigators.  The  recent  series  of  Critical  Sea  Test  (CST) 
experiments  (1988-1992)  has  provided  a  rich  set  of  observations, 
obtained  with  a  consistent  technique,  in  the  six  different  environments 
shown  in  Figure  1  [1].  The  calibrated  CST  results  can  be  readily  com¬ 
pared  with  earlier  measurements  such  as  those  of  Chapman  and  Harris 
obtained  north  of  Bermuda  in  1962  [2]. 


Figure  1  CST  Surface  Scatter  Measurement  Locations 


Surface  scattering  results  from  the  CST  program  have  been 
reviewed  in  a  series  of  reports  [1],  [3]  -  [6].  The  CST  results  most  rele¬ 
vant  to  our  study  are  listed  here: 


A  crucial  issue  remaining  from  the  CST  program  is  explanation  of  the 
large  site-to-site  differences  in  SSS  from  bubbles.  The  extended  analysis 
of  CST  observations  reported  here  has  led  to  a  possible  explanation  for 
these  differences. 


2.  Research  Objective 

Our  hypothesis  is  that  site-to-site  variations  in  SSS  are  a  result  of 
physical  and  biological  factors  related  to  the  supply,  mixing,  and  removal 
of  bubbles  in  the  upper  ocean.  As  the  wind  speed  input  of  SSS  models 
appears  to  adequately  prescribe  the  local,  short-term  forcing  of  the  upper 
ocean,  the  missing  environmental  factors  must  relate  to  the  background 
setting  of  each  site  (swell,  mixing,  temperatures,  dissolved  gasses,  sur¬ 
factants,  etc.).  Hence,  our  primary  research  objective  was  to  examine  the 
influence  of  bubble-related  environmental  factors  on  SSS  with  particular 
emphasis  on  parameters  linked  to  seasonal  and  geographic  variations  in 
near-surface  bubble  populations.  The  need  to  identify  the  ‘missing  link’ 
for  explaining  site-to-site  differences  in  SSS  is  recognized. 


3.  Site-to-Site  SSS  Variability:  Environmental  Factors 


3. 1  SSS  Prediction  Errors 


The  NRL  ONE  model  predicts  SSS  as  a  multiparameter  function  of 
frequency,  grazing  angle,  and  wind  speed.  Observation  departures  from 
ONE  predictions,  aside  from  measurement  errors,  result  from  environ¬ 
mental  influences  not  well  represented  by  wind  speed  alone.  Here  we  iso¬ 
late  these  departures  by  calculating  the  SSS  prediction  error 


SSSe 


SSS SSS  , 
ONE  obs 


(1) 


SSS  is  strongly  linked  to  short-term  (~  1  h)  wind  history. 

Supporting  environmental  data  suggest  that  SSS  is  more 
closely  associated  with  tenuous  bubble  clouds  than  with 
breaking  wave  events. 

Acoustic  model  comparisons  with  CST  results  indicate  that 
near-surface  (~  1-3  m)  microbubbles,  entrained  by  wave 
orbital  motions,  contribute  most  to  SSS. 

Significant  differences  (6-7  dB)  are  noted  between  CST4  and 
CST-7  SSS  results  at  similar  wind-forcing  conditions.  Unex¬ 
plained  differences  also  exist  between  other  CST  data  sets  and 
with  Chapman-Marris. 

CST  1, 2, 3, 4,  5,  and  7  results  used  to  construct  NRL  Ogden- 
Nicholas-Erskine  (ONE)  empirical  SSS  model.  Environmen¬ 
tal  input  is  the  1-hr  backaveraged  wind  speed  [1]. 


with  the  ‘ONE’  and  ‘obs’  subscripts  referring  to  model  predictions  and 
observations,  respectively. 

The  mean  SSSe  at  500  Hz  for  each  of  the  CST  and  Chapman-Harris 
sites  appears  in  Figure  2.  The  mean  levels  were  calculated  by  averaging 
the  prediction  errors  for  each  experiment  over  all  wind  speeds,  all  graz¬ 
ing  angles  >  10°,  and  over  the  frequency  band  400-600  Hz.  Error  bars 
depict  one  standard  deviation  about  the  means.  It  is  observed  that  CST-2 
and  CST-5  are  over-predicted  and  that  CST-1,  CST-3,  CST-4,  and  Chap¬ 
man-Harris  are  under-predicted.  The  CST-7  values  are  close  to  zero;  this 
is  expected  as  CST-7  has  contributed  by  far  the  most  observations  used 
for  the  ONE  model  fits.  The  differences  between  CST-4  and  CST-7  levels 
have  been  particularly  frustrating  to  the  research  community  as  both 
experiments  occurred  in  the  Gulf  of  Alaska  under  similar  wind  and  wave 
conditions.  Note  that  much  larger  differences  exist  between  the  remain¬ 
ing  CST  experiments,  such  as  extreme  differences  between  CST-3  and 
CST-5  of  nearly  15  dB. 


163 


CST-1  CST-2  CST-3  CST-4  CST-5  CST-7  Chapman- 

Harris 

Observation  Sites 

One  standard  deviation  error  bars  are  depicted. 

Figure  2  Mean  Surface  Scatter  Strength  Prediction  Error 

(sssONE  -  sssobs )  at  500  Hz 

Our  approach  is  to  empirically  relate  SSSe,  averaged  over  various 
frequency,  grazing  angle,  and  wind  speed  regimes,  with  the  bubble- 
related  environmental  descriptors  described  in  Section  3.2. 

3.2  Environmental  Descriptors 

The  ONE  model  wind  speed  input  represents  those  environmental 
processes  that  influence  surface  scatter  on  short  (hourly)  time  scales 
including  surface  wave  development  and  the  supply  of  bubbles  by  break¬ 
ing  waves.  Missing  from  this  model,  however,  are  environmental 
descriptors  for  the  background  setting  of  each  site,  such  as  swell  activity, 
mixed-layer  temperature  and  depth,  gas  saturation,  and  surfactants.  Both 
laboratory  experiments  and  theoretical  calculations  have  shown  the 
importance  of  these  background  conditions  on  processes  that  supply, 
entrain,  and  remove  bubbles  from  the  upper  ocean  [7]  -  [9].  The  full  com¬ 
plement  of  supporting  environmental  data  collected  during  CST,  com¬ 
bined  with  remote  sensing  products,  has  allowed  a  reasonable  test  of  their 
importance  to  SSS. 

The  environmental  descriptors  found  to  be  most  important  for  site- 
to-site  SSS  variability  appear  in  Table  I.  Four  factors  are  employed  to 
describe  bubble  supply,  entrainment,  and  removal  processes  in  the  ocean: 
wind  speed  (^jqX  ocean  temperature  ( sst ),  significant  wave  height 
( h  ),  and  chlorophyll  concentration  (chi).  The  importance  of  wind  speed 
has  already  been  demonstrated  by  its  success  in  the  various  SSS  model 
formulations  (for  example,  Chapman-Harris  and  ONE). 


Bubble  Issue 

Process 

Descriptor 

Supply 

Wave  breaking 

Wind  speed 

Ocean  temperature 

Entrainment 

Wave  mixing 

Wave  height* 

Ocean  temperature 

Removal 

Gas  dissolution 

Chlorophyll  concentration 

*  Mean  over  entire  test  duration. 

Table  I 

Environmental  Descriptors  for  Surface  Scatter  by  Bubbles 


Significant  wave  height,  averaged  over  the  entire  test  duration,  is 
employed  here  to  represent  the  test  site  background  energy  setting  and 
helps  account  for  the  effects  of  swell  on  wave  breaking  and  mixing.  It  is 
expected  that  high-energy  environments  will  support  denser  and  deeper 
bubble  populations. 


Sea  surface  temperature  (sst)  significantly  influences  both  the  sup¬ 
ply  and  removal  of  bubbles  in  the  upper  ocean.  Both  surface  tension  and 
viscosity  are  highest  in  cold  water;  this  fact  offers  a  preliminary  explana¬ 
tion  for  reduced  whitecap  coverage  in  high  latitudes  [10].  Water  tempera¬ 
ture  also  controls  gas  solubility.  As  less  air  can  dissolve  in  warmer  water, 
we  expect  longer  bubble  lifetimes  and  hence,  denser  bubble  populations 
with  water  temperature  increases.  CST  surface  temperatures  were  col¬ 
lected  from  0.5-1. 5  m  depth  and  represent  the  typical  ocean  temperature 
within  the  near-surface  bubble  layer. 

Phytoplankton  biomass,  characterized  by  remotely  sensed  chloro¬ 
phyll  concentrations,  will  also  influence  bubble  lifetimes  through  two 
complementary  mechanisms  [11].  First,  surfactants  secreted  by  biologi¬ 
cal  communities  are  known  to  provide  a  stabilizing  coating  to  seawater 
bubbles.  Second,  phytoplankton  blooms  can  supersaturate  the  water  with 
respect  to  oxygen  and  other  atmospheric  gases.  Both  of  these  effects  will 
decrease  the  rate  of  bubble  dissolution  and  promote  larger  bubble  popula¬ 
tions  in  biologically  productive  areas.  This  effect  will  be  most  important 
in  nearshore  and  coastal  waters  where  biological  productivity  is  greatest. 

Monthly  mean  phytoplankton  pigment  (chlorophyll)  concentrations 
for  the  CST  and  Chapman-Harris  sites  were  obtained  from  the  Coastal 
Zone  Color  Scanner  (CZCS)  mission  results.  This  observation  set  covers 
7.5  yr  from  October  1978  through  June  1986.  Global  color  maps  of  mean 
monthly  pigment  concentrations  from  CZCS  can  be  viewed  on  the  World 
Wide  Web  [http://seawifs.gsfc.nasa.gov/SEAWIFS.html].  These  maps 
depict  a  dramatic  seasonal  and  geographic  variability  in  ocean  chloro¬ 
phyll  production  by  marine  phytoplankton.  Driven  by  light  and  nutrient 
availability,  global  phytoplankton  blooms  occur  at  high  latitudes  between 
early  spring  and  late  summer.  Furthermore,  plankton  blooms  are 
observed  throughout  the  year  in  coastal  environments  as  a  result  of 
increased  nutrient  availability  from  coastal  runoff.  As  the  CST  program 
did  not  begin  until  1988,  the  CZCS  pigment  concentrations  can  only  be 
used  to  represent  typical  conditions  at  each  site. 

3.3  A  Simple  Check  of  Hypothesis 

The  dependence  of  gross  site-to-site  differences  in  surface  scatter¬ 
ing  on  the  bubble-related  environmental  descriptors  (Table  I)  can  be 
demonstrated  with  a  few  simple  empirical  tests.  SSSe  values  from  CST 
and  the  Chapman-Harris  model  were  first  averaged  over  three  distinct 
frequency  bands:  0-150  Hz,  400-600  Hz,  and  800-1000  Hz.  The  data 
from  all  runs  (individual  observation  sets)  within  each  CST  experiment 
were  included  in  the  averages  as  well  as  observations  at  all  grazing 
angles  >  10°.  This  gross  averaging  process  was  performed  to  minimize 
uncertainty  due  to  random  measurement  errors,  environmental  patchi¬ 
ness,  short-term  variability,  etc.  Each  experiment  is  now  conveniently 
described  by  the  set  of  mean  prediction  errors,  with  corresponding  base¬ 
line  environmental  descriptors,  listed  in  Table  II.  Note  that  wind  speed 
values  do  not  appear  in  Table  II.  The  objective  is  to  identify  additional 
environmental  factors,  beyond  local  wind  effects,  that  contribute  to  SSS 
variability.  It  is  assumed  that  wind  speed  contributions  are  adequately 
represented  by  the  ONE  model  and  are  hence  already  ‘accounted  for’  in 
the  SSSe  values. 

The  combined  SSSe  values  depend  on  the  three  environmental 
descriptors  in  a  manner  that  agrees  with  physical  intuition.  To  facilitate 
display  of  these  multidimensional  results,  we  will  first  normalize  the  data 
with  respect  to  the  dependence.  Note  that  CST-2  and  CST-4  are  both 
cold  water  experiments  with  close  chi  values,  and  that  CST-5  and  CST-3 
are  both  warm  water  experiments  with  close  chi  values.  The  SSSe  differ¬ 
ences  between  these  experiment  pairs  should  be  dominated  by  hs 
effects.  This  is  verified  by  the  SSSe  vs.  h$  plot  of  Figure  3.  The  differ¬ 
ences  between  SSSe  values  of  each  experiment  pair,  and  at  each 
frequency  range,  are  represented  by  a  series  of  linear  regressions.  Note 
that  all  of  the  regressions  are  of  similar  slope  with  higher  observed  scat¬ 
tering  strengths  (relative  to  ONE  predictions)  as  mean  wave  height 
increases.  The  regression  slopes  were  averaged  within  frequency  bands 


164 


Mean  SSSe  (dB) 

h 

sst 

°C 

chi 

mg/m3 

Source 

ns 

m 

0-150 

400-600 

800  -  1000 

Hz 

Hz 

Hz 

CST  1 

1.8 

10.7 

1.140 

1.1 

-1.3 

-  no  data  - 

CST  2 

2.5 

8.3 

0.516 

4.8 

2.9 

3.2 

CST  3 

1.4 

28.1 

0.045 

-2.3 

-5.3 

-0.1 

CST  4 

3.2 

3.3 

0.320 

2.1 

-1.4 

0.8 

CST  5 

0.6 

23.0 

0.088 

2.6 

2.9 

5.0 

CST  7 

3.3 

5.5 

0.176 

1.0 

-0.7 

0.3 

Chapman- 
Harris  * 

2.7 

18.0 

0.263 

-1.5 

-3.2 

-2.6 

*  Chapman-Harris  hs  and  sst  estimates  obtained  from  U.S.  Navy  Marine 
Climatic  Atlas  CD-ROM. 


Table  II 

Mean  Quantities  Used  for  Investigation  of  Site-to-Site  Differences 


Mean  regression  slopes  for  each  frequency  band  were  used  to  normal¬ 
ize  the  SSSe  averages  in  Table  II  for  surface  wave  effects. 

Figure  3  Influence  of  Background  Wave  Energy  on  Surface  Scatter 
Strength  for  Sites  with  Similar  Temperature  and  Chloro¬ 
phyll  Characteristics 

and  used  to  produce  wave-height  normalized  prediction  errors  (SSSn)  for 
each  of  the  observations  in  Table  2.  The  normalization  is  given  by 

SSSn  =  m{hs^p-hs)  +SSSe  (2) 

where  m  is  the  average  regression  slope  for  each  frequency  band  indi¬ 
cated  on  Figure  3  and  a  reference  wave  height  of  hsREp  -  2.0  m  was 
chosen. 

There  are  now  two  remaining  variables  on  which  SSSn  depends: 
phytoplankton  pigment  concentration  and  ocean  temperature.  Inspection 
of  the  site  environmental  data  in  Table  2  suggests  that  data  can  be  sorted 
into  two  groups:  (1)  a  set  of  cold-water  observations  ( sst  <  11  °C)  that 
includes  CST-1,  CST-2,  CST-4,  and  CST-7;  and  (2)  a  set  of  low-produc¬ 
tivity  observations  ( chi  <  0.3  mg/m3)  that  includes  CST-3,  CST-5,  CST-7, 
and  Chapman-Harris.  Note  that  only  CST-7  falls  into  both  groups. 

The  dependence  of  SSSn  on  pigment  concentration  for  the  cold- 
water  observation  set  appears  in  Figure  4.  The  results  imply  an  important 
role  of  biological  activity  in  surface  scatter.  This  trend  is  strongest  at 
mid-frequencies  (400-600  Hz).  Scattering  level  increases  (represented  by 
decreasing  SSSn)  with  biological  production  are  probably  due  to  higher 
dissolved  gas  levels  from  biological  productivity  and  the  presence  of  bio¬ 
logical  surfactants,  both  of  which  will  extend  the  life  of  ambient  bubbles. 


Phytoplankton  Pigment  Concentration  (mg/m3) 


Figure  4  Influence  of  Biological  Productivity  on  /^-Normalized 
Surface  Scatter  Strength  Prediction  Error  for  the  Cold 
Water  (<  11°C)  Observation  Sites 

The  dependence  of  SSSn  on  sst  for  the  low  pigment  observations 
appears  in  Figure  5.  A  definitive  trend  of  increasing  scatter  (represented 
by  decreasing  SSSn)  with  increasing  temperature  is  observed  at  all  fre¬ 
quencies.  These  results  indicate  an  important  role  of  ambient  ocean  tem¬ 
perature  in  modulating  surface  scatter  levels.  The  influence  of 
temperature  on  bubble  entrainment  and  gas  dissolution  results  in  high 
levels  of  ambient  bubbles  in  warm  water.  Furthermore,  near-surface  strat¬ 
ification  in  warmer  regions  may  effectively  trap  bubbles  near  the  surface 
where  the  scattering  effect  is  most  important. 

The  results  shown  in  Figures  3  through  5  suggest  that  a  linear 
model  for  the  dependence  of  SSSe  on  h  ,  sst ,  and  chi  might  explain  a 
significant  fraction  of  the  site-to-site  variance  in  SSS.  The  method  of 
least-squares  multiple  regression  was  employed  to  test  the  performance 
of  a  linear  model  for  the  surface  scatter  prediction  error 

SSSe  =  ah  +  $sst  +  ychl  +  b ,  (3) 


165 


Figure  5  Influence  of  Ocean  Temperature  on  /^-Normalized  Surface 
Scatter  Strength  Prediction  Error  for  the  Low  Productivity 
(chi  <  0.3  mg/m)  Observation  Sites 


with  fit  coefficients  a ,  p ,  and  y  for  wave  height,  ocean  temperature, 
and  chlorophyll  concentration,  respectively.  For  the  model  calculations, 
the  SSSe  averaging  was  restricted  to  narrow  wind  speed,  frequency,  and 
grazing  angle  bands  so  that  the  results  represent  a  specific  set  of  environ¬ 
mental  and  acoustic  conditions. 

This  preliminary  model  is  quite  successful  in  describing  gross  site- 
to-site  differences  in  SSS.  Typical  results  appear  in  Figure  6.  Here  the 
regression  coefficient  and  the  three  model  fit  coefficients  are  plotted  as  a 
function  of  acoustic  frequency  at  15-25°  grazing  angle  for  the  case  of  8- 
10  m/s  winds.  Note  that  a  high  regression  coefficient  is  obtained  at  all 
frequencies  indicating  that  the  model  explains  a  large  percentage  of  the 
total  variance.  There  is  a  linear  transition  of  all  model  parameters  across 
frequency  with  the  hs  and  sst  fit  coefficients  essentially  constants. 


Frequency  (Hz) 


P 


o 

-0.2 
-0.4 
-0.6 
-0.8 
-1 

100  200  300  400  500  600  700 

Frequency  (Hz) 


—i - 1 — 

sst  Coefficient 


a  -4 
-6 


100  200  300  400  500  600  700 


Frequency  (Hz) 


Frequency  (Hz) 

Figure  6  Multiple  Linear  Regression  Results  for  the  Case  of  U j  q 
8-10  m/s  and  15-25°  Acoustic  Grazing  Angle 


166 


Using  a  and  p  to  normalize  the  data  for  both  wave  height  and 
ocean  temperature  effects,  as  demonstrated  earlier,  allows  a  direct  com¬ 
parison  of  prediction  error  with  phytoplankton  pigment  concentration. 
This  normalization  is  given  by 

SSS  =  a(h  -h  1  +  pOysfr,,^- sst)  +SSSe  ,  (4) 

n  v  SREF  s' 

where  the  reference  values  h  =  2.0  m  and  sstDrr  =  15°Cwere 
Sref  ^f 

chosen.  The  normalized  500  Hz  SSS  prediction  errors  (SSSn)  at  each  site 
for  winds  of  ~10  m/s  appear  in  Figure  7.  A  logarithmic  fit  to  the  data  is 
given  by 

SSSn  =  -[4.8  +  3.61og(cA/)] ,  (5) 

with  regression  coefficient  r  =  0.91 .  The  CST-2  results  are  slightly  farther 
than  two  standard  deviations  from  the  mean  and  are  not  included  in  the 
regression.  This  is  perhaps  due  to  inaccuracy  of  the  monthly  mean  CZCS 
chi  value  in  representing  CST-2  conditions;  inspection  of  the  CZCS  data 
for  this  site  suggests  extreme  spatial  variability  in  chi  at  that  location  and 
time.  The  remaining  data  of  Figure  7  indicate  that  phytoplankton  blooms 
contributed  up  to  5  dB  in  average  SSS  site-to-site  differences  during 
CST.  Extrapolating  these  results  to  nearshore  phytoplankton  pigment 
concentrations  of  50  to  100  mg/m3  indicates  that  SSS  values  can  be 
10  to  12  dB  higher  than  ONE  model  predictions  in  shallow  water 
environments. 


Phytoplankton  Pigment  (mg/m3) 

Figure  7  Dependence  ofNormalized  SSS  Prediction  Error  on 
Phytoplankton  Pigment  Concentration  for  an  Acoustic 
Frequency  of  500  Hz  at  10  m/s  winds,  20°  Grazing  Angle 
and  with  h$  =  2.0  m  and  sst  =  1 5°C 

4.  Conclusions  and  Recommendations 

4. 1  Conclusions 

•  Gross  site-to-site  differences  in  low-frequency  acoustic  bub¬ 
ble  scatter  are  explained  by  seasonal  and  geographic  environ¬ 
mental  factors. 

•  Biological  productivity  increases  acoustic  bubble  scatter  in 
the  open  ocean.  This  is  likely  due  to  increased  dissolved  gas 
levels  and  the  presence  of  biochemical  surfactants,  both  of 
which  will  extend  bubble  lifetimes.  This  effect  will  be  ampli¬ 
fied  in  shallow  water  environments. 

•  Acoustic  bubble  scatter  is  higher  in  warm  water.  This  is  likely 
a  result  of  greater  bubble  supply  due  to  viscosity  and  surface 
tension  effects  and  decreased  gas  solubility  which  acts  to 
extend  bubble  lifetimes.  Increased  temperature  variability 
will  greatly  influence  scattering  strength  statistics  in  shallow 
water  environments. 


•  Acoustic  bubble  scatter,  in  similar  wind  conditions,  increases 
in  higher-energy  environments.  Here  the  background  ocean 
energy  level  was  characterized  by  significant  wave  height 
averaged  over  several  days. 

4.2  Recommendations  for  Continued  Research 

•  Determine  the  relevance  of  these  results  to  other  near-surface 
bubble  observation  sets 

•  Develop  a  near-surface  bubble  model  with  physical  and  bio¬ 
logical  parameters  for  site-to-site  variability 

5.  Acknowledgments 

Valuable  discussions  with  Alan  Brandt,  Fred  Erskine,  David 
Farmer,  Scott  Hayek,  Frank  Henyey,  John  Sweeney,  Eric  Thorsos,  and 
Svein  Vagle  helped  shape  the  hypotheses  leading  to  these  results.  Envi¬ 
ronmental  and  acoustic  data  were  provided  by  Rick  Marsden,  Mike 
Nicholas,  Pete  Ogden,  and  Larry  White.  Mike  Mandelberg  contributed  to 
the  data  assimilation,  organization,  and  preliminary  analyses.  Financial 
support  provided  by  the  Office  of  Naval  Research  (code  320A). 

6.  References 

1.  M.  Nicholas,  P.  M.  Ogden,  and  F.  T.  Erskine,  “Improved  Empirical 
Descriptions  for  Acoustic  Surface  Backscatter  in  the  Ocean,” 
accepted  for  publication  in  IEEE  J.  of  Ocean  Engr.,  1998. 

2.  R.  P.  Chapman  and  J.  H.  Harris,  “Surface  Backscattering  Strengths 
Measured  with  Explosive  Sound  Sources,”  J.  Acoust.  Soc.  Am.  34, 
1592-1597, 1962. 

3.  J.  L.  Hanson,  “Winds,  Waves,  and  Bubbles  at  the  Air-Sea  Bound¬ 
ary,”  Johns  Hopkins  APL  Tech  Dig.,  14,  pp.  200-208, 1993. 

4.  P.  M.  Ogden  and  F.T.  Erskine,  “Surface  Scattering  Measurements 
Using  Broadband  Explosive  Charges  in  the  Critical  Sea  Test  Exper¬ 
iments,”  J.  Acoust.  Soc.  Am.,  95,  pp.  746-761,  1994. 

5.  P.  M.  Ogden  and  F.  T.  Erskine,  “Surface  and  Volume  Scattering 
Measurements  Using  Broadband  Explosive  Charges  in  the  Critical 
Sea  Test  7  Experiment,”  J.  Acoust.  Soc.  Am.,  96,  pp.  2908-2919, 
1994. 

6.  E.  I.  Thorsos,  R.  C.  Gauss,  R.  J.  Soukup,  and  J.  M.  Fialkowski, 
“Measurements  and  Modeling  of  the  Spectral  Character  of  Low 
Frequency,  Low  Grazing  Angle  Surface  Reverberation,”  J.  Acoust. 
Soc.  Am.,  95,  pp.  2828,  1994. 

7  S.  A.  Thorpe,  P.  Bowyer,  and  D.  K.  Woolf,  “Some  Factors  Affecting 
the  Size  Distributions  of  Oceanic  Bubbles,”  J.  Phys.  Oceanogr.,  22, 
pp.  382-389,  1992. 

8.  J.  Wu,  “Variation  of  Whitecap  Coverage  with  Wind  Stress  and 
Water  Temperature,”  J.  Phys.  Oceanogr.,  18,  pp.  1448-1453, 1988. 

9.  P.  A.  Huang,  Y-K  Poon,  and  J.  Wu,  “Temperature  Effects  on  Gener¬ 
ation  and  Entrainment  of  Bubbles  Induced  by  a  Water  Jet,”  J.  Phys. 
Oceanogr. ,  21,  pp.  1602-1605, 1991. 

10.  J.  Wu,  “Individual  Characteristics  of  Whitecaps  and  Volumetric 
Description  of  Bubbles,”  IEEE  J.  Oce.  Engineering,  17(1),  pp.  150- 
158,  1992, 

11.  PS.  Liss  and  R. A.  Duce,  eds..  The  Sea  Surface  and  Global  Change , 
Cambridge  University  Press,  1997. 


167 


A  BOAT-MOUNTED  FOIL  TO  MEASURE  THE  DRAG  PROPERTIES  OF  ANTIFOULING 
COATINGS  APPLIED  TO  STATIC  IMMERSION  PANELS 

Brett  S.  Kovach  Dr.  Geoffrey  Swain 

Ocean  Engineering  Ocean  Engineering 

Florida  Institute  of  Technology  Florida  Institute  of  Technology 

Melbourne,  FL  32901  Melbourne,  FL  32901 

Tel  407  674  8005,  Fax  407  984  8461  Tel  407  674  7129,  Fax  407  984  8461 

Email:  bkovach@fit.edu  Email:  swain@fit.edu 

Abstract  -  Legislation  restricting  the  use  of  biocides  in  antifouling  paints  has  directed  attention  towards  the  development  of  nontoxic 
silicone  foul-release  coatings.  It  has  been  shown  that  these  coatings  will  become  fouled,  but  when  subjected  to  an  external  flow,  the  fouling  can 
be  removed  by  hydrodynamic  forces  generated  at  the  surface.  It  was  decided  to  investigate  the  drag  forces  experienced  by  fouling  communities 
and  determine  the  free  stream  velocities  required  for  foul-release  from  coatings  with  known  barnacle  adhesion  strengths. 

Two  identical  instrumented  foils  were  built  to  accept  standard  (0.254m  x  0.305m)  static  immersion  antifouling  panels  and  to  be  towed 
alongside  a  7m  powerboat.  The  flow  characteristics  of  the  foils  were  determined  by  wind  tunnel  testing.  Fully  fouled  test  panels  are  attached  to 
the  foil  which  is  dragged  through  seawater  at  predetermined  speeds.  During  testing  the  shear  force,  flow  velocity,  and  video  of  the  foul-release 
are  recorded  simultaneously.  The  foul-release  properties  are  then  correlated  with  barnacle  adhesion  shear  strength  according  to  ASTM  5618. 
Preliminary  testing  of  two  silicone  panels  demonstrates  the  relationship  between  barnacle  adhesion  strength,  foul-release,  and  drag. 


I.  INTRODUCTON 

Biofouling  of  ships,  boats  and  other  marine  vehicles  is  controlled 
by  the  use  of  antifouling  (AF)  paints  that  contain  biocides.  Marine 
organisms  increase  the  roughness  of  the  vehicle’s  surface,  which  causes 
an  increase  in  skin  friction  drag.  It  has  been  estimated  that  the  U  S. 
Navy  spends  an  extra  $100  million  annually  in  added  fuel  costs  due  to 
the  effects  of  biofouling  on  their  ships  [1].  This  does  not  include  the 
money  and  time  spent  for  biofouling  control  (AF  coatings,  dry  dockings, 
and  hull  cleanings). 

The  self-polishing  copolymer  organotin  systems  (SPC/TBT) 
provide  the  best  present  day  AF  coating.  These  have  in  excess  of  5 
years  operating  life  and  have  the  advantage  that  they  smooth  with  time, 
hence  reducing  skin  friction  drag  [2].  They  are  also  extremely  toxic  and 
have  been  shown  to  adversely  affect  the  environment  [3].  This  had 
precipitated  environmental  regulations  restricting  their  use  [4]  and  the 
requirement  to  develop  environmentally  friendly  alternatives  [1]. 

At  present  the  most  promising  alternatives  to  the  use  of  biocides 
are  the  non-toxic,  silicone,  and  foul-release  coatings.  The  concept  is  not 
new.  Oils,  greases,  fluorinated  polymers  and  silicones  have  all  been 
tried  as  a  means  to  prevent  the  permanent  attachment  of  fouling 
organisms  [5,  6,  7].  To  date,  the  silicones  have  provided  the  best 
performance,  and  they  are  now  accepted  as  a  viable  alternative  to 
traditional  antifouling  treatments  in  situations  where  there  are 
restrictions  with  regard  to  the  use  of  biocides.  Unfortunately  their 
performance,  in  terms  of  cost,  durability,  longevity  and  antifouling,  still 
does  not  meet  that  of  the  self-polishing  organotin  systems.  Therefore, 
further  research  and  development  are  required  to  better  understand  how 
they  function  and  to  improve  their  performance. 

Foul-release  coatings  work  by  reducing  the  adhesion  strength  of 
organisms  to  the  surface.  They  will  become  fouled  but  the  adhesive 
strength  are  sufficiently  low  that  the  hydrodynamic  forces  generated 
under  flow  will  detach  organisms.  Thus,  the  two  determining  factors 
controlling  foul-release  are  the  hydrodynamic  forces  acting  on  the 
fouling  and  the  adhesion  of  the  fouling  to  the  surface. 

The  purpose  of  this  investigation  was  to  develop  a  system  to 
evaluate  the  performance  of  foul-release  coatings  by  measuring 
biofouling  adhesion  strengths  and  the  hydrodynamic  forces  required  for 
removal. 

Biofouling  Adhesion 

Biofouling  adhesion  is  an  important  measure  of  the  effectiveness 
of  foul-release  coatings.  The  lower  the  adhesion  strength,  the  lower  the 
velocity  needed  for  foul-release.  Barnacles  are  good  candidates  to 
quantify  adhesion  on  surfaces.  A  method  to  measure  their  adhesion 
strength  in  shear  is  now  included  as  an  ASTM  standard  to  evaluate  the 
foul-release  properties  of  coatings  [8].  Barnacle  adhesion  strength  has 
been  measured  on  both  natural  and  artificial  surfaces  [7,  9,  10,  11,  12, 
13].  Furthermore,  it  has  been  shown  that  the  tensile  adhesion  strength  of 
barnacles  is  about  3  times  less  than  the  shear  adhesion  strength  [7,  14], 
This  is  important  when  considering  the  lift  and  drag  forces  imparted  to 
an  organism  by  hydrodynamic  flow. 


Biofouling  Hydrodynamics 

Fouling  organisms  subjected  to  an  external  flow  experience  lift  and 
drag  forces  [15,  16].  The  magnitude  of  the  forces  depends  on  the  size  of 
the  organism  and  the  thickness  of  the  boundary  layer.  Organisms 
extending  through  the  boundary  layer  will  experience  greater  form  drag 
as  compared  to  an  organism  within  the  boundary  layer.  They  act  to 
increase  the  roughness  of  the  surface. 

There  have  been  limited  studies  that  have  examined  the 
hydrodynamic  forces  on  fouling  organisms.  Denny  used  strain  gage 
force  transducers  to  measure  the  lift  and  drag  on  sessile  marine 
organisms  exposed  to  wave  swept  environments.  He  found  lift  and  drag 
coefficients  of  the  acorn  barnacle  to  be  0.5  at  Rex  of  105  [9,  15]. 
Schultz,  who  measured  the  lift  and  drag  of  barnacles  attached  to  a  foil 
towed  through  the  water,  found  similar  coefficients  (Cl=0.45,  Cd=0.5,  at 
Re=105)[16].  These  data  indicate  that  the  total  hydrodynamic  forces 
acting  on  a  barnacle  to  be  almost  90%  lift.  This  means  that  the  total 
hydrodynamic  force  acting  to  remove  a  barnacle  is  pulling  at  64  degrees 
from  the  surface  [17]. 

The  above  analysis,  however,  only  considers  solitary  barnacles. 
Barnacles  often  grow  in  clusters,  which  resemble  that  of  a  mound  with 
taller  barnacles  in  the  center  [18].  This  grouping,  along  with  the 
presence  of  other  fouling  organisms  makes  it  difficult  to  estimate  the 
forces  acting  on  individual  barnacles.  In  general,  the  lift  and  drag  forces 
acting  on  macrofoul ing  have  yet  to  be  defined  due  to  the  complexity  of 
the  flow  over  the  heterogeneous  communities. 

II.  INSTRUMENTED  FOIL 

Two  instrumented  foils  were  designed  and  built  to  hold  standard 
static  immersion  test  panels  (0.254m  x  0.305m)  (See  Figure  1).  One  foil 
acts  as  a  control  using  test  panels  with  known  surface  properties,  and  the 
other  foil  accommodates  the  fouled  panels.  The  foil  sections  are  NACA 
0012  symmetric  airfoils,  0.305m  high  and  1.03  m  long.  They  are 
mounted  to  32mm  diameter  stainless  steel  rods  which  are  attached  to 
either  side  of  an  aluminum  frame  mounted  on  the  rear  of  a  7m  power 
boat.  The  tops  of  the  foils  are  set  0.5m  below  the  surface  of  the  water 
and  each  is  trimmed  to  be  normal  to  the  flow  by  an  electromechanical 
actuator. 

The  test  panels  are  mounted  on  a  portal -type  floating-element  force 
balance  which  is  built  into  the  foil  [19].  There  is  a  3mm  gap  around  the 
test  panel.  The  force  gage  uses  four  strain  gages  connected  in  a  full 
bridge  circuit  which  creates  a  linear  voltage  response  force  gage  that  is 
insensitive  to  moments.  The  advantage  of  using  this  type  of  gage  is  that 
it  can  be  optimized  for  a  specific  range  of  forces  thus  increasing 
sensitivity.  Inside  the  foil  the  dead  space  around  the  force  gage  is  filled 
with  high-density  foam  to  minimize  the  inertial  effects  of  seawater 
circulation  on  the  measurements. 

A  pitot-static  probe  extends  above  the  test  section  to  measure  the 
dynamic  pressure  that  can  be  used  to  determine  the  freestream  flow 
velocity,  U,  using  Bernoulli’s  equation. 


169 


•HoH 


Pitot-Static  Probe  - 


Top  View  Of  Testing  Foil 
Figure  1.  Instrumented  Foil  Drawing 


The  foil  used  to  test  the  foul-release  coatings  has  a  video  camera 
mounted  adjacent  to  the  test  section.  This  enables  real  time  foul-release 
to  be  observed. 

The  foils  are  dragged  through  the  seawater  creating  a  flow  around 
the  test  section  (See  Figure  2).  The  force  gage  measures  the  shear  force 
due  to  the  flow  over  the  test  surface  at  different  velocities.  Each  foil  is 
adjusted  to  keep  the  foil  into  the  flow  of  the  seawater  as  the  boat’s  trim 
angle  changes  with  increasing  speed.  Instrumentation  on  the  boat 
includes  a  datalogger  to  record  the  drag  forces  on  the  panels  and  the  free 
stream  velocity  (See  Figure  3).  A  HI-8  video  recorder  provides  real  time 
images  of  foul-release.  The  video  is  digitized  and  a  real-time  movie  is 
recorded  with  the  force  and  velocity  data  displayed  as  the  fouling  is 
released  from  the  coating. 


Wind  Tunnel  Calibration 

Several  tests  were  run  in  a  low  speed  wind  tunnel  to  characterize 
the  flow  around  the  foil.  This  enabled  errors  to  be  minimized  in  the 
floating-element  region.  Floating-element  force  balances  are  subject  to 
errors  associated  with  the  gap  around  the  test  section  [20,  21,  22,  23]. 
These  include:  flow  through  the  gap  and  circulation  around  the  test 
section,  misalignment  errors  of  the  test  section  height,  pressure  effects 
caused  by  a  normal  pressure  distribution  acting  nonuniformly  across  the 
test  section,  and  nonuniform  flow  patterns  across  the  test  section. 

The  wind  tunnel  tests  included:  flow  visualization  tests  using  tufts 
of  yam  and  titanium  dioxide  streaks,  pressure  profiles  measured  with  the 
gaps  sealed  and  unsealed,  and  boundary  layer  profiles  using  hot  wires 
located  before  and  after  the  test  section  to  examine  the  consistency  of 
the  flow. 

The  flow  visualization  tests  revealed  that  there  was  no  extraneous 
flow  around  the  gaps  and  no  separation  anywhere  on  the  foil.  Static 
pressure  taps  were  used  to  investigate  the  flow  in  the  region  of  the  test 
section  with  the  gaps  sealed  and  unsealed  (See  Figure  4).  The  pressure 
distribution  shows  that  the  gaps  had  no  effect  on  the  flow  and  the  curves 
are  almost  identical.  Notice  the  pressure  distribution  over  the  test 
section  is  nearly  constant.  This  indicated  that  there  is  no  significant 
pressure  gradient  over  the  test  section. 


-400 

-350 

-300 

'e? 

-250 

t 

-200 

L 

-150 

-100 

-50 

0 


- , - 

Test  Section! 

;wB22.3m/s 

•  wl8.0m/s 

i 

^  ~  J3313.4H/S 

-  -  -  G-  -  -  Sealed 

0  0.2  0.4  0.6  0.8  1 

x/c 


Figure  4.  Pressure  Distribution  Across  the  Foil  Test  Section  with 
the  Gap  Sealed  and  Unsealed  (p  is  the  static  pressure,  p*  is  the 
freestream  pressure,  x  is  the  distance  from  the  leading  edge  of  the 
foil,  c  is  the  chord  length  of  the  foil) 

The  boundary  layer  profiles  were  obtained  using  a  hotwire 
anemometer  at  four  locations  before  and  over  the  test  section  (See 
Figure  5).  Because  of  the  error  associated  with  the  determination  of 
boundary  layer  thickness,  the  data  were  nondimensionalized  using  the 
displacement  thickness,  6*.  The  boundary  layer  profiles  are  similar 
over  the  test  section,  and  are  typical  of  turbulent  boundary  layer  profiles 
[24,  25].  The  boundary  layer  thickness  was  approximately  18mm  over 
the  middle  of  the  test  section  at  a  Rex  of  8.3xl05. 

These  tests  suggest  that  if  the  misalignment  of  the  test  section  is 
kept  to  a  minimum,  the  instrumented  foil’s  systematic  errors  should  be 
small. 


of  Fou!  Release 

Figure  3.  Foil  Testing  System 


III.  TEST  PROCEDURE 

The  roughness  of  the  coating  is  first  measured  using  the  British  Marine 
Technology  hull  roughness  analyzer.  The  coatings  are  then  immersed  in 
seawater  at  the  Florida  Institute  of  Technology  Static  Immersion  site. 
The  panels  are  caged  to  prevent  disturbance  by  fish  and  other  grazing 
organisms  that  have  been  shown  to  remove  fouling  from  the  test  panels 
[26].  The  coatings  are  visually  inspected  for  physical  condition  and 
fouling  according  to  ASTM  D3623  Testing  Antifouling  Panels  in 
Shallow  Submergence  [27].  When  sufficient  fouling  has  become 
established  the  panels  are  removed  from  the  water  and  one  side  is 
evaluated  for  fouling  adhesion. 


170 


Figure  5.  Mean  Velocity  Distribution  for  Free  Transition  Over  the 
Length  of  the  Instrumented  Foil  (UAir  =  22.3  m/s,  u  is  the  local 
velocity,  y  is  the  distance  normal  to  the  surface,  5*  is  the 
displacement  thickness) 


Figure  6.  Barnacle  Adhesion  Data 

The  force  data  of  each  test  is  plotted  in  Figure  7.  A  moving 
average  of  ten  data  points  was  used  to  reduce  noise. 


On  the  backside  of  the  test  panel  barnacle,  shear  adhesion 
measurements  are  performed  according  to  ASTM  5618  [8].  This 
method  uses  a  force  gage  to  apply  steadily  increasing  shear  force  to  the 
base  of  a  barnacle.  The  force  for  detachment  is  recorded  and  the  base 
diameter,  d,  of  the  barnacle  measured  in  four  directions.  The  adhesion 
strength  in  shear,  tb,  is  calculated  by  dividing  the  force  for  removal  by 
the  base  area  of  the  barnacle. 


(1) 


The  panel  is  then  attached  to  the  instrumented  foil.  Care  is  taken 
to  ensure  that  the  panel  is  flush  with  the  foil  surface.  The 
instrumentation  is  then  zeroed  with  the  external  devices  off  and  repeated 
with  the  devices  on.  This  step  is  a  check  to  confirm  that  all  the  devices 
are  working  properly.  The  water  temperature  is  recorded  and  a  water 
sample  taken  to  determine  density  and  kinematic  viscosity.  The  foil  is 
then  run  at  4,  8,  12,  16,  and  20  knots  for  a  period  of  one  minute  at  each 
velocity.  During  the  speed  runs,  velocity,  shear  force  and  video  readings 
are  taken  continuously.  At  the  end  of  the  20  knot  run  the  panel  is 
cleaned  back  and  the  runs  at  the  5  speeds  repeated  to  obtain  the  skin 
friction  drag  in  the  clean  condition. 

Testing  is  dependent  on  weather  conditions  permit  (a  flat  sea 
surface ,  <0.3m  chop,  and  wind  <5knots). 


IV.  RESULTS 

Preliminary  data  is  presented  for  two  silicone-based  foul-release 
coatings  with  known  barnacle  adhesion  characteristics  (silicone  A  and 
silicone  B).  Each  coating  was  applied  using  a  draw  down  process  which 
leaves  a  very  smooth  (<  20  micron  roughness)  and  uniform  surface.  The 
coatings  were  allowed  to  foul  for  three  months  (See  Figures  8,  12). 
Each  coating  had  a  thick  (15mm)  accumulation  of  fouling  consisting 
mainly  of  encrusting  bryozoans,  barnacles,  silts,  slimes  and  some 
tubeworms. 

Barnacle  adhesion  data  was  collected  for  Balanus  eburneus  on  the 
backsides  of  the  test  panels  (See  Figure  6).  Each  shear  strength  value 
was  the  average  of  at  least  20  measurements.  Silicone  A  had  the  highest 
barnacle  shear  strength  (7.5xl04Pa),  and  silicone  B  had  a  lower  adhesive 
strength  (2.5x1 04Pa). 

Hydrodynamic  tests  were  run  on  the  front  side  of  each  panel. 
After  each  run  was  complete,  the  last  frame  from  the  video  footage  was 
used  as  the  after  photograph  for  foul  release  (See  Figures  8-15).  It  can 
be  seen  that  no  foul-release  occurred  on  silicone  A.  Foul-release  on 
silicone  B,  however,  started  to  occur  at  4  knots.  This  was  mainly 
encrusting  bryozoans.  At  12  knots  barnacles  started  to  be  removed. 


V.  DISCUSSION 

The  barnacle  shear  adhesion  strength  for  the  silicones  was  much 
less  than  that  found  on  other  surfaces.  For  example,  it  has  been  reported 
that  typical  barnacle  adhesion  strength  (Balanus  eburneus)  on  epoxy  is 
1.5xl06Pa  and  Teflon,  the  lowest  reported  non-silicone  coating,  is 
5.9xl05Pa  [28].  The  silicones  are  an  order  of  magnitude  lower,  clearly 
outperforming  all  other  coatings. 

No  foul-release  occurred  on  silicone  A.  Foul-release,  however,  did 
occur  on  silicone  B  and  it  is  interesting  to  compare  the  observed  foul- 
release  velocities  for  barnacles  to  those  predicted  by  theory.  A  simple 
analysis  was  made  to  relate  the  velocity  for  foul-release  to  the  measured 
barnacle  adhesion  strength.  This  was  made  for  a  solitary  acorn  barnacle 
using  the  following  assumptions:  the  barnacle  was  subjected  to 
freestream  velocity;  the  drag  and  lift  coefficients  were  CL=0.45  and 
Cd=0  5  [9,  15,  16];  the  barnacle  base  diameter,  base  height,  and  top 
diameter  ratios  were  6:4:3  (See  Figure  16).  It  can  be  seen  that  lift  forces 
are  greater  than  drag  forces.  It  has  also  been  shown  that  the  tensile 
adhesion  strengths  are  about  3  times  less  than  the  shear  adhesion 
strengths  [7,  14].  Using  this  information,  theory  would  predict  that  the 
minimum  velocity  to  remove  barnacles  on  silicone  A  is  about  20  knots. 
On  silicone  B,  however,  foul-release  should  occur  at  12  knots. 
Observations  of  the  video  showed  that  barnacles  were  removed  from 
silicone  B  at  12  knots  but  no  barnacles  were  removed  from  silicone  A. 
It  is  apparent  that  silicone  based  systems  are  close  to  providing  a 
hydrodynamically  self-cleaning  surface  for  barnacles. 


Figure  7.  Drag  Force  Data  Comparison 


171 


'■‘if  "■  K: 


Figure  12.  Silicone  B  Before 


Figure  8.  Silicone  A  Before 


Figure  13.  Silicone  B  After  4  knots 


Figure  9.  Silicone  A  After  4  knots 


Figure  14.  Silicone  B  After  8  knots 


Figure  10.  Silicone  A  After  8  knots 


Figure  11.  Silicone  A  After  12  knots 


Figure  15.  Silicone  B  After  12  knots 


Figure  16.  Prediction  of  Foul  Removal  for  a  Single  Acorn  Barnacle 

The  drag  force  measurements  allow  skin  friction  to  be  compared  to 
foul-release.  The  increase  in  drag  force  associated  with  velocity 
increases  measured  on  silicone  A  were  representative  of  a  panel  with 
constant  roughness  (See  Figure  7).  This  was  expected,  since  only  small 
parts  of  the  overlying  fouling  was  seen  to  release.  The  drag  force  data 
for  silicone  B,  however,  shows  a  reduction  in  skin  friction  which 
corresponded  to  foul  release.  At  10  knots,  the  force  data  started  at  the 
higher  point,  and  as  the  fouling  was  released,  the  measured  force 
decreased  at  the  higher  velocities.  The  force  at  the  same  velocities  was 
then  reduced.  This  verified  quantitatively  that  the  coating  was  releasing 
fouling.  For  the  preliminary  data  presented  here,  the  foil  was  only  run  to 
a  maximum  velocity  of  12  knots.  This  was  due  to  strengthening 
requirements  on  the  cross  frame. 

The  instrumented  foil  has  given  us  the  opportunity  to  observe  the 
interaction  between  hydrodynamic  forces  and  foul-release  from  silicone- 
based  coatings.  It  is  gratifying  to  see  that  performance  characteristics  of 
fouling  organisms  with  well  defined  morphology  and  adhesion 
characteristics  parallel  theoretical  predictions.  Future  work  will 
investigate  the  adhesion  strength  and  foul  release  of  other  hard  fouling 
organisms  (oysters/  tubeworms/  limpets)  and  the  more  complex  issues 
involved  with  fouling  communities.  This  should  enable  predictive 
models  to  be  created  that  can  forecast  foul-release  from  ship  hulls. 

VI.  CONCLUSIONS 

The  instrumented  foil  provides  a  method  for  evaluating  the  foul- 
release  properties  of  coatings.  Preliminary  data  has  demonstrated  that 
silicone  foul-release  coatings  with  low  barnacle  adhesion  strengths  will 
hydrodynamically  self-clean.  For  the  barnacle,  Balanus  eburneus ,  there 
is  also  a  good  correlation  between  predicted  and  observed  foul-release 
velocities.  Future  testing  and  analysis  will  further  improve  our 
understanding  of  the  interaction  between  fouling  adhesion, 
hydrodynamic  forces,  and  foul-release. 

VII.  ACKNOWLEDGEMENTS 

This  work  was  supported  by  the  Office  of  Naval  Research 
(N000 14-9 1-J- 1465),  the  Defense  Advanced  Research  Project  Agency, 
and  General  Electric.  Also,  much  appreciation  goes  to  Judith  Stein  and 
Jim  Celia  for  their  continued  assistance.  We  would  also  like  to 
acknowledge  everyone  at  the  Center  for  Corrosion  and  Biofouling 
Control  at  F.I.T.  who  have  contributed  to  this  project. 

VIII.  REFERENCES 

1.  R.  S.  Alberte,  S.  Snyder,  B.  J.  Zahuranec,  and  M.  Whetston. 
“Biofouling  Research  Needs  for  the  United  States  Navy:  Program 
History  and  Goals”,  Biofouling.  6  (2),  1994,  91-95. 

2.  R.  L.  Townsin,  D.  Byrne,  A.  Milne  and  T.  Svensen.  “Speed,  Power 
and  Roughness:  The  Economics  of  Outer  Bottom  Maintenance”,  Trans. 
RINA  123,  1981:459-483. 

3.  M.  A.  Champ  and  W.  C.  Pugh.  “Tributyltin  Antifouling  Paints: 
Introduction  and  Overview”,  Oceans  97  Proc.,  1987:  1296-1308. 


4.  Senate  of  the  United  States.  “Organotin  Antifouling  Paint  Control 
Act  of  1988”,  April  18,  1988. 

5.  J.  D.  Bultman,  J.  R.  Griffith  and  D.  E.  Field.  Fluoropolymer 
Coatings  for  the  Marine  Environment”,  In  Proc.  Symp.  on  Marine 
Biodeterioration ,  eds.  J.D.  Costlow  and  R.C.  Tipper,  Naval  Institute 
Press,  Annapolis,  MD.,  1981,  237-249. 

6.  W.  A.  Finzel  and  H.  L.  Vincent.  “Silicones  in  Coatings”, 
Federation  Series  on  Coatings  Technology ,  March  1996,  Federation  of 
Societies  for  Coatings  Technology. 

7.  G.  W.  Swain,  J.  R.  Griffith,  J.  D.  Bultman  and  H.  L.  Vincent.  “The 
Use  of  Barnacle  Adhesion  Measurements  for  the  Field  Evaluation  of 
Non-toxic  Foul  Release  Surfaces”,  Biofouling.  6  (2),  1992,  105-1 14. 

8.  ASTM  D5618  Standard  Test  Method  for  Measurement  of  Barnacle 
Adhesion  Strength  in  Shear.  American  Standard  for  Testing  and 
Materials,  Paint-Tests  for  Formulated  Products  and  Applied  Coatings. 
6.01, 1994. 

9.  M.  W.  Denny,  T.  L.  Daniel,  and  M.  A.  R.  Koehl.  “Mechanical 
Limits  to  Size  in  Wave-Swept  Organisms”,  Ecological  Monographs  55, 
1985:  69-102. 

10.  G  Walker.  “The  Adhesion  of  Barnacles”,  J.  Adhesion ,  12,  1981:  51- 
58. 

11.  A.  B.  Yule  and  G.  Walker.  “The  Adhesion  of  the  Barnacles,  Balanus 
Balanoides,  to  Slate  Surfaces”,  J.  Marine  Biology ,  1984:  147-156. 

12.  A.  B.  Yule  and  D.  J.  Crisp.  “Adhesion  of  Cypris  Larvae  of  the 
Barnacle,  Balanus  balanoides ,  to  Clean  and  Arthropodin  Treated 
Surface”,  J. Mar. Biol. Ass.  U.K.,  63,  1983,  261-271. 

13.  A.  Becka  and  G.  Loeb.  “Ease  of  Removal  of  Barnacles  from 
Various  Polymeric  Materials”,  Biotechnology  and  Bioengineering , 
XXVI,  1984,  1245-1251. 

14.  K.  Becker.  “Attachment  Strength  and  Colonization  Patterns  of  Two 
Macrofouling  Species  on  Substrata  with  Different  Surface  Tension  (in 
situ  studies)”.  Marine  Biology  117,  1993:  301-309. 

15.  M.  W.  Denny.  “Forces  on  Intertidal  Organisms  due  to  Breaking 
Ocean  Waves:  Design  and  Application  of  a  Telemetry  System”, 
Limnology  and  Oceanography  Vol.  27,  1982:  178-183. 

16.  M.  Schultz.  The  Measurement  of  Hydrodynamic  Forces  on  Fouling 
Organisms.  Florida  Institute  of  Technology,  Master’s  Thesis,  1992. 

17.  M.  W.  Denny.  “  A  Limpet  Shell  Shape  that  Reduces  Drag: 
Laboratory  Demonstration  of  a  Hydrodynamic  Mechanism  and  an 
Exploration  of  its  Effectiveness  in  Nature”,  Can.  J.  Zool.  67,  1989: 
2098-2106. 

18.  S.  Vogel.  Life  in  Moving  Fluids.  Princeton:  Princeton  University 
Press,  1983. 

19.  R.  G.  Dean  and  R.  A.  Dalrymple.  Water  Wave  Mechanics  for 
Engineers  and  Scientists.  Prentice-Hall,  Englewood  Cliffs,  NJ.,  1984. 

20.  J.  M.  Allen.  “Experimental  Study  of  Error  Sources  in  Skin-Friction 
Balance  Measurements”,  J.  Fluids  Eng.  March  1977,  197-204. 

21.  J.  G.  Winter.  “An  Outline  of  the  Techniques  Available  for  the 
Measurement  of  Skin  Friction  in  Turbulent  Boundary  Layers”,  Prog. 
Aerospace  Sci.  Vol.  18,  1977:  1-57. 

22.  S.  Dhawan.  Direct  Measurement  of  Skin  Friction.  California 
Institute  of  Technology,  Ph.D  Dissertation,  1951. 

23.  F.  B.  O’Connell  and  J.  C.  Westkaemper.  “Measurement  of  Errors 
Caused  by  Misalignment  of  Floating  Element  Skin  Friction  Balances:, 
AIAA  Journal,  January  1965:  163-165. 

24.  P.  S.  Klebanoff,  P.  S.  “Characteristics  of  Turbulence  in  a  Boundary 
Layer  with  Zero  Pressure  Gradient”,  NACA  Rep.  1247,  1955. 

25.  H.  Schlichting.  Boundary  Layer  Theory.  New  York:  McGraw-Hill, 
1979. 

26.  G.  W.  Swain,  W.  G.  Nelson,  and  S.  Preedeekanit.  “The  Influence  of 
Biofouling  Adhesion  and  Biotic  Disturbance  on  the  Development  of 
Fouling  Communities  on  Non-Toxic  Surfaces”,  Biofouling  12,  1998: 
257-269. 

27.  ASTM  D3623.  Standard  Test  Method  for  Testing  Antifouling 
Panels  in  Shallow  Submergence.  American  Standard  for  Testing  and 
Materials,  Paint  Products  and  Applications.  6.02,  1994. 

28.  G.  W.  Swain,  M.  P.  Schultz  and  H.  L.  Vincent.  “Shear  Force 
Measurements  of  Barnacle  Adhesion  for  Field  Evaluation  of  Nontoxic 
Foul -Release  Surfaces”,  Recent  Developments  in  Biofouling  Control. 
Oxford  and  IBH  Publishing  Co.,  New  Delhi,  1994. 


173 


THE  EFFECT  OF  BIOFILMS  ON  TURBULENT  BOUNDARY  LAYER  STRUCTURE 


Michael  Schultz 

Division  of  Marine  and  Environmental  Systems 
Ocean  Engineering  Program 
Florida  Institute  of  Technology 
150  West  University  Blvd. 

Melbourne,  FL  32901 
schultzm@winnie.fit.edu 


Geoffrey  Swain 

Division  of  Marine  and  Environmental  Systems 
Ocean  Engineering  Program 
Florida  Institute  of  Technology 
1 50  West  University  Blvd. 
Melbourne,  FL  32901 
swain@fit.edu 


Abstract  -  Practical  application  of  drag  reduction  techniques  on  marine  vehicles  requires  that  the  effects  of  biofouling  be  addressed. 
Materials  exposed  in  the  marine  environment,  even  those  protected  by  antifouling  (AF)  paints,  are  rapidly  colonized  by  microfouling.  In  order  to 
gain  a  better  understanding  of  its  effects,  this  study  compares  the  mean  and  turbulent  boundary  layer  velocity  characteristics  of  surfaces  covered 
with  a  marine  biofilm  with  those  of  a  smooth  surface.  Measurements  were  made  in  a  nominally  zero  pressure  gradient,  boundary  layer  flow  with 
a  two-component  laser  Doppler  velocimeter  (LDV)  at  momentum  thickness  Reynolds  numbers  of  5,500  to  19,000  in  a  recirculating  water  tunnel. 
Profiles  of  the  mean  and  fluctuating  velocity  components,  including  the  longitudinal -plane  turbulent  shear  stress,  were  measured.  An  average 
increase  in  the  skin  friction  coefficient  of  33%  to  187%  was  measured  on  the  fouled  specimens.  The  skin  friction  coefficient  was  found  to  be 
dependent  on  not  only  biofilm  thickness  but  also  its  morphology.  Relative  increases  in  the  longitudinal-plane  shear  stress  as  well  as  the 
longitudinal  and  wall-normal  turbulence  intensities  were  also  noted  for  the  fouled  specimens. 


I.  INTRODUCTION 

Any  attempt  to  make  seawater  drag  reduction  a  reality  must 
contend  with  marine  biofouling.  While  modem  antifouling  (AF) 
systems  are  effective  in  controlling  most  macrofouling  (e.g.  barnacles, 
tubeworms,  macroalgae,  etc.),  they  do  become  colonized  by 
microfouling  organisms  that  produce  a  slime  film.  In  some  cases,  the 
growth  of  this  film  is  stimulated  on  copper  and  organo-tin  AF  paints  [1]. 
The  effect  of  biofilms  on  frictional  resistance  and  turbulent  boundary 
structure  is,  therefore,  of  great  interest  in  predicting  the  hydrodynamic 
performance  of  marine  vehicles. 

A  significant  body  of  research  has  been  devoted  to  studying  the 
effects  of  marine  fouling  on  frictional  resistance.  Much  of  the  early 
work  is  documented  in  Marine  Fouling  and  Its  Prevention  [2].  Most  of 
this  research  addressed  the  effects  of  macrofouling.  However,  studies 
by  Sir  Archibald  Denny  and  researchers  at  Langley  Field  both 
demonstrated  that  slime  films  can  significantly  increase  skin  friction 
resistance. 

An  extensive  investigation  into  the  effects  of  microbial  slime 
layers  on  pipe  flow  was  carried  out  by  Picologlou  et  al.  [3].  They  noted 
that  the  thickness  and  morphology  of  the  slime  film  is  effected  by  the 
hydrodynamic  conditions  to  which  it  is  exposed.  It  was  also  observed 
that  the  viscoelastic  character  of  the  biofilm  combined  with  its 
filamentous  nature  seemed  to  cause  additional  energy  dissipation 
mechanisms  that  led  to  higher  frictional  resistance. 

Lewkowicz  and  Das  [4]  used  uniformly  distributed  nylon  tufts 
attached  to  a  rough  flat  plate  in  order  to  model  a  marine  slime  growth. 
Detailed  profiles  of  both  mean  and  turbulent  flow  velocities  were 
measured.  They  found  that  the  local  shear  stress  coefficient,  cf,  in  a  zero 
pressure  gradient  flow  was  an  average  of  18%  higher  for  the  model 
slime  film  with  a  background  roughness  than  for  the  background 
roughness  alone. 

Loeb  et  al.  [1]  measured  the  influence  of  microbial  biofims  on  the 
hydrodynamic  drag  of  rotating  discs  Their  data  showed  an  increase  in 
frictional  resistance  of  10  to  20%  due  to  slime  films.  Pre-roughened 
discs  were  also  tested  both  before  and  after  exposure  to  biofilm 
formation,  since  it  was  hypothesized  that  a  thin  slime  film  might  reduce 
the  drag  of  rough  surfaces  by  effectively  smoothing  them.  This  was  not 
the  case,  as  an  increase  in  frictional  drag  of  10%  was  measured  for  the 
fouled,  rough  disc. 

Lewthwaite  et  al.  [5]  conducted  an  experiment  in  which  velocity 
profiles  were  taken  on  a  vessel  at  sea  over  a  two  year  period.  In  this 
study,  a  23  m  fleet  tender  was  operated  in  temperate  waters  and  was 
subjected  to  marine  biofouling  buildup.  A  pitot-static  tube  traverse 
system  was  outfitted  on  the  ship  through  several  sea  tubes  located  along 
the  length  of  the.hull.  From  the  velocity  profiles,  the  local  skin  friction 
coefficient,  cf,  was  found.  They  measured  an  increase  in  cf  from  0.0023 
to  0.0042  over  the  exposure  period.  A  corresponding  15%  reduction  in 
ship  speed  was  observed.  There  were  no  quantitative  measurements 
made  on  the  fouling  settlement  on  the  hull.  However,  it  was  noted  that 
when  the  vessel  was  pulled,  it  was  virtually  free  of  hard  fouling  and 
macroalgae.  It  was  covered  with  a  dense  slime  film  estimated  to 
be  1  mm  thick.  When  the  hull  was  cleaned  and  returned  to  the  water, 
measurements  confirmed  that  cf  returned  approximately  to  its  clean 
hull  value. 


Haslbeck  and  Bohlander  [6]  conducted  a  full-scale  ship  trial  in 
order  to  better  quantify  the  effect  of  microbial  biofilms  on  ship  drag.  In 
their  investigation,  the  USS  BREWTON,  a  Knox  class  frigate,  was 
instrumented  to  measure  shaft  horsepower  and  ship  speed  over  a  mile 
course.  The  ship,  which  was  coated  with  an  ablative  antifouling  paint 
containing  both  cuprous  oxide  and  tributyltin  oxide,  had  been  subjected 
to  fouling  in  Pearl  Harbor,  Hawaii  for  22  months.  An  initial  hull 
inspection  by  divers  indicated  the  presence  of  a  microbial  biofilm  but 
little  hard  fouling.  Ship  power  trials  over  a  mile  course  were  made.  The 
USS  BREWTON  then  returned  to  port  to  undergo  hull  cleaning. 
Another  ship  power  trial  was  then  conducted.  It  was  found  that  there 
was  as  much  as  an  18%  decrease  in  the  required  shaft  horsepower  to 
propel  the  ship  at  same  speed  after  the  microbial  biofilm  was  removed. 

While  it  can  be  concluded  that  biofilms  have  the  potential  to 
markedly  increase  ship  drag,  the  authors  are  unaware  of  any  study  in 
which  the  mean  and  turbulence  structure  of  boundary  layer  flows  over 
natural  marine  biofilms  were  measured.  This  information  is  vital  in  the 
understanding  and  prediction  of  flows  over  fouled  hulls.  The  goal  of  the 
present  research  is  to  address  these  issues. 

II.  EXPERIMENTAL  FACILITIES  AND  METHOD 

The  experimental  work  was  carried  out  at  the  Harbor  Branch 
Oceanographic  Institution  (HBOI)  water  tunnel  [7].  The  tunnel  is  2.44 
m  in  height,  8.53  m  in  length,  and  1.22  m  in  width  and  is  constructed  of 
mild  steel  coated  with  marine  polyamide  epoxy.  The  test  section  is  0.61 
m  by  0.61  m  and  is  2.54  m  in  length.  The  contraction  ratio  in  the  tunnel 
is  4  to  1.  Flow  management  devices  include  turning  vanes  placed  in  the 
tunnel  comers  and  a  polycarbonate  honeycomb  flow  straightener  in  the 
entrance  to  the  contraction  section.  The  resulting  ffee-stream  turbulence 
intensity  in  the  test  section  ranged  from  2.5  %  to  3.5  %  in  the  velocity 
range  that  was  used  in  the  present  experiment.  The  tunnel  is  powered  by 
a  7.5L,  V8  internal  combustion  engine  that  turns  a  0.81  m  diameter, 
three  bladed,  brass  propeller.  The  engine  is  rated  at  167  kW  at  4400  rpm 
and  484  N-m  of  torque  at  2800  rpm.  The  ffee-stream  velocities  in  the 
test  section  can  be  adjusted  from  1.2  m/s  to  4.0  m/s.  The  velocity  can  be 
maintained  to  within  0.05  m/s  throughout  the  range.  A  hinged  glass 
window,  1.22  m  in  length  located  in  the  tunnel’s  test  section,  allows 
viewing  of  experiments  as  well  as  access  to  the  test  section. 

The  test  matrix  consisted  of  five  specimens.  Two  smooth, 
unfouled  surfaces  were  used  as  controls.  The  remaining  three  specimens 
were  subjected  to  biofilm  build  up  for  6,  14,  and  17  days.  In  order  to 
look  at  boundary  layer  development  and  the  effect  of  varying  Reynolds 
number,  velocity  profiles  were  taken  at  three  downstream  positions.  The 
profiles  were  taken  at  1.13  m,  1.43  m,  and  1.73  m  from  the  leading  edge 
and  at  three  ffee-stream  velocities  (nominally  1.5  m/s,  2.25  m/s,  and  3.0 
m/s).  Velocity  profiles  consisted  of  about  50  logarithmically  spaced 
sampling  locations  across  the  boundary  layer. 

The  test  specimens  were  mounted  in  a  splitter  plate  type  fixture 
that  was  inserted  into  the  tunnel  and  generated  a  fully  developed, 
turbulent  boundary  layer.  The  plate  was  0.58  m  in  width,  2.06  m  in 
length,  and  54  mm  thick.  It  was  constructed  of  polyvinylchloride  (PVC) 
and  stainless  steel  and  was  mounted  horizontally  in  the  tunnel’s  test 
section.  The  leading  edge  of  the  test  plate  was  shaped  to  mimic  the 
forward  portion  of  aNACA  0012-64  air  foil.  The  forward  most  280  mm 


175 


of  plate  was  covered  with  #36  grit  sandpaper  to  hasten  development  of  a 
turbulent  boundary  layer  and  to  artificially  thicken  it. 

The  top  of  the  boundary  layer  plate  was  mounted  370  mm  from  the 
top  tunnel  wall  and  was  held  in  place  with  four,  38  mm  diameter, 
stainless  steel  rods  that  allowed  slight  adjustments  to  the  ffee-stream 
pressure  gradient.  The  plate  had  a  removable  section  to  facilitate 
interchanging  of  test  specimens.  The  test  specimens  were  fabricated 
from  cast  acrylic  sheet.  Each  specimen  measured  558  mm  in  width, 
1 168  mm  in  length,  and  12.7  mm  in  thickness.  The  forward  edge  of  the 
specimen  was  located  710  mm  from  the  leading  edge  of  the  plate. 

Mean  velocity,  turbulence  intensities,  and  Reynolds  shear  stress 
measurements  were  made  using  a  two-component,  fiber-optic  laser 
Doppler  velocimeter  (LDV)  system.  A  5W  Coherent  Innova  Model  70A 
Argon-ion  laser  served  as  the  light  source.  The  remainder  of  the 
integrated  system  was  manufactured  by  TSI.  This  included  a  Model 
9201  ColorBurst®  beam  separator,  Model  9271  fiber-optic  couplers,  a 
Model  9832  fiber-optic  probe,  a  Model  9230  multi-color  receiver,  and 
an  IFA  655  digital  burst  correlator  signal  processor.  All  components 
were  controlled  by  a  personal  computer  using  TSI’s  FIND- Windows® 
software.  The  probe  was  fitted  with  a  TSI  Model  9253  lens.  The  focal 
length  of  the  lens  was  349.8  mm.  The  resulting  probe  volume  diameter 
was  90  pm,  and  its  length  was  1.3  mm.  The  probe  was  mounted  on  an 
AMPRO  System  1618,  three-axis  traverse  unit.  The  traverse  allowed 
the  position  of  the  probe  to  be  maintained  to  ±  l‘pm  in  all  directions. 

In  order  to  facilitate  two-component,  near  wall  measurements,  the 
probe  was  tilted  downwards  at  an  angle  of  4°  with  the  horizontal  and 
was  rotated  45°  about  its  axis.  This  minimized  bias  error  due  to 
introduction  of  the  w’  fluctuations  into  the  v’  measurements.  Using  this 
setup,  measurements  as  close  as  40  pm  to  the  wall  were  made.  Velocity 
measurements  were  conducted  in  coincidence  mode  with  10,000  random 
samples  per  location.  Doppler  bursts  for  the  two  channels  were  required 
to  fall  within  a  set  coincidence  window  or  the  sample  was  rejected.  This 
coincidence  window  was  set  at  50  ps,  30  ps,  and  20  ps  for  the  1.5  m/s, 
2.25  m/s,  and  3.0  m/s  flows,  respectively. 

The  biofilms  on  the  fouled  test  specimens  were  grown  at  the  HBOI 
Aquaculture  facility.  Water  from  the  Indian  River  Lagoon  was 
continuously  pumped  through  a  sand  filtration  system  and  into  three 
grow-out  tanks.  The  tanks  were  2.3  m  in  length,  0.9  m  in  width,  and 
0.55  m  in  height.  A  valve  at  one  end  of  the  tank  allowed  seawater  to 
flow  in.  Each  tank  was  fitted  with  a  stand-pipe  that  maintained  the 
water  depth  at  130  mm  and  allowed  water  to  drain.  One  test  specimen 
was  placed  face  up  on  the  bottom  of  each  tank  and  allowed  to  foul  over  a 
period  of  days.  During  these  experiments,  the  salinity  of  the  water  in  the 
tanks  ranged  from  20  ppt  to  36  ppt.  The  water  temperature  ranged  from 
25°  C  to  35°  C.  The  thickness  of  the  biofilm  on  the  test  specimens  was 
determined  using  a  Gardco  comb-type  wet  film  paint  thickness  (WFT) 
gauge.  It  had  a  thickness  measurement  range  of  25  pm  to  2032  pm  with 
a  resolution  of  25  pm  in  the  25  pm  to  305  pm  range.  Sixty  thickness 
measurements  were  made  both  before  and  after  subjecting  each  biofilm 
to  hydrodynamic  testing  in  the  water  tunnel.  These  were  made  on  the 
damp  biofilm  in  air.  After  hydrodynamic  testing,  a  sample  of  the 
biofilm  was  taken  and  examined  under  a  compound  microscope  to 
identify  the  organisms  present.  For  a  more  detailed  description  of  the 
experimental  setup,  the  reader  may  refer  to  [8]. 

The  mean  and  turbulence  statistics  for  each  measurement  location 
were  found  using  the  basic  statistical  package  in  the  aforementioned 
FIND- Windows®  software.  These  results  were  then  used  to  calculate  the 
boundary  layer  parameters.  In  the  present  investigation,  three  methods 
were  used  to  determine  the  local  skin  friction  coefficient,  cf,  for  the 
smooth  walls  and  two  methods  were  used  for  the  fouled  walls. 

For  the  smooth  specimens,  cf  was  found  using  Bradshaw’s  method, 
the  sublayer  slope  method,  and  the  Reynolds  stress  method.  The  details 
of  Bradshaw’s  method,  which  is  based  on  inner  layer  similarity,  are 
given  in  references  [9,10].  Log-law  reference  values  of  y+=100  and 
U+=  16.24  were  used  in  the  present  study.  The  sublayer  slope  method 
simply  involves  finding  the  velocity  gradient  in  the  linear  sublayer  to 
obtain  the  wall  shear  stress.  The  final  method  that  was  used  to  find  cf  on 
the  smooth  specimens  was  the  Reynolds  stress  method,  which  is  detailed 
in  [11].  For  the  fouled  plates,  the  analysis  was  a  bit  more  complex. 
First,  before  Cf  could  be  found,  the  location  of  the  virtual  origin  (y+e=0) 
had  to  be  determined.  An  adaptation  of  the  method  proposed  by  Perry 
and  Joubert  [12]  for  the  determination  of  the  virtual  origin  on  rough 


surfaces  was  used.  The  log-law  slope  method,  which  is  detailed  in  [5], 
and  the  Reynolds  stress  method  were  then  used  to  find  cf. 

III.  RESULTS  AND  DISCUSSION 

In  order  to  reference  each  of  the  test  samples,  an  alpha-numeric 
code  is  used.  The  first  letter  represents  the  test  specimen  type.  “S”  is  a 
smooth  plate.  “F”  is  fouled  plate.  The  first  number  indicates  the 
replicate  number.  To  further  facilitate  the  reference  of  individual 
velocity  profiles,  an  additional  letter  and  number  are  added  to  the 
previous  designation.  To  indicate  the  downstream  distance  from  the 
leading  edge,  x,  the  letters  A-C  are  used.  “A”  represents  the  1.13  m 
profiling  station,  “B”  the  1.43  m  station,  and  “C”  the  1.73  m  station. 
The  nominal  ffee-stream  velocity  is  indicated  with  the  numbers  1-3. 
The  number  “1”  represents  1.5  m/s,  “2”  represents  2.25  m/s,  and  “3” 
represents  3.0  m/s.  For  example,  “S2B3”  refers  to  a  profile  made  on 
smooth  specimen  replicate  2  at  x  =1.43  m  and  Ue  =  3.0  m/s. 

The  biofilm  on  each  of  the  three  fouled  plates  was  characterized  by 
visual  assessment  both  before  and  after  hydrodynamic  testing.  The 
results  of  this  evaluation  are  shown  in  table  I.  Examination  of  the 
biofilm  with  the  aid  of  a  microscope  showed  that  the  film  on  FI  was 
composed  mainly  of  extracellular  polymer  substances  (EPS),  blue-green 
algae  (Anabaina  oscillarioides),  and  marine  diatoms  (dominated  by 
Melosira  spp.).  F2  was  fouled  with  EPS,  green  algae  {Enteromorpha 
spp.),  and  marine  diatoms  (dominated  by  Melosira  spp  and 
Thallasiothrix  spp.).  The  biofilm  on  F3  was  almost  entirely  composed 
of  filamentous  green  algae  {Enteromorpha  spp.).  The  overall  mean 
thickness  (±  SD)  of  the  biofilms  based  on  60  individual  measurements 
was  found.  Before  hydrodynamic  testing,  the  thicknesses  of  FI,  F2,  and 
F3  were  347  pm  ±  69  pm,  163  pm  ±  41  pm,  and  310  pm  ±  100  pm, 
respectively.  After  hydrodynamic  testing,  the  thicknesses  of  FI,  F2,  and 
F3  were  74  pm  ±  46  pm,  126  pm  ±  27  pm,  and  344  pm  ±  145  pm, 
respectively. 

The  mean  boundary  layer  velocity  profiles  for  the  three  fouled 
specimens  were  affected  to  varying  degrees  (See  Figure  1).  The  profiles 
for  F3,  the  biofilm  dominated  by  filamentous  green  algae,  were 
generally  shifted  the  most  from  the  smooth  curve.  Biofilms  FI  and  F2, 
which  consisted  of  a  slime  film,  had  less  effect  on  the  profile.  Figure  2 
shows  the  law  of  the  wall  profiles  of  SI  and  the  fouled  specimens  as 
they  develop  down  the  plate.  The  downward  velocity  shift,  AU+,  can  be 
noted  on  all  the  fouled  plate  profiles.  The  magnitude  of  the  shift  varied 
greatly  with  specimen  as  well  as  the  downstream  position.  The  large 
variation  in  AU+  with  x  may  have  been  due,  in  large  degree,  to  the 
heterogeneity  of  the  biofilm  over  the  specimen  surface.  One  can  note 
that  the  smooth  specimen  wakes  are  lower  than  is  typical  for  a  zero 
pressure  gradient,  fully  developed  boundary  layer.  This  was  due  to  the 
relatively  high  background  turbulence  levels  (2.5%  -  3.5%)  in  the  test 
section.  Hancock  and  Bradshaw  [13]  have  shown  that  ffee-stream 
turbulence  of  this  magnitude  can  alter  outer  layer  structure  and  depress 
the  wake.  Also  of  note  is  the  variability  in  the  wake  on  the  fouled 
specimens.  There  was,  however,  no  statistically  significant  trend  of 
increase  or  decrease  in  n  for  the  fouled  specimens. 

The  basic  boundary  layer  parameters  calculated  for  the  smooth  and 
fouled  test  plates  are  shown  in  table  II.  To  determine  if  the  differences 
seen  were  significant  within  the  experimental  uncertainty,  statistical  tests 
were  conducted.  These  consisted  of  two-way  analyses  of  variance 
(ANOVAs)  with  specimen  and  Rex  as  factors.  In  cases  where  the 
ANOVA  indicated  significant  differences  for  one  of  the  factors,  multiple 
pairwise  comparisons  were  run  using  Tukey’s  test.  The  significance 
level  for  all  the  tests  was  set  at  a  =  0.05  (95%  confidence). 

The  ANOVA  carried  out  on  the  boundary  layer  thickness  results 
showed  that  neither  specimen  nor  Rex  had  a  significant  effect.  This  may 
have  been  due  to  the  high  degree  of  variability  in  8.  For  example,  the 
absolute  deviation  of  8  between  the  smooth  plate  replicates  ranged  from 
2.0%  to  13.2%  of  the  mean  for  the  9  profiles  and  averaged  7.1%.  This 
was  due  in  part  to  the  inability  to  control  Ue  more  precisely  in  the  water 
tunnel.  Thole  and  Boggart  [14]  have  also  observed  that  high  ffee-stream 
turbulence  levels  increase  the  uncertainty  in  finding  8.  Results  from 
Lewkowicz  and  Das  [4],  on  a  simulated  biofilm  roughness,  showed  that 
biofilms  had  a  thickening  effect  on  the  boundary  layer  of  25%  to  30% 
above  that  of  a  background  roughness. 

The  presence  of  the  biofilm  did  have  a  significant  effect  on  the 
boundary  layer  displacement  thickness,  8*.  The  ANOVA  indicated  an 
effect  of  specimen  as  well  as  Rex.  Multiple  pairwise  comparisons 


176 


indicated  a  significant  increase  in  8*  over  that  of  the  smooth  specimens 
as  a  result  of  the  biofilm  for  all  the  fouled  specimens  tested.  Differences 
between  all  specimens  were  found  with  the  exception  of  SI  versus  S2 
(the  controls)  and  FI  versus  F2.  The  biofilm  also  had  an  effect  on  the 
momentum  thickness  of  the  boundary  layer,  0.  The  ANOVA  again 
showed  significant  differences  with  specimen  as  well  as  Rex.  Pairwise 
comparisons  indicated  a  significant  increase  in  0,  resulted  from  the 
fouling.  The  only  exception  was  F2,  which  was  not  significantly 
different  than  SI.  Differences  were  also  found  between  all  the 
remaining  specimens  except  SI  versus  S2  and  FI  versus  F2. 

The  shape  factor,  H,  was  significantly  increased  by  the  presence  of 
the  biofilm  as  well.  This  suggests  that  the  mass  flux  is  altered  to  a 
higher  degree  than  the  momentum  flux  for  these  flows.  The  ANOVA 
indicated  differences  due  to  both  specimen  and  Rex.  Multiple  pairwise 
comparisons  showed  differences  for  all  the  specimens  with  the  exception 
of  SI  versus  S2  and  FI  versus  F2.  The  average  increase  in  H  with 
fouling  was  7.0%  for  FI,  4.8%  for  F2,  and  12.6%  for  F3  compared  to  the 
smooth  plates.  The  increase  in  H  with  the  presence  of  fouling  was  also 
seen  by  Lewkowicz  and  Das  [4]  in  flow  over  a  model  biofilm  and  is  a 
typical  surface  roughness  effect.  The  Clauser  length.  A,  was  not 
significantly  affected  by  the  presence  of  the  biofilm.  There  was  a  higher 
degree  of  variability  for  the  fouled  specimens,  however.  It  seems  that 
the  variability  was  related  to  the  fouling  extent,  as  F3,  the  most  heavily 
fouled  specimen,  had  the  largest  variability. 

The  wall  shear  stress  results  for  the  smooth  and  fouled  specimen 
profiles  are  shown  in  tables  III  and  IV.  The  cf  results  for  the  two 
replicate  smooth  plates  were  compared  using  paired  t-tests.  No 
significant  differences  between  the  replicates  were  found  for  the  three  Cf 
determination  methods.  The  Cf  results  obtained  for  each  of  the  smooth 
profiles  were  then  pooled  by  Cf  method  and  a  two-way  ANOVA  was 
carried  out.  In  order  to  compare  the  present  results  to  previous  results, 
Cf’s  predicted  by  Falkner’s  fit  of  Cf  versus  Ree  were  also  included  [15]. 
It  is  given  by  the  following  [1]: 


Cf 


0.013 

Ree‘ 


(1) 


The  two  factors  for  the  ANOVA  were  Cf  method  and  Rex.  Since 
the  data  were  not  normally  distributed  and  attempts  to  transform  to 
obtain  normality  failed,  Friedman’s  test,  a  non-parametric  two-way 
ANOVA,  was  carried  out.  This  indicated  that  there  was  statistical 
agreement  between  all  the  cf  methods  and  Falkner’s  formula.  The  cf 
values  obtained  using  Bradshaw’s  method  were  chosen  to  serve  as  a 
baseline  with  which  to  compare  the  fouled  plate  results.  This  was 
because  of  the  lack  of  sufficient  sublayer  points  in  two  smooth  plate 
profiles  and  because  of  the  larger  scatter  in  the  results  obtained  using  the 
Reynolds  stress  method. 

Of  particular  interest  from  a  practical  perspective  was  the  effect  of 
the  biofilms  on  the  wall  shear  stress  coefficient.  Both  the  log-law  slope 
method  and  the  Reynolds  stress  method  showed  increases  in  cf  for  the 
fouled  plates.  The  increase  varied  widely,  however.  The  cf  values  for 
the  fouled  plates  found  using  the  Reynolds  stress  method  ranged  from 
57%  less  than  to  65%  greater  than  the  values  obtained  by  the  log-law 
slope  method.  In  order  to  statistically  compare  the  results  from  the  two 
methods,  a  signed  rank  test  (a=0.05)  was  used.  No  statistically 
significant  difference  between  the  methods  was  found.  It  was  decided  to 
use  the  log-law  slope  method  for  comparison  with  the  smooth  plate 
results. 

In  order  to  observe  the  change  in  cf  for  the  fouled  specimen  results, 
comparison  with  the  smooth  plate  results  at  the  same  Re0  was  carried 
out.  Since  Ree  was  increased  significantly  for  the  fouled  specimens,  a 
profile  by  profile  comparison  with  the  controls  was  not  feasible.  For  this 
reason,  the  cf’s  for  the  fouled  plates  were  compared  to  the  following 
equation  that  was  fit  to  the  present  smooth  plate  results  found  using 
Bradshaw’s  method  [2]: 


cf  = 


0.0105 
Re  e  0,14 


(2) 


All  the  fouled  plates  had  increased  cf  values  compared  to  the 
smooth  condition.  Fouled  specimens  FI,  F2,  and  F3  showed  increases 
in  Cf  of  8%  to  133%,  3%  to  70%,  and  1 1%  to  369%,  respectively.  The 
average  increase  was  68%  for  FI,  33%  for  F2,  and  187%  for  F3.  It  has 


been  postulated  that  thin  biofilms  may  reduce  drag  by  acting  as  a 
compliant  surface.  This  effect  was  not  observed  in  the  present  study, 
however. 

The  variation  in  cf  was  greatly  increased  for  the  fouled  plates.  To 
put  this  in  better  perspective,  SI  had  a  mean  cf  (xlO3)  (±  SD)  of  2.91  ± 
0.13,  and  S2  had  a  mean  Cf  (xlO3)  of  2.92  ±0.16.  Fouled  plates  FI,  F2, 
and  F3  had  mean  Cf  (xlO3)  values  of  4.83  ±  1.59, 3.85  ±  0.78,  and  8.12  ± 
4.15,  respectively.  A  Kruskal-Wallis  ANOVA  on  ranks  and  Student- 
Newman-Keuls  pairwise  comparisons  indicated  a  significant  difference 
between  all  of  the  smooth  panels  and  the  fouled  panels  with  the 
exception  of  SI  versus  S2  (the  controls)  and  FI  versus  F2.  The  Cf  results 
for  the  fouled  specimens  show  that  not  only  biofilm  thickness  but  also 
composition  and  morphology  are  important  in  determining  the  wall 
shear  stress.  The  average  increase  in  cf  for  slime  films  with  a  mean 
thickness  before  testing  of  163  pm  and  347  pm  was  33%  and  68%, 
respectively.  The  increase  in  cf  for  a  surface  dominated  by  filamentous 
green  algae  (Enteromorpha  spp.)  with  a  mean  thickness  of  310  pm 
averaged  1 87%.  It  seems  that  the  flapping  motions  of  filamentous  algae 
can  remove  larger  amounts  of  momentum  from  the  mean  flow  than  non- 
filamentous  films  of  the  same  thickness. 

Much  of  the  variability  within  Cf  results  on  the  same  specimen  can 
be  attributed  to  the  complex  and  dynamic  nature  of  the  biofilm.  First,  it 
is  not  homogenous  and  uniform,  but  is  splotchy.  This  was  especially 
true  for  F3.  Biofilms  may  be  thought  of  as  a  constantly  varying 
streamwise  roughness,  not  only  in  height  but  also  in  morphology.  This 
brings  the  underlying  assumption  of  boundary  layer  equilibrium,  which 
is  inherent  to  wall  similarity  methods,  into  question.  A  study  by 
Andreopoulos  and  Wood  [16],  in  flows  subjected  to  a  short  length  of 
surface  roughness,  has  found  that  boundary  layers  do  not  fully  recover  to 
a  self-preserving  state  for  large  downstream  distances  (>558).  Work  by 
Antonia  and  Luxton  [17]  has  shown,  that  on  k-type  surface  roughness, 
the  boundary  layer  adjusts  rather  slowly  to  a  step  change  from  rough  to 
smooth  surface  condition.  Antonia  and  Luxton  [18]  have  also  observed 
that  flows  moving  from  smooth  to  rough  surfaces  adjust  much  more 
rapidly  (~  108).  Further  complicating  the  present  situation  was  removal 
of  the  biofilm  from  the  surface  due  to  shear  stress  over  the  duration  of 
the  experiment. 

Some  of  the  variation  in  the  cf  results  for  the  fouled  plates  may 
also  be  attributed  to  the  method  itself.  Using  Bradshaw’s  method  for 
smooth  plate  flows,  there  is  only  a  single  free  parameter,  cf.  Additional 
parameters,  AlF  and  e,  enter  the  analysis  for  rough  wall  flows.  While 
the  extra  two  degrees  of  freedom  can  produce  a  “better”  log-law  fit  in  a 
statistical  sense,  they  can  also  lead  to  increased  error  in  cf.  Natural 
scatter  in  the  inner  region  data  due  to  the  influence  of  roughness 
elements  may  be  masked  in  producing  a  least-squares  fit  of  the  log-law. 
Archary  a  and  Escudier  [19]  report  that  the  use  of  rough  wall  analyses 
with  AU+  and  e  not  identically  set  to  zero  on  smooth  wall  data  produced 
Cf’s  with  an  average  error  of  12%. 

Research  by  Perry  et  al.  [20],  Bandyopadhyay  [21],  Ligrani  and 
Moffat  [22]  and  others  has  furthered  the  understanding  of  boundary 
layer  flows  over  k-type  and  d-type  roughnesses.  Even  in  these  “regular” 
roughness  arrangements,  the  determination  of  cf  can  be  problematic.  In 
general,  an  independent  method  for  finding  Cf  is  desirable.  But,  the 
common  methods  used  on  “regular”  roughnesses,  such  as  a  floating 
element  force  balance  or  pressure  taps,  are  not  generally  feasible  on 
biofilms  and  could  not  be  used  in  the  present  investigation. 

Granville’s  method  [23]  of  finding  the  velocity  shift,  AU+,  at  the 
same  value  of  Re5*  resulted  in  AU+  ranging  from  2.18  to  9.60,  0.54  to 
6.19,  and  1.81  to  14.98  for  FI,  F2,  and  F3,  respectively.  Plots  of  AU+ 
versus  k+  for  the  three  fouled  specimens  did  not  show  a  good  collapse  to 
a  Colebrook  or  Nikuradse  type  roughness  function  (see  Figure  3).  There 
was  a  high  degree  of  scatter  in  these  plots,  although  there  was  a 
significant  trend  of  increasing  AU+  with  increasing  k+.  This  may  be  due 
to  the  use  of  an  inappropriate  roughness  length  scale.  The  scale  used 
was  the  mean  biofilm  height  before  testing.  Attempts  to  incorporate 
other  scaling  lengths  including  the  mean  biofilm  height  after  testing,  the 
r.m.s.  biofilm  roughness,  the  boundary  layer  thickness,  and  the  origin 
offset  did  not  lead  to  any  better  collapse  than  the  mean  roughness  alone. 
The  equivalent  sand  roughness,  ks,  was  calculated  for  each  fouled 
profile.  It  was  of  interest  to  see  if  a  relationship  existed  between  the 
measured  mean  roughness  height,  k,  and  ks.  However,  the  two 
parameters  were  poorly  correlated.  It  can  be  concluded  that  the  mean 
roughness  height  of  the  biofilm  measured  with  a  paint  wet  film  thickness 


177 


gauge,  by  itself,  does  not  provide  an  appropriate  roughness  scaling 
factor.  Picologlou  et  al.  [3]  indicated  a  better  correlation  between  ks  and 
the  mean  biofilm  height  in  their  pipe  flow  experiments.  They  also  had 
difficulty  in  finding  a  functional  dependency  between  the  two,  however. 

The  inability  to  scale  the  roughness  effects  using  a  single  length 
scale  parameter  is  not  surprising,  especially  for  a  surface  as  complex  as  a 
marine  biofilm.  Patel  and  Yoon  [24]  note  that  at  present  there  is  no 
theoretical  way  to  predict  the  roughness  function  based  on  roughness 
configuration  alone,  and  a  single  length  parameter  is  usually  not 
sufficient  to  characterize  the  surface.  A  profile  of  the  surface  might 
allow  a  more  meaningful  parameter  to  be  obtained.  Since  the  biofilm  is 
compliant,  changes  in  the  profile  would  occur  with  time  and  flow 
conditions.  Surface  topography  obtained  using  a  laser  interferometer,  as 
was  used  by  Lee  et  al.  [11]  on  compliant  surfaces,  might  make  a  more 
meaningful  surface  characterization  possible. 

The  turbulence  intensities  across  the  boundary  layer  for  SI  and  the 
fouled  specimens  are  shown  in  Figures  4  and  5,  respectively.  Both  the 
u’  and  v’  turbulence  intensities  were  greatly  increased  in  the  presence  of 
the  biofilm.  The  effect  was  noted  not  only  in  the  near  wall  region  but 
also  out  to  the  edge  of  the  boundary  layer  in  some  cases.  This  seems  to 
indicate  an  increase  in  large  scale  motions  over  these  biofilms.  The 
largest  percent  increase  in  the  longitudinal  turbulence  was  observed  for 
0.2<y/S<0.5  for  all  the  profiles.  For  FI,  the  increase  in  the  average  u’ 
and  v’  turbulence  intensities  in  this  region  were  29%  and  25%, 
respectively.  There  was  an  average  increase  of  23%  and  19%  for  F2  and 
an  increase  of  52%  and  45%  for  F3.  The  effect  is,  therefore,  dependent 
on  the  extent  and  morphology  of  the  fouling.  F3,  a  biofilm  dominated 
by  filamentous  green  algae,  showed  the  largest  increase  in  turbulence 
intensity.  It  can  also  be  seen  from  Figure  5  that  the  turbulence  intensity 
profiles  for  FI  and  F2  remain  nearly  constant  down  the  surface 
indicating  a  near  equilibrium  boundary  layer  condition.  The  profiles  for 
F3  do  not  collapse  well  to  a  single  curve,  and  therefore,  have  not  reached 
equilibrium.  This  may  have  been  due  to  the  splotchy  nature  of  F3. 
Another  possibility  could  be  an  insufficient  development  length  after  the 
step  change  in  roughness,  as  the  profiling  stations  were  located  between 
-158  to  -408  from  the  start  of  the  fouling.  Bandyopadhyay  [21]  has 
shown  that  sand  roughnesses  require  much  greater  length  to  reach  a  state 
of  equilibrium. 

Figure  6  shows  the  Reynolds  shear  stress  profiles  for  SI  and  the 
fouled  specimens.  The  fouled  specimens  not  only  show  an  increase  in 
the  peak  Reynolds  stress  in  the  inner  region  but  also  exhibit  higher 
values  well  into  the  outer  region.  The  profiles  followed  trends  similar  to 
the  turbulence  intensities  with  respect  to  boundary  layer  equilibrium. 
Again,  the  profiles  for  F3  do  not  collapse  to  a  single  curve.  Fair  collapse 
of  the  data  is  seen  for  FI  and  F2  with  the  exception  of  profile  F1B1, 
which  exhibited  a  peak  that  was  atypical  of  the  other  profiles  for  this 
specimen.  The  peaked  nature  of  the  profiles  for  F2,  F3,  and  F1B1 
indicate  a  smaller  equilibrium  or  constant  stress  region  than  for  the 
smooth  plate  flows. 

The  eddy  diffusivity  across  the  boundary  layer  for  SI  and  the 
fouled  plates  are  shown  in  Figure  7.  The  peak  in  the  smooth  profile 
occurs  at  about  y/5  =  0.3,  where  vT/(u*8)  reaches  0.068.  Hinze  [25]  has 
calculated  a  similar  profile  using  data  from  Klebanoff  and  Townsend. 
Not  only  the  shape  of  this  profile,  but  also  the  value  and  location  of  the 
peak  agrees  well  the  present  results.  One  notable  feature  of  both  the 
smooth  and  fouled  profiles  is  the  almost  linear  variation  in  the  eddy 
diffusivity  in  the  inner  region. 

The  task  of  accurately  scaling  laboratory  Cf’s  to  ship  scale 
frictional  resistance  coefficients  (CF)  is  a  complex  one.  Even  if  reliable 
lab  results  for  a  given  biofilm  are  available,  fouling  on  an  actual  ship 
hull  is  likely  to  be  much  more  heterogeneous.  Differences  in  fouling 
over  a  hull  can  occur  for  various  reasons  including  light  shading  effects, 
larval  zonation  in  the  water  column,  and  differences  in  the  flow  patterns 
and  stresses  along  the  hull.  The  complexities  in  boundary  layer  flows 
over  biofilms  such  as  surface  compliance,  deformation,  and  removal 
may  also  increase  the  error  in  the  prediction  of  ship  scale  effects.  Given 
the  inability  to  obtain  a  suitable  length  scale  parameter  to  express  the 
roughness  function  for  these  biofilms  and  the  aforementioned 
difficulties,  predictions  of  CF  at  ship-scale  are  not  offered  here.  It 
seems,  however,  that  there  is  the  potential  for  significant  performance 
penalties  as  a  result  of  low-form  fouling  on  marine  vehicles,  and  this 
should  not  be  ignored  when  assessing  the  viability  of  seawater  drag 
reduction  methods. 


IV.  CONCLUSION 

The  results  of  the  present  study  have  demonstrated  the  importance 
of  low  form  fouling  on  hydrodynamic  drag.  Seawater  drag  reduction 
methods  must  address  their  effects  in  order  to  be  practical.  This  study 
has  also  shown  that  the  increase  in  skin  friction  in  flows  over  biofilms  is 
not  only  dependent  on  the  their  thickness  but  also  their  composition  and 
morphology.  For  example,  the  average  increase  in  the  skin  friction 
coefficient  (Cf)  for  slime  films  with  a  mean  thickness  of  163  pm  and  347 
pm  was  33%  and  68%,  respectively.  The  average  increase  in  Cf  for  a 
surface  dominated  by  filamentous  green  algae  (Enteromorpha  spp .)  with 
a  mean  thickness  of  310  pm  was  187%.  Waving  algae  filaments  seem  to 
draw  a  greater  amount  of  momentum  from  the  mean  flow  than  do  slime 
films  alone.  A  statistically  significant  increase  in  the  displacement 
thickness  (5*),  momentum  thickness  (0),  and  shape  factor  (H)  was  found 
for  flows  over  the  biofilms.  The  roughness  functions  indicate  that 
relatively  thin  biofilms  (mean  biofilm  thickness  <  350  pm)  can  produce 
fully  rough  flow  conditions.  Standard  Colebrook-type  and  Nikuradse 
sand  roughness  functions  do  not  sufficiently  collapse  the  biofilm  results 
to  a  universal  curve  using  the  mean  roughness  height  as  a  characteristic 
length  scale.  A  method  of  characterizing  these  complex  surfaces  under 
flow  may  lead  to  a  more  appropriate  scaling  parameter.  The  present 
study  showed  that  biofilms  can  increase  turbulence  intensities  across  a 
large  part  of  the  boundary  layer.  Average  increases  in  the  longitudinal 
and  wall-normal  intensities  of  23%  to  52%  and  19%  to  45%, 
respectively,  were  measured  for  0.2<y/8<0.5  on  the  fouled  specimens. 
Reynolds  shear  stress  was  also  increased  significantly. 

Acknowledgements 

We  would  like  to  thank  the  Office  of  Naval  Research,  the  Defense 
Advanced  Research  Projects  Agency,  the  Environmental  Security  and 
Technology  Certification  Program,  and  the  General  Electric  Corporation 
for  their  support  of  this  research  and  their  commitment  to  the 
advancement  of  biofouling  control.  Thanks  go  to  Dr.  Andrew  Clark  and 
the  engineering  staff  at  Harbor  Branch  Oceanographic  Institution  for 
their  assistance  and  use  of  their  facilities.  We  are  also  grateful  to 
Professor  C.S.  Subramanian  for  helpful  comments  about  this  manuscript. 

V.  REFERENCES 

1.  G.l.  Loeb,  D.  Laster,  and  T.  Gracik  “The  Influence  of  Microbial 
Fouling  Films  on  Hydrodynamic  Drag  of  Rotating  Discs”,  in  Marine 
Biodeterioration,  An  Interdisciplinary  Study,  edited  by  J.D.  Costlow  and 

R.  Tipper,  Naval  Institute  Press,  Annapolis,  MD,  1984,  pp.  88-94. 

2.  Marine  Fouling  and  Its  Prevention ,  U.S.  Naval  Institute  Press, 
Annapolis,  MD,  1952. 

3.  B.F.  Picologlou,  N.  Zelver,  and  W.G.  Characklis  “Biofilm  Growth 
and  Hydraulic  Performance”,  A.S.C.E.  Journal  of  the  Hydraulics 
Division ,  HY5,  1980,  pp.  733-746. 

4.  A.K.  Lewkowicz  and  D.K.  Das  “Turbulent  Boundary  Layers  on 
Rough  Surfaces  With  and  Without  a  Pliable  Overlayer:  A  Simulation  of 
Marine  Fouling”,  Proceedings  of  the  A.S.M.E/A.S.C.E.  Bioengineering, 
Fluid  Engineering,  and  Applied  Mechanics  Conference ,  1981,  pp. 
174-186. 

5.  J.C.  Lewthwaite,  A.F.  Molland,  and  K.W.  Thomas  “An 
Investigation  into  the  Variation  of  Ship  Skin  Frictional  Resistance  with 
Fouling”,  Transactions  Royal  Institute  of  Naval  Architects ,  Vol.  127, 
1985,  pp.  269-284. 

6.  E.G.  Haslbeck  and  G.  Bohlander  “Microbial  Biofilm  Effects  on 
Drag  -  Lab  and  Field”,  Proceedings  1992  S.N.A.M.E.  Ship  Production 
Symposium,  1992. 

7.  S.  Gangadharan,  C.R.  Wimberly,  A.  Clark,  and  B.  Collino 
“Design,  Construction  and  Operation  of  a  Cost  Effective  Water  Tunnel 
at  Harbor  Branch  Oceanographic  Institution”,  Paper  presented  at 

S. N.A.M.E.  Southeast  Section  Meeting,  October  11,  1996,  Fort  Pierce, 
FL. 

8.  M.P.  Schultz  “The  Effect  of  Biofilms  on  Turbulent  Boundary 
Layer  Structure”,  Florida  Institute  of  Technology,  Ph  D.  dissertation, 
May,  1998. 

9.  P.  Bradshaw  “A  Simple  Method  for  Determining  Turbulent  Skin 
Friction  from  Velocity  Profiles”,  Journal  of  Aeronautical  Science,  Vol. 
26,  1959,  p.  841. 

10.  K.G.  Winter  “An  Outline  of  the  Techniques  Available  for  the 
Measurement  of  Skin  Friction  in  Turbulent  Boundary  Layers”,  Progress 
in  the  Aerospace  Sciences,  Vol.  18,  1977,  pp.  1-57. 


178 


11.  T.  Lee,  M.  Fisher,  and  W.H.  Schwarz  “Investigation  of  the  Stable 
Interaction  of  a  Passive  Compliant  Surface  with  a  Turbulent  Boundary 
Layer”,  Journal  of  Fluid  Mechanics ,  Vol.  257, 1993,  pp.  373401. 

12.  A.E.  Perry  and  P.N.  Joubert  “Rough-Wall  Turbulent  Boundary 
Layers”,  Journal  of  Fluid  Mechanics,  Vol.  37,  1963,  pp.  383413. 

13.  P.E.  Hancock  and  P.  Bradshaw  “The  Effect  of  Free-Stream 
Turbulence  on  Turbulent  Boundary  Layers”,  Journal  of  Fluids 
Engineering ,  Vol.  105,  1983,  pp.  284-289. 

14.  K.A.  Thole  and  D.G.  Bogard  “High  Freestream  Turbulence  Effect 
on  Turbulent  Boundary  Layers”,  Journal  of  Fluids  Engineering ,  Vol. 
118,  1996,  pp.  276-284. 

15.  R.J.  Garde  Turbulent  Flows ,  John  Wiley  and  Sons,  New  York, 
1994. 

16.  J.  Andreopoulos  and  D.H.  Wood  “The  Response  of  a  Turbulent 
Boundary  Layer  to  a  Short  Length  of  Surface  Roughness”,  Journal  of 
Fluid  Mechanics,  Vol  118,  1982,  pp.  143-164. 

17.  R.A.  Antonia  and  R.E.  Luxton  “The  Response  of  a  Turbulent 
Boundary  Layer  to  a  Step  Change  in  Surface  Roughness  Part  2.  Rough 
to  Smooth”,  Journal  of  Fluid  Mechanics ,  Vol.  53,  Pt.  4,  1972,  pp. 
737-757. 

18.  R.A.  Antonia  and  R.E.  Luxton  “The  Response  of  a  Turbulent 
Boundary  Layer  to  a  Step  Change  in  Surface  Roughness  Part  1.  Smooth 
to  Rough”,  Journal  of  Fluid  Mechanics ,  Vol.  48,  Pt.  4,  1971,  pp. 
721-761. 

19.  M.  Acharya  and  M.P.  Escudier  “Measurements  of  the  Wall  Shear 
Stress  in  Boundary  Layers”,  Proceedings  of  the  4th  International 
Symposium  on  Turbulent  Shear  Flows ,  Karlsruhe,  Germany,  1983,  pp. 
277-286. 

20.  A.E.  Perry,  W.H.  Schofield,  and  P.N.  Joubert  “Rough  Wall 
Turbulent  Boundary  Layers”,  Journal  of  Fluid  Mechanics ,  Vol.  37,  Pt. 
2,  1969,  pp.  383413. 

21.  P.R.  Bandyopadhyay  “Rough-Wall  Turbulent  Boundary  Layers  in 
the  Transition  Regime”,  Journal  of  Fluid  Mechanics ,  Vol.  180,  1987, 
pp.  231-266. 

22.  P.M.  Ligrani  and  R.J.  Moffat  “Structure  of  Transitionally  Rough 
and  Fully  Rough  Turbulent  Boundary  Layers”,  Journal  of  Fluid 
Mechanics,  Vol.  162, 1986,  pp.  69-98. 

23.  P.S.  Granville  “Three  Indirect  Methods  for  the  Drag 
Characterization  of  Arbitrarily  Rough  Surfaces  on  Flat  Plates”,  Journal 
of  Ship  Research ,  Vol.  31,  No.  1, 1987,  pp.  70-77. 

24.  V.C.  Patel  and  J.Y.  Yoon  “Application  of  Turbulence  Models  to 
Separated  Flow  over  Rough  Surfaces”,  Journal  of  Fluids  Engineering , 
Vol.  117,  June,  1995,  pp.  234-241. 

25.  O.  Hinze  Turbulence,  John  Wiley  and  Sons,  New  York,  1975. 

VI.  LIST  OF  NOMENCLATURE 
CF  frictional  resistance  coefficient  =  (2FD)/(pUe2s) 

Cf  wall  shear  stress  or  skin  friction  coefficient  =  (2t0)/^Ue2) 

Fd  drag  force 

k  some  measure  of  roughness  height 

k+  roughness  Reynolds  number  =  kin/v 

ks  sand  roughness  height  or  equivalent  sand  roughness  height 
Rex  Reynolds  number  based  on  x  =  xUe/v 

Res*  displacement  thickness  Reynolds  number  -  8*Ue/v 
Ree  momentum  thickness  Reynolds  number  =  0Ue/v 

S  wetted  surface  area 

x  streamwise  distance  from  plate  leading  edge 
U,  V  mean  velocity  in  the  x  and  y 

Uc  freestream  velocity 

U+  inner  layer  non-dimensional  velocity  «  u/u* 

AU+  roughness  or  velocity  loss  function 

u,  v  instantaneous  velocity  in  the  x  and  y  direction 

u’,  v’  fluctuating  velocity  component  in  the  x  and  y  direction 

u*  shear  velocity  =  Jx0/p 

y  normal  distance  from  the  boundary 

y+  inner  layer  non-dimensional  distance  =  yu  *  J\ 

a  statistical  significance  level 

A  Clauser  length  scale  =  5*Ue  /u* 

8  boundary  layer  thickness 


8*  displacement  thickness 

e  wall  datum  error 

k  von  Karman  constant  (=  0.41 ) 
v  kinematic  viscosity  of  the  fluid 
vT  eddy  diffusivity  =  -uV/(3U/5y) 

n  wake  parameter 

0  momentum  thickness 

p  density  of  the  fluid 

t0  wall  shear  stress 


Table  L  Visual  assessment  of  fouled  test  specimens. 


Specimen 

Total  % 
Fouling 
Cover 

Constituents  and  Their  %  Cover 

FI  before 

97 

Slime  97%  (light  to  medium  density  film) 

FI  after 

70 

Slime  70%  (very  light  density  film) 

F2  before 

98 

Slime  94%  (medium  density  film) 
Filamentous  green  algae  4% 

F2  after 

91 

Slime  90%  (medium  density  film) 
Filamentous  green  algae  1% 

F3  before 

95 

Slime  70%  (medium  density  film) 
Filamentous  green  algae  25% 

F3  after 

82 

Slime  70%  (medium  density  film) 
Filamentous  green  algae  12% 

Table  II.  Boundary  layer  parameters. 


Profile 

Ree 

H 

S1A1 

6537 

gfclg 

glEB 

raa 

Ti'.-l:! 

1.29 

gonna 

6499 

guv 

Kwa 

E1HE1 

1.31 

IS1C1 

8106 

gHtV 

Ena 

MSSS 

1.28 

MUM 

8539 

EH 

eem 

WEE1 

IKiM 

1.29 

909 

12510 

■wi 

gKEV 

WWif* 

■KiEl 

1.27 

IS1C2 

10380 

MtfcfV 

■IM 

waa 

■Kill 

1.28 

10560 

EB 

■wl 

EM 

■bum 

1.30 

11480 

masm 

EM 

KWH 

mesh 

1.25 

S1C3 

14410 

Mi*M 

mi'im 

ebb 

■H»l 

1.25 

S2A1 

5575 

■MEM 

msm 

iniii 

■‘Ml 

1.29 

6332 

KBI 

Util 

1.28 

|S2C1 

6973 

■cWEl 

4.71 

ma 

■MEM 

1.32 

MV 

8517 

W5EM 

■tliEH 

wmt 

■hwei 

1.29 

ggSM 

9973 

msm 

Kgfa 

■IBM 

1.27 

IS2C2 

9101 

mwm 

KKIil 

■bm.M 

1.26 

i-vjt.v 

11980 

Mllli 

ESDI 

Ma 

maa 

1.29 

kSO:« 

12650 

■EHV 

mssm 

BBtl 

heh 

1.25 

15170 

■Hil 

msm 

■lfia 

1.25 

IF1A1 

6457 

■atini 

«aa 

HEM 

1.41 

mm 

7563 

BB 

Eira 

■Wi»l 

1.44 

9208 

BUM 

B3 

bebi 

1.37 

9730 

g»:lg 

ita 

vara 

1.39 

ana® 

10100 

■tEia 

msm 

kepi 

g:wa 

1.41 

12090 

■ttiV 

Ewa 

■wura 

1.42 

BEM 

13930 

EM 

BUM 

KliTM 

■Bran 

1.28 

annv 

12290 

EM 

msm 

■new 

■naa 

1.30 

F1C3 

14920 

EM 

g«V 

Kill 

1.31 

F2A1 

5672 

wi»m 

■-HV 

Kgia 

giZM 

1.40 

[BUM 

7455 

EEM 

Elia 

1.36 

IF2C1 

8222 

■ct'JtV 

li'il 

EEE1 

issa 

1.33 

BESS 

gr.iv 

KEE1 

■HIE 

1.34 

11020 

■t>gv 

■itti 

EliHI 

■EilM 

1.35 

GggM 

12200 

gmV 

HU 

■KM 

1.31 

IMiV 

9753 

E.fV 

eesh 

rasa 

gga 

1.37 

ttt'M 

15370 

Ktll‘1 

Ewa 

1.30 

F2C3 

12990 

EM 

gl:« 

Kiaa 

■Miia 

1.31 

F3A1 

6680 

IBM 

■Orf.M 

gflEl 

1.49 

7713 

BtHIg 

EM 

SSM 

1.48 

F3C1 

9380 

■H:l 

KEIE 

1.49 

F3A2 

10190 

VEU 

em 

■3EB1 

E2H 

1.44 

aiiUB 

11760 

EEE1EH 

g»ig 

ttu 

■mra 

1.41 

Emm 

13640 

mssm 

hbem 

■ana 

Baa 

1.48 

13840 

mwm 

BJEIV 

tta 

gr/*l 

1.39 

[rtf' 

18630 

»:!■ 

BB 

HEI 

■rcai 

1.36 

IF3C3 

19100 

■tMV 

gJBV 

BHa 

■HilH 

1.42 

179 


Cr^lO3) 

crCxlO5) 

cf  (xlO3) 

Profile 

Ree 

Bradshaw 

Sublayer 

Reynolds 

Cross  Plot 

Slope 

Stress 

somi 

era™ 

Bgl 
SUM  | 
SWI 


2.99 

2.81 

2.84 

2.90 

2.76 

2.61 

2.85 

2.78 

2.81 

2.50 

6537 


6499 


8106 


8539 


12510 


10380 


10560 


11480 


14410 


5575 


6332 


6973 


8517 


9973 


9101 


11980 


12650 


15170 


-  missing  data 


Table  IV.  Wall  shear  stress  coefficients  for  the  fouled  specimens. 


lProfile  Re( 


*  *  a*  ^  - 

T  v 

.  ▼ 

0°o  8  tt  •  «T  T 

*><*>$□5 .  •  t’ 


• 

Profile  SI  A1 

— 

U'  *  5.S2  logfy+e)’  *  5.0 

tr«y 

■ 

Prom*  PI  A1 

V 

Profit#  F2A1 

O 

Profll*  P3A1 

•  Profit*  SIM 

- U‘  «  5.12  lotfy*««r  +  5-® 

25  .  .  .  IT*/ 

:  ■  Profit*  PI  B1 

20  -  V  ProfH*  P2*1 
;  O  Profll*  FW1 


•  ProlH*  SI  Cl 

- U'-5.f2l0fl{y*or  +  5.e 

-  •  -  u4«/ 

■  ProfH*  PI  Cl 
20  -  V  Profll*  P2C1 

:  o  Profll*  F3C1 


(y+s)* 

Figure  2.  Law  of  the  wall  plots  for  smooth  and  fouled  specimens. 


•  Fouled  Specimen  FI 
□  Fouled  Specimen  F2 
T  Fouled  Specimen  F3 


Figure  3.  Roughness  functions  for  the  fouled  specimens. 


0.3  ' 

/  _ 

> 

FI  Cl 

0.2  \ 

►  □ 

F2C1 

>  ▼ 

F3C1 

0.1  j 

o 

Smooth  Wall  (SI Cl) 

0.0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.0 

(y+s )/8 

Figure  1.  Plot  of  U/Ue  vs.  y/8  showing  the  effect  of  fouling  extent. 


S] 


0.0  0.2  0.4  0.6  0.8  1.0  1.2 


y/5 

Figure  4.  Turbulence  intensity  plots  smooth  specimen,  S 1 . 


(ye)/5 

Figure  5.  Turbulence  intensity  plots  for  the  fouled  specimens. 


1 1 


0.008 

0.007 

0.006 

0.005 

0.004 

0.003 

0.002 

0.001 

0.000 

0.007 

0.006 

0.005 

0.004 

0.003 

0.002 

0.001 

0.000 

0.007 

0.006 

0.005 

0.004 

0.003 

0.002 

0.001 

0.000 


0.0 


0.2 


0.4 


0.6 


0.8 


1.0 


1.2 


(y+e)/8 

Figure  6.  Reynolds  shear  stress  plots  for  the  smooth  and  fouled 
specimens. 


(y+e)/6 

Figure  7.  Eddy  diffusivity  plots  for  the  smooth  and  fouled  specimens. 


181 


Turbulent  Drag  Reduction 
Methods:  Compliant 
Coatings 


183 


RECENT  ADVANCES  IN  THE  USE  OF  COMPLIANT  WALLS  FOR  DRAG  REDUCTION 


Peter  W.  Carpenter 
University  of  Warwick 
Coventry,  CV4  7AL,  England 
pwc  @eng.warwick.ac.uk 

Abstract  -  Recent  work  on  the  use  of  compliant  walls  for  laminar  flow  control  in  low-disturbance  marine  environments  is  reviewed.  The 
key  role  of  hydroelastic  instability  is  explained  and  discussed.  It  now  appears  that  it  may  well  be  possible  to  maintain  laminar  flow  at 
indefinitely  high  Reynolds  numbers  by  the  use  of  multiple-panel  compliant  walls  with  properties  tailored  to  the  local  flow  conditions.  The 
recent  theoretical  and  experimental  work  on  transition  in  the  three-dimensional  boundary  layer  over  rotating  compliant  disks  is  also 
reviewed.  Wall  compliance  has  a  stabilizing  effect  on  the  crossflow  vortices  and  an  even  more  marked  stabilizing  effect  on  the  absolute 
instability  recently  discovered  by  Lingwood.  Finally  the  effects  of  wall  compliance  on  fully  turbulent  boundary  layers  are  briefly  discussed. 


I.  INTRODUCTION 

More  than  forty  years  have  elapsed  since  Kramer  [1]  first 
reported  his  pioneering  experiments  on  the  use  of  compliant  coating 
for  drag  reduction  in  sea  water.  The  general  acceptance  of  the 
validity  of  his  findings  has  waxed  and  waned  several  times  since 
then.  Kramer,  himself,  believed  that  his  coatings  reduced  drag  by 
postponing  the  onset  of  laminar-turbulent  transition.  There  is 
certainly  supporting  theoretical  and  experimental  evidence  for  this 
view  [2,3, 4, 5].  An  alternative  explanation  for  the  drag  reduction 
could  be  that  wall  compliance  favourably  affects  the  fully  turbulent 
boundary  layer.  Here  the  evidence  is  less  clear  and  certainly  a 
convincing  theoretical  explanation  is  lacking.  However,  there  have 
been  carefully  conducted  experiments  in  water  where  a  drag  reduction 
is  clearly  observed.  Such  a  study  was  described  recently  by  Choi  et 
al  [6]. 

In  this  paper  the  recent  work  on  the  use  of  wall  compliance  for 
laminar  flow  control  will  be  reviewed  in  Section  II.  Most  of  the  work 
on  compliant  walls,  both  experimental  and  theoretical,  has  involved 
the  flat-plate  boundary  layer.  However,  the  effect  of  wall  compliance 
on  the  three-dimensional  boundary  layer  over  a  rotating  disc  has  also 
been  studied  experimentally  [7-9]  in  the  past.  The  problem  with 
these  earlier  studies  was  that  only  the  torque  was  measured,  so  when 
it  fell  or  increased  for  a  compliant  disc  compared  with  a  rigid  one,  the 
underlying  physical  cause  was  not  revealed.  Recently,  at  Warwick, 
we  have  undertaken  a  combined  theoretical  [10],  computer  simulation 
[11]  and  experimental  [12]  study  of  transition  in  the  rotating-disc 
boundary  layer.  The  results  will  be  briefly  presented  in  Section  IH. 
The  effects  of  wall  compliance  on  fully  turbulent  boundary  layers  will 
be  briefly  considered  in  Section  IV. 

Since  there  have  been  several  reviews  on  these  and  related 
topics  in  recent  years  [13-15],  I  will  mainly  discuss  recent  work  at 
Warwick. 

II  LAMINAR  FLOW  CONTROL 

Little  is  currently  known  about  the  effects  of  wall  compliance  on 
laminar-turbulent  transition  in  high-disturbance  environments  where 
by-pass  transition  comes  into  play.  On  the  other  hand  a  great  deal  is 
now  known  about  the  effects  of  wall  compliance  on  transition  in  the 
low-disturbance  environments  typical  of  many  aeronautical  and 
marine  applications.  Accordingly  the  present  review  will  focus  on 
transition  in  low-disturbance  environments.  In  such  cases,  when  the 
boundary  layers  are  similar  to  that  found  over  a  flat  plate,  the  route  to 
transition  begins  with  the  amplification  of  quasi-two-dimensional 
Tollmien-Schlichting  waves  as  they  propagate  along  the  boundary 
layer.  In  the  great  majority  of  experimental  studies  such  waves  are 
produced  artificially  as  monochromatic  wavetrains  using  a  vibrating 
ribbon  or  some  other  driver.  Likewise  most  theoretical  studies 
implicitly  address  this  artificial  situation.  It  is  important  to 
appreciate,  however,  that  T/S  waves  have  been  observed  many  times 
in  natural  transition  (see,  for  example,  [16,17]).  But,  as  first 
demonstrated  by  Schubauer  and  Skramstadt  [16],  the  use  of  a  driver 
to  excite  the  boundary  layer  artificially  produces  much  cleaner 
signals. 

In  natural  transition  the  boundary  layer  is  excited  via  freestream 
turbulence,  acoustic  radiation,  vibration,  roughness  or  some  other 
agency.  The  process  whereby  T/S  waves  are  generated  through  such 


sources  of  natural  excitation  is  known  as  receptivity.  The  effect  of 
wall  compliance  on  receptivity  may  well  be  important,  but  it  has 
been  little  studied  to  date.  Some  relevant  information  is  given  in 
[18].  For  the  rigid  wall  T/S  waves  grow  as  they  propagate 
downstream  and  eventually  reach  sufficiently  large  amplitudes  for 
nonlinear  effects  to  become  significant.  At  this  point  the  disturbances 
become  three-dimensional  and  the  several  stages  of  transition  proper 
rapidly  ensue.  The  actual  transition  zone  itself  is  characterized  by 
turbulent  spots  and  there  is  no  direct  evidence  by  this  stage  of  the 
original  T/S  waves.  Nevertheless  the  final  stage  of  transition  would 
not  have  occurred  without  the  intial  amplification  of  the  T/S  waves. 
In  the  sort  of  low-disturbance  environment  often  found  in 
aeronautical  and  marine  applications  the  initial  amplification  of  T/S 
waves  (the  so-called  linear  regime  of  transition)  typically  extends  over 
70  to  80  percent  of  the  total  transition  process.  The  aim  of  using 
compliant  walls  for  laminar  flow  control  is  greatly  to  extend  this 
linear  regime  or  even  to  suppress  the  growth  of  T/S  waves  entirely. 

It  has  been  known  since  the  seminal  theoretical  studies  of 
Benjamin  and  Landahl  [19,20]  (see  [2]  also)  that  the  more  compliant 
the  wall  the  greater  is  the  stabilizing  effect  on  T/S  waves.  Indeed  if 
the  wall  is  made  sufficiently  compliant  T/S  waves  can  be  completely 
suppressed.  The  problem  is  that  highly  compliant  wall  are  vulnerable 
to  hydroelastic  instabilities.  Accordingly,  the  key  to  the  successful 
use  of  wall  compliance  for  laminar  flow  control  is  to  make  the  wall  as 
compliant  as  possible  without  making  it  hydroelastically  unstable. 
There  appear  to  be  two  main  classes  of  hydroelastic  instability, 
namely  travelling-wave  flutter  which  is  convective,  and  divergence 
which  is  absolute  in  nature  [3].  Although  this  simple  picture  is 
broadly  correct,  it  is  further  complicated  by  the  fact  that  it  is  now 
known  that  for  compliant  walls  with  good  transition-delaying 
properties  divergence  tends  to  be  replaced  by  another  absolute 
instability  which  forms  through  a  coalescence  of  the  T/S  waves  and 
travelling-wave  flutter  [2,13,21]. 

The  theory  explaining  the  effect  of  wall  compliance  on  T/S 
waves  has  been  corroborated  by  the  careful  experiments  in  water  by 
Gaster  [4]  and  his  co-workers.  The  compliant  panels  used  in  these 
experiments  comprised  a  relatively  thick  and  soft  silicone-rubber 
substrate  covered  with  a  thin,  much  stiffer,  latex-rubber  sheet.  As 
well  as  Gaster  and  his  co-workers,  other  authors  [22,23]  have 
investigated  the  stability  of  boundary  layers  over  such  surfaces.  Since 
the  theoretical  model  is  essentially  the  same  in  all  these  cases, 
Gaster* s  study  can  be  regarded  as  confirmation  of  the  essential 
validity  of  the  theoretical  approach.  In  brief,  he  measured  the  growth 
of  artificially  generated  monochromatic  T/S  waves  as  they  propagated 
along  the  boundary  layer  over  various  compliant  walls.  In  all  cases, 
including  the  rigid  control,  good  agreement  was  found  between  the 
predicted  and  measured  growth.  A  more  recent  account  of  Gaster’ s 
experimental  study  is  given  by  Lucey  and  Carpenter  [5].  Their  work 
is  based  on  a  slightly  modified  theory  which  accounts  for  the  tension 
applied  to  the  outer  sheet,  leading  to  slightly  improved  predictions  of 
T/S  amplitudes  when  compared  with  the  experimental  data. 

The  Gaster  study  confirmed  that  the  growth  of  T/S  waves  could 
be  reduced  by  wall  compliance.  A  30  percent  increase  in  the 
transitional  Reynolds  number  was  also  obtained.  The  transition  delay 
was  limited  by  the  experiments!  set-up  rather  than  the  compliant  wall. 
It  should  be  appreciated,  however,  that  obtaining  a  transition  delay 


185 


was  not  the  aim  of  the  study;  in  fact,  it  was  undertaken  in  order  to 
confirm  that  the  evolution  of  T/S  waves  over  compliant  walls  could 
be  theoretically  predicted  with  confidence.  Another  very  significant 
outcome  of  the  study  was  the  observation  that  over  most  of  the 
compliant  panels  transition  did  not  occur  because  of  the  amplification 
of  T/S  waves.  What  was  observed  instead  was  a  very  sudden 
breakdown  when  the  flow  speed  exceeded  a  certain  critical  flow 
speed.  It  has  been  shown  in  [5]  that  this  sudden  breakdown  can  be 
fully  explained  and  predicted  using  the  linear  theory  for  travelling- 
wave  flutter  [3,24].  The  discovery  of  this  new  route  to  transition 
shows  how  vital  an  understanding  of  hydroelastic  instability  is  for 
designing  compliant  walls  for  laminar  flow  control. 

The  mechanism  for  the  other  hydroelastic  instability, 
divergence,  is  easy  to  understand.  When  a  small  disturbance  induces 
a  small  displacement  to  a  compliant  surface  a  pressure  force  is 
generated.  The  magnitude  of  this  force  is  proportional  to  the  dynamic 
pressure  of  the  freestream.  Consequently,  when  a  sufficiently  high 
flow  speed  is  reached  the  pressure  force  will  outweigh  the  restorative 
structural  forces  in  the  wall  and  divergence  waves  will  form  in  the 
wall.  These  waves  would  act  much  like  roughness  and  trigger 
transition.  Thus  divergence  must  be  avoided  if  laminar  flow  control 
is  to  be  achieved.  Divergence  has  been  observed  many  times  for 
compliant  walls  [3,13,14].  The  most  detailed  experimental  study  was 
carried  out  by  Gad-el-Hak  and  his  co-workers  [25,26].  They  found 
that  divergence  waves  travelled  very  slowly,  typically  a  few  percent  of 
the  freestream  flow  speed.  Divergence  was  only  observed  over  highly 
damped  walls  in  turbulent  flow.  Travelling-wave  flutter  supplanted 
divergence  when  the  compliant  walls  were  lightly  damped. 
Theoretical  studies  of  divergence  [3,13]  suggested  that  divergence  is 
an  absolute  instability.  This  has  been  confirmed  more  recently  by 
numerical  simulation  [27]  and  a  rigorous  theoretical  study  [28]. 

The  requirement  of  a  turbulent  flow  for  the  existence  of 
divergence  has  only  recently  been  fully  appreciated  in  the  theoretical 
work.  It  has  been  known  for  some  time  [29]  that  the  presence  of  the 
boundary  layer  alters  the  phase  and  magnitude  of  the  wall  pressure 
compared  with  the  pressure  in  the  potential  flow  just  outside  of  the 
boundary  layer.  Indeed,  for  the  laminar  boundary  layer  there  are 
accurate  approximate  expressions  for  estimating  the  pressure  at  the 
wall  [24].  What  our  recent  numerical  simulations  [30]  have  shown  is 
that  the  amplitude  in  pressure  is  reduced  to  a  much  greater  extent  in 
laminar-boundary  layers  than  in  turbulent  ones.  Accordingly,  the 
critical  flow  speed  for  divergence  is  much  greater  for  a  laminar 
boundary  layer.  Actually,  it  now  appears  that  theoretically  in  the  case 
of  a  laminar  boundary  layer,  divergence  is  replaced  by  another 
absolute  instability  formed  by  the  coalescence  of  a  Tollmien- 
Schlichting  wave  and  travelling-wave  flutter.  This  has  been 
demonstrated  analytically  in  the  case  of  the  plane  channel  flow[21]. 
It  has  been  long  suspected  that  this  instability  is  absolute  [3,13]. 
Recent  numerical  simulations  [10]  have  established  this  for  certain. 
Experimentally  it  would  probably  be  difficult  to  distinguish  this  new 
absolute  instability  from  divergence. 

Previously  [3,13,23]  the  divergence  onset  speed  was  estimated 
using  potential  flow  theory.  From  the  recent  work  on  divergence  and 
the  other  absolute  instability  it  is  now  known  that  this  is  a  very 
conservative  estimate  and  that  the  walls  can  be  made  substantially 
more  compliant  without  incurring  the  danger  of  absolute  instability. 
In  fact,  it  is  possible  to  suppress  T/S  waves  completely  over  a 
streamwise  length  of  the  surface  [18].  The  compliant-wall  properties 
can  be  tailored  to  suppress  the  T/S  waves  for  a  range  of  Reynolds 
number  based  on  boundary  layer  thickness.  In  this  way  multiple- 
panel  surfaces  [31]  could  be  used  in  order  to  suppress  the  T/S  waves 
for  the  entire  surface.  The  practical  question  then  becomes:  How 
short  can  a  compliant  panel  be  without  losing  its  capability  of 
suppressing  T/S  waves?  This  question  was  addressed  in  [18]  for 
plane  channel  flow.  The  simulations  have  been  repeated  [11]  for  the 
boundary  layer  with  much  the  same  results.  It  turns  out  that,  although 
the  response  of  a  finite  compliant  panel  can  be  very  complex,  those 
with  appropriate  properties  continue  to  suppress  T/S  waves  even 
when  as  short  as  a  single  T/S  wave.  This  implies,  that  in  the  absence 
of  an,  as  yet  undiscovered,  receptivity  mechanism,  T/S  waves  can  be 
completely  suppressed  at  indefinitely  high  Reynolds  numbers  and 
laminar  flow  maintained  by  the  use  of  multiple-panel  compliant 


walls  composed  of  relatively  short  panels.  Small  compliant  panels 
have  the  further  advantage  of  being  less  vulnerable  to  hydroelastic 
instability. 

Even  using  the  very  conservative,  previous  estimates  of  the 
critical  flow  speed  for  divergence,  very  substantial  postponement  of 
transition  is  possible  (up  to  a  six-fold  increase  in  transitional 
Reynolds  number)  according  to  the  theory  [23,31],  Moreover,  the 
mechanical  properties  of  the  compliant  wall  required  to  maintain 
laminar  flow  could  be  readily  realized  in  practice  in  a  marine 
environment.  In  fact,  in  most  respects,  the  properties  required  at 
relatively  high  speeds  are  probably  less  demanding  than  those 
corresponding  to  the  flow  speeds  typical  of  the  Gaster  experiments. 
The  maximum  flow  speed  in  Kramer’s  tests  was  18  m/s.  These  tests 
were  carried  out  in  the  sea  and  the  compliant  coatings  were  made 
from  natural  rubber.  At  similar  flow  speeds  the  theoretical  optimum 
wall  properties  for  maintaining  laminar  flow  are  quite  similar  to  those 
of  the  Kramer  coatings.  Accordingly  it  should  not  be  too  difficult  in 
practice  to  make  such  optimum  coatings. 

HI.  TRANSITION  OVER  ROTATING  COMPLIANT  DISKS 

Transition  in  the  three-dimensional  boundary  layer  over  a 
rotating  disk  has  been  widely  studied  because  it  is  a  simple  model 
exhibiting  many  of  the  features  exhibited  by  the  three-dimensional 
flows  found  in  practical  aeronautical  and  marine  applications.  There 
have  been  several  experimental  studies  of  the  rotating  compliant  disk, 
e.g.  [7-9].  In  these  experiments  the  only  quantitative  measurements 
were  of  the  torque  required  to  drive  the  disk.  A  change  in  the  torque 
required  to  drive  a  compliant  disk  compared  with  a  rigid  one  at  the 
same  rotational  speed  was  regarded  as  evidence  of  a  drag  increase  or 
reduction.  Torque  reduction  was  observed  in  some  cases  [9].  Visual 
observations  could  also  be  made  of  hydroelastic  instabilites  forming 
on  the  disk  surface.  In  that  way  torque  increases  could  sometimes  be 
explained  [7,8].  But,  until  our  recent  research  programme,  it  was  not 
known  how  boundary-layer  stability  or  transition  would  be  affected 
by  wall  compliance  for  the  rotating  disc. 

The  transition  process  in  the  boundary  layer  over  a  rigid  rotating 
disk  is  quite  different  from  and  possibly  more  complex  than  that  for 
the  flat-plate  boundary  layer.  Wall  compliance  brings  additional 
complexity.  Three  different  instabilities  have  been  identified.  The 
most  widely  studied  is  the  so-called  Type  I  instability  or  crossflow 
vortex.  This  is  found  in  many  other  three-dimensional  flows.  The 
instability  mechanism  is  essentially  inviscid  and  is  associated  with 
the  presence  of  an  inflexion  point  in  the  velocity  profile.  This 
instability  is  much  more  powerful  than  Tollmien-Schlichting  waves 
for  which  the  instability  mechanism  is  essentially  viscous.  It  was 
shown  recently  that,  nevertheless,  wall  compliance  has  a  strong 
stabilizing  effect  on  these  more  powerful  inflexion-point  instabilities 
[32].  Both  stationary  (with  respect  to  the  disk)  and  travelling  cross- 
flow  vortices  can  exist.  The  former  are  by  far  the  most  commonly 
studied  experimentally,  but  the  latter  are  the  most  rapidly  growing. 
Our  recent  theoretical  [10]  and  numerical  simulation  [11]  studies 
show  that  wall  compliance  has  a  strong  stabilizing  effect  on  both 
travelling  and  stationary  cross-flow  vortices.  The  experimental  study 
[12]  is  less  clear.  It  appears  to  corroborate  the  theory  in  that  there  is 
an  apparent  rise  in  the  critical  Reynolds  number  for  the  cross-flow 
vortices  for  the  compliant  disk  as  compared  with  a  rigid  one. 
Transition  occurs  earlier  for  the  compliant  disk,  however. 

The  second  instability  found  in  the  rotating-disk  boundary  layer 
is  the  so-called  Type  0.  The  instability  mechanism  is  viscous  and 
involves  Coriolis  acceleration.  The  effect  of  wall  compliance  appears 
to  be  more  complex  in  this  case  in  that  small  levels  of  compliance 
lead  to  a  substantial  drop  in  the  critical  Reynolds  number  for  this 
instability  whereas  larger  levels  of  compliance  appear  to  be 
stabilizing.  Under  certain  circumstances  the  Type  I  and  Type  II 
instability  coalesce,  giving  rise  to  local  algebraic  growth  even  when 
the  instability  is  convectively  stable.  This  seems  to  be  of  little 
practical  consequence  for  rigid  walls  [11].  In  contrast  wall 
compliance  seems  to  lead  to  this  algebraic  growth  occurring  at 
considerably  lower  Reynolds  numbers  than  for  the  rigid  wall.  It  is 
possible  that  this  mechanism  is  responsible  for  the  earlier  transition 
seen  in  the  experiments  on  a  rotating  compliant  disk. 


186 


An  absolute  instability  is  also  found  in  the  rotating-disk 
boundary  layer.  [33,34]  This  also  comes  about  due  to  the  coalescence 
of  two  eigenmodes,  namely  the  Type  I  and  Type  in  --  a  hitherto  rather 
obscure  eigenmode.  It  appears  that  this  absolute  instability  is  a 
common  route  to  transition.  According  to  our  theoretical  [10]  and 
numerical  simulation  [11]  studies  even  a  low  level  of  compliance  has 
a  strongly  stabilizing  effect  on  the  absolute  instability.  This  may  well 
be  the  most  practically  significant  effect  of  wall  compliance  on  the 
rotating  disc  because  it  appears  that  the  absolute  instability  occurs  in 
several  other  flows  some  of  which  are  of  practical  interest  [25]. 

IV.  EFFECT  OF  WALL  COMPLIANCE  ON  TURBULENCE 

Much  of  the  experimental  evidence  of  the  effects  of  wall 
compliance  on  turbulent  boundary  layers  is  rather  inconclusive. 
Direct  numerical  simulations  [36]  suggest  that  compliant  walls  with 
properties  selected  to  be  effective  in  the  linear  regime  of  transition 
remain  highly  effective  well  into  the  nonlinear  regime  where  the  flow 
structures  have  become  highly  three-dimensional.  One  might  expect, 
therefore,  that  such  relatively  highly  compliant  surfaces  would  be 
effective  in  reducing  turbulence  levels  in  the  fully  turbulent  boundary 
layer.  On  the  other  hand,  the  scale  and  form  of  the  near-wall 
structures  in  a  turbulent  boundary  layer  are  completely  different  from 
those  found  in  the  linear  and  weakly  nonlinear  transition  regimes. 

Recently  Choi  et  al.  [6]  have  reported  small  reductions  in  drag 
(up  to  7  percent)  and  in  skin  friction  and  wall-pressure  fluctuations  in 
boundary  layers  over  compliant  walls  in  the  form  of  a  single 
viscoelastic  layer.  These  results  confirm  earlier  results  obtained  in 
Russia  with  the  same  compliant  coatings.  What  is  particularly 
noteworthy  in  these  experiments  is  that  the  degree  of  wall  compliance 
is  very  low  (the  walls  are  about  100  stiffer  than  the  Kramer  coatings 
when  allowance  is  made  for  the  differences  in  flow  speed.  This 
suggests  a  quite  different  mechanism  is  involved  than  for  the  walls 
used  for  transition  delay.  It  is  also  worth  noting  that  the  compliant 
rotating  disks  used  in  our  experimental  study  [12]  were  also  much 
stiffer  relative  to  the  Kramer  coatings.  In  this  case  also,  although  wall 
compliance  brought  earlier  transition,  it  also  led  to  markedly  lower 
levels  of  turbulence  intensity  in  the  full  turbulent  boundary  layer. 

What  physical  mechanism  could  come  into  play  for  fairly  stiff 
compliant  walls?  Our  theoretical  analysis  shows  that  when  the  wall 
compliance  is  small,  the  main  effect  is  the  pseudo-random  wall 
displacements  due  to  the  effect  of  the  turbulent  pressure  fluctuations 
driving  the  wall.  It  appears  that  the  effect  of  these  wall  displacements 
on  the  near-wall  structures  is  much  larger  than  the  direct  interaction 
between  the  near-wall  structures  and  the  compliant  wall.  It  is  known 
from  the  work  of  Sirovich  and  his  co-workers,  e.g.  see  [37],  that 
random  phase  changes  to  the  near-wall  structures  can  interfere  with 
bursting  process  thereby  lead  to  substantial  drag  reduction.  This 
effect  was  realized  in  experiments  by  using  randomized  chevron¬ 
shaped  roughness  elements.  It  may  be  that  the  pseudo-random 
displacements  created  in  the  compliant  wall  by  the  fluctuating 
turbulent  pressure  field  has  much  the  same  effect. 

V.  CONCLUSIONS 

Recent  work  on  the  use  of  wall  compliance  to  maintain  laminar 
flow  in  a  low-disturbance  marine  environment  has  been  reviewed. 
All  the  evidence  suggests  that  appropriately  designed  multiple-panel 
compliant  walls  could  maintain  laminar  flow  at  indefinitely  high 
Reynolds  numbers.  The  material  properties  required  for  these  panels 
should  be  practically  achievable.  Further  work  is  required  on  the 
effects  of  wall  compliance  on  receptivity  mechanisms.  Also  further 
experimental  study  is  desirable,  including  proof-of-concepts  tests  at 
the  flow  speeds  of  practical  interest  in  a  marine  environment. 

The  recent  work  on  the  rotating-disk  boundary  layer  was  also 
reported.  It  appears  that  wall  compliance  also  has  a  strong  effect  on 
transition  in  this  highly  three-dimensional  boundary  layer.  In 
particular,  even  low  levels  of  wall  compliance  have  a  strongly 
stabilizing  effect  on- the  absolute  instability  which  provides  the  route 
to  transition  in  some  practical  flows. 

Recent  work  on  the  effects  of  wall  compliance  on  fully  turbulent 
flows  is  briefly  reviewed.  It  appears  that  using  fairly  stiff  compliant 
walls  leads  to  reductions  in  drag  and  turbulence  intensity.  A  possible 
physical  mechanism  which  could  account  for  this  is  outlined. 


ACKNOWLEDGEMENTS 

The  work  at  the  University  of  Warwick  reported  here  was 
supported  by  the  UK  Engineering  and  Physical  Sciences  Research 
Council. 

VI.  REFERENCES 

1.  M.O.  Kramer  “Boundary-layer  stabilization  by  distributed 
damping”,  J.  Aero.  Sci.  24,  459,  1957;  J.  Amer.  Soc.  Naval  Engrs. 
72,  25-33, 1960. 

2.  P.W.  Carpenter  and  A.D.  Garrad  “The  hydrodynamic  stability  of 
flow  over  Kramer-type  compliant  surfaces.  Part  1.  Tollmien- 
Schlichting  instabilities”,  J.  Fluid  Mech.  155, 465-510, 1985. 

3.  P.W.  Carpenter  and  A.D.  Garrad  “The  hydrodynamic  stability  of 
flow  over  Kramer- type  compliant  surfaces.  Part  2.  Flow-induced 
surface  instabilities”,  J.  Fluid  Mech.  170, 199-232, 1986. 

4.  M.  Gaster  “Is  the  dolphin  a  red  herring?”,  Proc.  IUTAM  Symp.  on 
Turbulence  Management  and  Relaminarisation,  Bangalore,  India 
(edited  by  H.W.  Liepmann  and  R.  Narasimha),  Springer,  New  York, 
285-304,  1987. 

5.  A.D.  Lucey  and  P.W.  Carpenter  “Boundary  layer  instability  over 
compliant  walls:  comparison  between  theory  and  experiment”,  Phys. 
of  Fluids  7,  2355-2363, 1995. 

6.  K.-S.  Choi,  X.  Yang,  B.R.  Clayton,  E.J.  Glover,  M.  Atlar,  B.N. 
Semenov  and  V.M.  Kulik  “Turbulent  drag  reduction  using  compliant 
surfaces”,  Proc .  Roy.  Soc.  London  A  453, 2229-2240,  1997. 

7.  R.I  Hansen  and  D.L.  Hunston  “An  experimental  study  of  turbulent 
flows  over  compliant  surfaces”,  J.  Sound  &  Vib.  46,  297-308,  1974. 

8.  R.I.  Hansen  and  D.L.  Hunston  “Fluid-property  effects  on  flow¬ 
generated  surface  waves  in  compliant  surfaces”,  J.  Fluid  Mech.  133, 
161-177, 1983. 

9.  K.  Chung  “Composite  compliant  coatings  for  drag  reduction 
utilising  low  modulus  high  damping  silicone  rubber”,  PhD 
dissertation,  MIT,  1985. 

10.  A.J.  Cooper  and  P.W.  Carpenter  “The  stability  of  rotating-disc 
boundary-layer  flow  over  a  compliant  wall.  J.  Fluid  Mech.  350 ,  231- 
270,  1997. 

11.  C.  Davies  and  P.W.  Carpenter  “Non-parabolic  disturbance 
behaviour  in  incompressible  boundary  layers”,  Bull.  Amer.  Phys. 
Soc.  42,  2138,  1997. 

12.  A.J.  Colley,  P.J.  Thomas  and  P.W.  Carpenter  “An  experimental 
investigation  of  the  stability  of  the  boundary  layer  over  a  rotating  disk 
covered  with  a  compliant  coating”,  3rd  Euro.  Fluid  Mech.  Conf, 
Gottingen,  Germany ,  Sept.  1997. 

13.  P.W.  Carpenter  “Status  of  transition  delay  using  compliant 
walls”.  Viscous  Drag  Reduction,  Prog,  in  Astro,  and  Aero.  123 
(edited  by  D.M.  Bushnell  and  J.N.  Hefner)  AIAA,  79-113, 1990. 

14.  M.  Gad-el-Hak  “Compliant  coatings:  The  simpler  alternative”. 
Experimental  Thermal  and  Fluid  Science  (to  appear),  1998. 

15.  P.W.  Carpenter  “Current  status  of  the  use  of  wall  compliance  for 
laminar  flow  control”,  Experimental  Thermal  and  Fluid  Science  (to7 
appear),  1998. 

16.  G.B.  Schubauer  and  H.K.  Skramstadt  “Laminar  boundary  layer 
oscillations  and  transition  on  a  flat  plate”,  NACA  Rep.  909 ,  1948. 

17.  H.  Schlichting  Boundary  Layer  Theory.  7th  Ed.,  McGraw  Hill, 
1979. 

18.  C.  Davies  and  P.W.  Carpenter  “Numerical  simulation  of  the 
evolution  of  Tollmien-Schlichting  waves  over  finite  compliant 
panels”,  J.  Fluid  Mech.  335,  361-392,  1997. 

19.  T.B.  Benjamin  “Effects  of  a  flexible  boundary  on  hydrodynamic 
stability”,  J.  Fluid  Mech.  9,  513-532, 1960. 


187 


20.  M.T.  Landahl  “On  the  stability  of  a  laminar  incompressible 
boundary  layer  over  a  flexible  surface”,  /.  Fluid  Mech.  13,  609-632, 
1962. 

21.  C.  Davies  and  P.W.  Carpenter  “Instabilities  in  a  plane  channel 
flow  between  compliant  walls”,  J.  Fluid  Mech .  352,  205-243. 

22.  K.S.  Yeo  “The  stability  of  boundary  layer  flow  over  single-  and 
multi-layer  viscoelastic  walls”,  J.  Fluid  Mech.  196,  359-408,  1988. 

23.  A.E.  Dixon,  A.D.  Lucey  and  P.W.  Carpenter  “Optimization  of 
viscoelastic  compliant  walls  for  transition  delay”,  AIAA  J.  32,  256- 
267,  1994. 

24.  P.W.  Carpenter  and  J.S.B.  Gajjar  “A  general  theory  for  two-  and 
three-dimensional  wall-mode  instabilities  over  isotropic  and 
anisotropic  compliant  walls”,  Theor.  Comp.  Fluid  Dynamics  1,  349- 
378,  1990. 

25.  M.  Gad-el-Hak,  R.F.  Blackwelder  and  J.J.  Riley  “On  the 
interaction  of  compliant  coatings  with  boundary  layer  flows”,  J .  Fluid 
Mech.  140,  257-280,  1984. 

26.  M.  Gad-el-Hak  “The  response  of  elastic  and  viscoelastic  surfaces 
to  a  turbulent  boundary  layer”,  J.  Applied  Mech  53,  206-212,  1986. 

27.  A.D.  Lucey  and  P.W.  Carpenter  “A  numerical  simulation  of  the 
interaction  of  a  compliant  wall  and  inviscid  flow”,  J.  Fluid  Mech. 
234,  121-146,  1992. 

28.  K.S.  Yeo,  B.C.  Khoo  and  H.Z.  Zhao  “The  absolute  instability  of 
boundary-layer  flow  over  viscoelastic  walls”,  Theor.  Comp.  Fluid 
Dynamics  8,  237-252,  1996. 

29.  J.H.  Duncan,  A.M.  Waxman  and  M.P.  Tulin.  “The  dynamics  of 
waves  at  the  interface  between  a  visco-elastic  coating  and  a  fluid 
flow”,  J.  Fluid  Mech.  158,  177-197,  1984. 

30.  A.D.  Lucey,  G.J.  Cafolla  and  P.W.  Carpenter  “Numerical 
simulation  of  a  boundary-layer  flow  interacting  with  a  passive 
compliant  boundary”,  Lecture  Notes  in  Physics  490,  406-41 1,  1997. 

31.  P.W.  Carpenter  “The  optimization  of  multiple-panel  compliant 
walls  for  delay  of  laminar-turbulent  transition”,  AIAA  J  31,  1187- 
1188,  1993. 

32.  A.J.  Cooper  and  P.W.  Carpenter  “The  effect  of  wall  compliance 
on  inflexion  point  instability  in  boundary  layers”,  Phys.  of  Fluids  9, 
468-470,  1997. 

33.  R.J.  Lingwood  “Absolute  instability  of  the  boundary  layer  on  a 
rotating  disk”,./  Fluid  Mech.  299,  373-405,  1995. 

34.  R.J.  Lingwood  “An  experimental  study  of  absolute  instability  of 
the  rotating-disk  boundary-layer  flow  ”,  J.  Fluid  Mech.  314,  373-405, 
1996. 

35.  R.J.  Lingwood  “Absolute  instability  of  the  Ekman  layer  and 
related  rotating  flows”,  J.  Fluid  Mech.  331,  405-428,  1997. 

36.  R.W.  Metcalfe,  F.  Battistoni,  J.  Ekeroot  and  S.  A.  Orszag 
“Evolution  of  boundary  layer  flow  over  a  compliant  wall  during 
transition  to  turbulence”,  Boundary  Layer  Transition  and  Control, 
Cambridge,  UK,  Royal  Aero.  Soc.,  36.1-36.14,  1991. 

37.  L.  Sirovich  and  S.  Karlsson  “Turbulent  drag  reduction  by  passive 
mechanisms”,  Nature  388,  753-755,  1997. 


188 


RECENT  DEVELOPMENTS  IN  INTERFERENCE  ANALYSIS 
OF  COMPLIANT  BOUNDARY  ACTION  ON  NEAR  -  WALL  TURBULENCE 


Boris.N.  Semenov  &  Alena. V.  Semenova 
Institute  of  Thermophysics,  Siberian  Branch  of  Russian  Academy  of  Sciences, 
Prospekt  Ac.  Lavrentyev,  1,  Novosibirsk,  630090,  Russia 
irena@hy  dr  o  .nsc.ru . 


Abstract  -  The  interference  form  of  the  compliant  boundary  action  is  analysed  on  the  base  of  linear  harmonic  solution,  for  viscous  sublayer  of 
turbulent  near- wall  flow.  This  action  can.  lead  to  decrease  or  to  increase  of  turbulence  production,  (accordingly,  of  turbulent  friction. and 
noise),  depending  on.the  vibrational  characteristics  of  flowed  surface.  The  phase-frequency  region  of  positive  action  -  PFRPA  (the  turbulence 
production,  decrease)  of  compliant  boundaiy  is  determined.  The  main. result  of  these  calculations  is  the  prognostication,  of  the  necessary 
vibrational  characteristics  of  compliant  surface.  PPRPA  was  calculated  for  boundary  layer  on.  smooth  and.  rough,  flat  plate.  Reynolds  number 
increase  from  1  million  till  200  millions  leads  to  PFRPA  decrease.  Calculations  show  the  decrease  and.  degeneration,  of  PFRPA  for  increased 
roughness.  Calculations  lead  to  the  conclusion  that  small  polymer  additives  in  a  flow  extend  PFRPA  and,  accordingly,  the  drag  reduction, 
possibilities  of  compliant  coatings.  The  same  prognosis  follows  from  PFRPA  calculations  for  compliant  coating  with  drag  reducing  riblets  on  its 
surface. 


1.  INTRODUCTION 

Two  forms  of  wave  action  of  the  viscoelastic  boundary  on. near¬ 
wall  turbulence  caused  by  specific  properties  of  compliant  coating  are 
considered  for  the  modelling  of  a  phenomenon.  Firstly,  it  is  absorbtion, 
dissipation  (inside  viscoelastic  coating)  of  the  energy  of  pressure 
fluctuations  deforming  a  wall.  This  hypothesis  was  offered  by  Kramer 
[1-3]  for  the  laminar  flow  stabilization.  That  was  used  by  Semenov  [4], 
Voropaev  and.  Babenko  [5],  Korobov  and.  Babenko  [6]  for  modelling 
the  near-wall  turbulence  transformation.  But  a  priori  it  is  clear  that  the 
Kramer  hypo  thesis  of  the  energy  absorption  can’t  explain  a  cause  of 
many  facts  of  the  turbulent  friction  increase.  And  that  compromised. the 
idea  of  drag  reduction  using  compliant  coatings.  Kulik:[7]  analysed  ,  our 
experimental  data[8]  for  turbulent  drag  decrease  and  increase  using 
one-layer  coatings  and  determined,  that  the  production  and.  dissipation 
of  turbulent  energy  in  turbulent  boundary  layer  is  greater  by  many 
times  than,  the  absorbtion.  and.  dissipation  of  fluctuation  energy  by 
viscoelastic  coating.  That  is  why,  this  (dissipative)  factor  can’t  be 
essential.  Moreover,  there  axe  experimental  data  contradicting  the 
hypothesis  of  “distributed  damping”.  The  coatings  lose  the  ability  to 
reduce  turbulent  friction  and  even  increase  it  with  the  increase  of 
energy  absorbtion  by  coating. 

Another  form  of  the  compliant  boundary  action  was  analysed  ,  by 
Semenov  [9,  4,  10]  on  the  base  of  linear  harmonic  solution. of  problem 
on  its  kinematic-dynamic  interaction  with  viscous  sublayer  of  turbulent 
near-wall  flow.  He  used,  the  near-wall  turbulence  model  of 
Stemberg[l  l].  This  simplified. linear  model  allowed  him  to  obtain  the 
solution. in  the  analytical  form.  This  is  important  for  the  analysis  of 
phenomenon  (and  . for  estimations  of  new  numerical  solutions  too).  The 
field,  of  velocity  fluctuations  as  well  as  the  Reynolds  stresses  are 
formed  as  a  result  of  superposition  of  two  waves:  1)  going  out  of 
turbulent  core,  being  powerful  stable  generator  of  long-wave 
perturbations,  and.  2)  reflexed  . from  a  wall.  Addition,  of  compliance  to 
boundary  properties  leads  to  variation,  of  amplitude  and.  phase  of  the 
induced. wave  and. respectively  to  a  change  of  interference  picture  of 
turbulence  production.  Its  action,  can  lead  to  decrease  or  increase  of 
turbulent  stresses  in  dependence  upon  the  wave  properties  of  flowed  , 
surface.  The  comparison  with,  the  experimental  data  testified  to  the 
validity  of  the  interference  approach.  [7].  That  is  why,  the  term 
“interference  compliant  coatings”  should  be  used,  unstead,  of  the  term 
“damping  coatings”. 

The  next  solutions  (in.  interference  theory)  were  obtained  by 
Skripatchev  [12,  13]  for  the  near- wall  turbulence  model  of  Schubert  & 
Corcos  [14],  by  Trifonov  [15,  16]  and.Kereyko  [7]  for  monoharmonic 
model  of  Goldshtik  .&  Shtem  [18].  Voropaev  &  Popkov  [19]  used  the 
model  of  Sternberg  [11]  for  consideration,  of  near- wall  turbulence  for 
coatings  deformed  in  all  directions. 

Alas!  Some  scientists  continue  wasting  their  time  on. calculations 
of  dissipative  action  of  compliant  coatings  in  turbulent  flows  still.  And. 
unfortunately,  even,  the  last  review  (Gad-el-Hak  [20])  contains  an. 
information  about  these  investigations  without  a  criticism..  So  here  it  is 
necessary  to  consider  the  main. difference  in. possibilities  of  two  forms 
of  compliant  surface  action  again  in  spite  of  repeated  former 
publications  [21-23]. 

Real  isotropic  compliant  coatings  can  change  mainly  the  normal 
(to  a  wall)  velocity  component  0  .  Longitudinal  (  U  )  and  transversal 
(  W)  components  can  be  changed  by  compliant  surface  a  little.  So  the 


possible  direct  variation,  of  turbulent  energy  balance  is  very 
small:  A  <,/')/((, r)  +  (L.=>+(„.))  « 1 ,  because 

.  The  interference  action,  leads  to  the 
variation  of  the  Reynolds  stress  production 

A  (-p  (uV^=A^~p(uf  (vf  R^  ,  where 


p  is  the  density  of  fluid.  Here  both  U  and  correlation  coefficient 
Ruv  can  be  changed,  by  compliant  surface.  So  the  possible  variation. 


A(uu)  A  Ivf  M 

can  be  enough  great:  A  »  *  &  — ' — L—  + - - 

(MU)  (of  ^ 


The  analogous  conclusion  follows  from  estimations  for 
anisotropic  coatings.  In.  this  case  longitudinal  and.  normal  components 
of  velocity  fluctuation  . of  surface  can  have  identical  levels.  And  so 


2  A  (^2>/^«2>  +  2>+<w2  ))<«!  but 


A(uv)  A(u)^ 

W =  (»’>  + 


,  i.e.  the  possible 


variation  of  Reynolds  stress  ean.be  larger  for  small  as  before  variation 
of  turbulent  energy  balance. 

Thus  the  main. factor  of  compliant  surface  action  on.  near-wall 
turbulence  isn’t  an  absorption,  of  turbulent  energy  by  viscoelastic 
coating  but  it  is  the  change  of  Reynolds  stress  production  determined, 
from  the  interference  theory. 


ILTURBUUENCE  MANAGEMENT  FOR  DRAG  REDUCTION 

Turbulence  management  is  a  total  problem  of  investigations  of 
well-known  methods  of  drag  reduction  using  polymeric  additives,  gas 
microbubbles,  compliant  coatings,  riblets.  And  here  it  is  important  to 
determine  the  main  aim  of  this  management. 

It  is  known  from  the  analysis  of  energy  balances  for  turbulent 
flows  on  smooth  plate  and  in  pipes  [24]  that  turbulence  production  is 
the  greatest  part  of  friction  work:  It  is  possible  to  suppose  that  it  is  an. 
universal  property  of  all  near-wall  turbulent  flows  and  that  it  is  right  for 
turbulent  drag  reduction* 

Calculations  of  ratio  (is  )  of  turbulence  production,  to  friction, 
work  were  carried  . out  for  a  check-up  of  this  hypothesis  according  to: 


„  1  dU 


(i) 


Where  U0  is  the  mam-stream  velocity  or  the  velocity  on.  the  axis, 
U (y)  -the  mean  velocity  profile,  T  w  -  the  friction  stress  on  a 


189 


wall.  It  is  known.  [24]  that  the  total  shear  stress  is  constant  for  flows  in  pipes 
and  in  near- wall  region  of  turbulent  boundary  layer,  i.e. 


/  V  dU 

-p(uo)+pv— =  r„ 


.  So  it  is  possible  to  write  (1)  in.  universal 


coordinates  (  y+  =  yod  /  V  ,  U+  -U fvd>  where  the  friction  velocity 
Dd  =  (r  /  pf  and  the  viscous  scale  v!  vd  are  used.  in.  order  to  obtain 
non-dimensional  values,  p  and  V  -  density  and  kinematic  viscosity  of 
fluid)  [24]: 


■y.\ 


dU+)dU+ 


dy*  )  df 


dy+ 


(2) 


Calculations  were  carried  out  for  different  efficiency  of  drag  reduction 
^  =  \  —  xjx  w  to  ¥  =0.6.  These  values  are  observed,  in. tests  for  flows 


with  polymeric  additives.  Velocity  profiles  are  described  below  -  in  part 
Y3.  Here  the  pipe  flow  with.  R+  =5000  for  ¥  =0  is  considered,  as  an. 
example  (2 R  is  the  pipe  diameter,  R+  =  Rvd  /  V  and  R+ = 


5000  (1  —  VP)  $  for  drag  reduction).  The  results  are  shown  in.  Table  I  and  . 
in  Figures  1,2. 


¥ 

0 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.70 

0.68 

0.66 

0.64 

0.62 

0.60 

0.58 

Table  I.  The  ratio  of  total  turbulent  energy  production  to  friction  work  for 
different  efficiencies  of  drag  reduction 


And  so  the  quota  of  turbulence  production  in.  sp ended,  energy  (or 
friction  work)  decreases  for  drag  reduction,  efficiency  increase  as 
E  (R)  =  0.70-0.2  ¥ . 


Figure  1.  Calculated  dependence  (2)  of  turbulent  energy  production,  on.  the 
distance  from  a  wall:  (1)¥  =  0,  (2)  ¥  =  0.1,  (3)  ¥  =  0.2,  (4)  ¥=0.3, 
(5)  ¥  =  0.4,  (6)  ¥=0.5,  (7)  ¥  =  0.6 

Here  (in.  Figure  1)  all  lines  have  the  crossing  point  about  y+  =  400 

and  is  =  0.465.  So  it  is  possible  to  use  the  region  preceding  this  point  for 
estimations  of  drag  reduction  depending  on  turbulence  production 
decrease. 

According  to  data  in. Figure  2,  the  quota  of  region,  between,  a  wall 
andy  =  400  in  total  turbulent  energy  production,  increases  for  (frag 

reduction,  efficiency  increase  from  E/E(R)  =  0.66  at  ¥  =0  to  E/E(R)  = 
0.79  at  ¥  =0.6. 

Conclusions: 

-  Directly  proportional  cross-correlation  between  the  wall  friction  ,  and  the 
turbulence  production  exists. 

-  It  is  right  for  drag  reduction  0  <¥  <  0.6  that  the  turbulence  production. is 
the  main  and  stable  quota  in  spended  energy. 


-  The  main  aim  of  turbulence  management  for  achievement  of  drag 
reduction  is  the  decrease  of  turbulence  production. 


Figure  2.  The  quota  of  region  between  a  wall  and  y+  in  .  the  total  turbulent 
energy  production  .(from  a  wall  to  R+  ) 

III.  INTERFERENCE  ANALYSIS 

The  existing  analysis  was  elaborated,  on.  the  base  of  theoretical 
solutions  determining  1)  the  interference  effect  of  compliant  boundary  on. 
near-wall  turbulence  [9]  and.  2)  the  correlation,  of  oscillation 
characteristics  of  compliant  boundary  with,  viscoelastic  properties  of 
materials  for  some  scheme  of  real  *  isotropic  coatings  [10,  25].  Here  the 
first  problem  is  considered  mainly. 

According  to  the  interference  theory  [9,  10,  21,  26]  the  main, 
modelling  parameter  is  the  dimensionless  complex  compliance  of  boundary 

lTexp(z'0)  where  the  module  is  n  =  pv  iflvCi)9  argument  0  is  the 

phase  of  the  boundary  displacement  relative  to  the  turbulent  pressure 
fluctuation.  Here  Cd  =CQIKd;  C0i s  the' equilibrium  stiffriess  and.  Kd  is 
the  dynamic  coefficient  of  coating  oscillation,  i.e.  the  ratio  of  amplitude  of 
forced  . oscillations  at  frequency  CO  =  2  71  f  to  the  displacement  for  static 

loading  ( (0  -  0 ),  where  (0  is  the  angular  frequency  of  pressure 
fluctuation  acting  on  the  boundary.  In  practice  it  is  more  convenient  to 
consider  an  opposite  dimensionless  parameter,  called  the  complex  dynamic 
stiffness  ^  •exp(i6>)’  where. ^=l/n. 

For  correct  theoretical  consideration  of  this  problem  two  conditions  in 
the  modelling  and.  selection  of  oscillation  characteristics  of  compliant 
boundary  for  drag  reduction,  are  required.  The  aperiodicity  of  turbulent 
fluctuations  and  their  wide  spectrum  lead,  to  the  first  condition,  that  the 
coatings  shouldnot  have  any  free  vibrations.  Only  this  approach,  permits  to 
obtain  a  single-valued  solution  of  this  problem.  In.practice,  one  can.  assume 
a  sufficiently  rapid  damping  of  the  free  vibrations. 

The  second,  logical  condition. imposes  restriction,  on.  the  compliance 
module  following  from  the  requirement  of  hydraulic  smoothness  of  an 
oscillating  surface.  This  restriction  results  in  a  necessary  condition  for  the 
considered,  problem  of  interaction  between,  compliant  boundary  and. 
viscous  sublayer  since  the  viscous  sublayer  exists  only  over  a  smooth.wall. 
The  analysis  of  experimental  data  [4]  has  shown  that  this  condition 
determines  the  limiting  compliance  values,  so  the  required. stiffness  is  given, 
by 

Q  >  0.007pf7oReou3/  v  (3) 

The  Reynolds  number  Re0  is  based.on  the  distance  from  the  nosing  edge  to 
the  compliant  coating  beginning  xQ  •  For  large  Reynolds  numbers  the 
above  condition  will  become 

Q  >  0.003p  C/oReo°  21/  v  (3a) 

The  obtained,  solution. [9]  shows  that  variation  of  Reynolds  stress  in. 
near-wall  region  by  compliant  surface  depends  on. 


*  Now  some  researchers  try  to  prepare  anisotropic  coatings.  But  here 
technological  difficulties  are  very  great.  And  they  were  not  overcome  still. 


190 


complex  compliance  and.  distance  y  from  a  wall.  So  it  was  necessary  to 
determine  an  integral  characteristic  of  compliant  surface  action  in. the  full 
near-wall  region.  According  to  considerations  described  .in.  section.  II,  the 
turbulence  production  was  selected,  as  a  criterion,  of  compliant  wall 
action.  However  it  is  possible  to  calculate  Reynolds  stresses  only  Tory  less 
then  limited  . ordinate  yVm  ,  determined  . according  to  the  restrictions  of  the 

theoretical  model  of  Sternberg  [11].  The  wall  influence  is  observed,  only 
for  short  distance  from  a  wall:  for  y  <  l,  but  the  main  problem  of  these 
investigations  is  exactly  the  study  of  wall  action.  There  /  is  called,  the 
dynamic  viscous  sublayer  thickness  [11],  determined. as: 

i*5fcf/v y*  (4) 

And.  so  everything  an.be  OK  if  the  solved,  problem  is  restricted: 

-  The  turbulence  production,  for  different  frequencies  must  be 
integrated . for  0  <y  <  /(/)<  yhm  •  This  idea  can  be  realized,  by  a 

restriction  of  low  frequency  considered  in. this  analysis. 

-  Only  the  change  of  turbulence  production,  by  compliant  surface 
action  (but  not  the  turbulence  production  itself)  is  considered  here. 

-  The  analysis  is  carried  out  at  abscissa  x0  of  the  compliant  coating 

beginning  since  used. parameters  (  the  mean  velocity  profile  U(y),  the 
ratio  of  transversal  and.  longitudinal  wave  numbers  kzJkx ,  the 

convection. velocity  \J  )  can.be  determined  from  well-known, 
experiments  on  a  rigid  surface. 

-  The  calculations  are  carried,  out  separately  for  every  frequency 
without  a  generalization,  in.  all  frequency  region,  that  permits  to 
except  the  inherent  (in.  Sternberg  model  [1.1])  mistake  in  frequency 
spectrum  determination. 


21.6;  (\)u*  =16  (  -exp (-7* /16))  (2)  U*  =  y*  . 


(3)  Phase  characteristic  of  tested,  coating  [25]:  Y  =  42%,  Re  -  (1.5- 
5.3)106,  U0  =  5.1  m/s,  a>o  =  3500  I/s,  „/  ^  =  1.3  ±  0.3. 

The  positive  effect  of  compliant  surface  on.  turbulent  friction,  and 
noise  (i.e.  their  decrease)  is  connected,  with,  the  decrease  of  turbulence 
production  that  was  considered,  above  -in  Section.il.  So  for  the  fixed 
frequency/ the  turbulence  production  change  should.be: 


Here,  index  */”  shows  the  belonging  only  to  the  considered,  frequency, 
index  “c  “corresponds  to  the  compliant  surface  action.  The  interference 
action  for  the  fixed'  frequency /is  neutral  ( y =  0)  if  this  integral  is  equal 

to  zero.  In  this  (neutral)  case  the  dependence  of  phase  delay  0  on 


frequency  is  independent  on. the  compliance  module.  Two  examples  of 
the  neutral  line  are  shown,  in  .  Figure  3  (lines  1,  2).  The  region,  above  the 
neutral  line  corresponds  to  turbulence  production,  decrease  ( >  0,  i.e. 

positive  action,  of  compliance)  below  -  to  an.  increase  ( <  0,  i.e. 

negative  action. of  compliance). 

One  calculated,  variant  corresponds  to  the  linear  profile  of  mean 
velocity,  other  variant  -  to  velocity  profile  written. by  Schubert  &  Corcos 
[14]  with.  good,  accuracy  for  turbulent  flow  near  smooth,  hard  wall  at 

y+  <  50.  These  examples  demonstrate  the  importance  of  accurate 

description  of  velocity  profile.  They  show  also  that  the  profile 
linearization,  increases  the  phase-frequency  region,  of  positive  action 
(PFRPA).  So  the  second,  calculated,  variant  shows  a  possible  way  of 
searches  of  new  conditions  for  drag  reduction. 

The  first  calculated,  variant  was  used,  for  the  choice  of  phase- 
frequency  conditions  on  the  compliant  boundary  for  drag  reduction.  It  is 

shown,  that  in.  the  region.  ID'2  <71  fv  jy  \  <  0.2  a  tongue-like 

extension  of  positive  action  region  is  observed.  It  is  important  to  note  that 
this  is  the  region  of  the  main  production  of  Reynolds  stresses  according  to 
experimental  investigations  of  near-wall  turbulence  [24].  Therefore,  in. 
order  to  obtain  the  turbulent  drag  reduction,  it  is  necessary  to  find,  the 
phase-frequency  characteristics  of  compliant  coatings  within,  this  zone 
above  the  neutral  line.  This  is  the  third,  condition,  for  turbulent  drag 
reduction.  It  was  written  for  the  choice  of  the  natural  frequency  /  [25]: 

0.02  <  n  f0v  /V  l  <0.06  (.6) 

This  condltion.was  approved.  [25]  with. the  use  of  experimental  data  of 
Kramer  [2],  Blick.et  al.  [27]  and  Semenov  [25].  One  example  from  [25] 
is  shown,  in  Figure  3. 

Both  this  comparison,  and  the  prognostication,  and  searches  of 
necessary  viscoelastic  materials  required,  to  elaborate  some  methods  of 
calculation. of  correlation  between  oscillation  characteristics  of  compliant 
surface  and  viscoelastic  properties  of  materials  [21,  25,  28],  to  create  the 
necessary  equipment  and.  the  experimental  methodology  for  investigations 
of  viscoelastic  properties  of  materials  [29,  30,  31]. 


Figure  4.  Required .  elastic  module  {£[  -  E^  )  of  porous  impregnated  , 
coating  for  drag  reduction  in  water,  jc0=  0.2  m,  V  =  10'6  m2  /s 

Taking  into  account  these  additional  remarks,  it  is  possible  to  use  the 
design  and  manufacturing  process  of  compliant  coating  for  turbulent  drag 
reduction,  suggested,  by  Semenov  [26,  32].  Figures  4  and.  5  show  the 
predicted. results  for  drag  reduction. in  water  (details  were  described,  in. 
[28]).  The  density  of  porous  impregnated,  material  must  be  similar  to  that 
of  the  flow  (since  open. pores  of  material  are  connected,  with  flow)  i.e. 
p  o  =  p  =  103  kg/m3  .  Poisson’s  ratio  for  elastic  porous  materials 

p0  «  0.5  .  The  value  of  nf(O0  depends  on. 


191 


size  of  pores  (  n  is  the  damping  factor  of  free  vibration s,  £>0  is  the 
natural  angular  frequency  of  the  first  harmonic)  but  it  is  taken  as  ~ 
1  for  the  present  analysis.  Figure  4  shows  the  dependence  of  the  required 
elastic  modulus  E0  on. the  flow  velocity,  where  a  suitable  material  must 
have  the  elastic  module  within  the  noted  region. 


e  5.  Predicted  region,  of  turbulent  drag  reduction  in  water  for  one-layer 
smooth  coating  made  from  a  porous  viscoelastic  material  with. ventilated 
pores,  Ea=E'  “  105  ///m2,  j/0  =  0.5,  pQ=103  kg/m3,  n/co0=  U  *0  =  0.2 

m,  V  —  10'6  m2  /s 

In  Figure  5  the  required,  coating  thickness  H  is  plotted,  against  the 
flow  velocity:  As  it  is  shown  here  only  a  narrow  “wedge’  formed  from 
the  condition. (3)  (indicated .  by  the  bold  line  3)  and  the  condition.  (6) 
(indicated  by  the  usual  lines  1,  2)  will  provide  a  region,  of  turbulent  drag 
reduction.  The  above  mentioned  methodology  of  the  choice  of  compliant 
coatings  and  conditions  of  their  test  was  used.  in.  investigations  of  one- 
layer  coatings  [8,  23,  33,  34]. 

IY.  IMPROVEMENTS  OF  INTERFERENCE  THEORY 

Recently  the  interference  theory  (elaborated. in 70tfrr80th. [9,  10,  21, 
26]  )  satisfied  the  needs  of  researchers  and  engineers  since  it  gave  a 
possibility  to  find  compliant  coatings  and.  flow  conditions  for  drag 
reduction.  But  there  was  some  dissatisfaction  too  since  the  existing  theory 
didn’t  permit  to  find,  the  optimum.  And  formerly  many  questions  (about 
the  influence  of  Reynolds  number,  roughness,  pressure  gradient, 
background  turbulence  and  other)  had  not  both  a  theoretical  and 
experimental  answers.  Now  new  problems  arise  while  using  coatings 
jointly  with  other  drag  reducing  means. 

The  attempts  of  improvements  of  interference  theory  were  made 
for  a  long  time.  New  models  of  the  near-wall  turbulence  were 
considered.  But  the  use  of  Schubert  &  Corcos  model  [14]  considering  the 
full  system  of  linearized  equations  of  Navier-Stokes  didn’t  improve  the 
possibilities  of  interference  theory  [12,  13].  The  monoharmonic  model  of 
Goldshtik  &  Shtem.  [18]  can’t  give  the  right  conclusions  and 
recommendations  for  compliant  boundary  since  this  theory  considers 
unreal  structure  of  velocity  fluctuation.  (  kzfkx  -1/12  -  see  further 
Figure  8).  Now  the  hope  of  the  development  of  interference  theory  is 
connected .  with  the  new  wave  model  of  Semenov  [35]  considering 
Cauchy  problem  for  linearized  . equations  of  Navier-Stokes.  But  the  work  , 
was  only  began.  The  described,  here  improvements  of  interference 
theory  are  connected  with  more  accurate  definition  of  turbulent  flow 
parameters  used  for  calculations. 

Mean  velocity  profile. 

Formerly  the  exponential  profile  supposed  by  Schubert  &  Corcos 
[14]  was  used. for  calculations.  But  this  profile  is  correct  only  for  y+<  50 

according  to  estimations  made  by  these  authors  while  comparing  it  with 
experimental  data  of  Coles.  Now  it  is  necessary  to  extend  ,  the  region  of 
calculations  to  y  »  400  and  . to  have  a  possibility  to  take  into  account  the 

friction  increase  and  decrease  . 

The  new  profile  was  obtained,  by  growing  together  the  modified 
exponential  profile  for  near- wall  region,  with  the  logarithmic  profile  for 
turbulent  core.  This  operation  was  carried,  out  by  continuity  of 
( dUjdy*  )  and  U+(y+^-  And. so  the  new  profile  was  written.as; 

U*  =  \6A  |j-exp(V/(l6j|}]  at  0<y- 

IT  =25h.^yB  +  S+  at  y+>y+r,  (7) 

where  B  =  5.526657;  S+  and  A  depend  on. a  friction  increase  by 
surface  roughness  or  a  friction  decrease  by  drag  reducing  means. 


S+  =  0,  A  =1,  =  46.911.6  are  the  parameters  for  a  smooth 

surface  without  drag  reducing  means.  The  comparison,  (in.  Figure  6)  of 
this  profile  with  experimental  data  shows  their  good  concordance. 


Figure  6.  Comparison  of  velocity  profile,  calculated  ,  according  to  (7)  for 
near-wall  region  of  turbulent  flow  (S+  =  0,  A  =  1),  with. experimental 
data:  ^  Coles  [14],  D  Kchabakhpasheva  &  Perepelitza  [36], 

A  Poznajaja  [37],  ®  Kchabakhpasheva  &  Mikhailova  [38],  'A 

T.Mizushina  &  H.Usui  [39] 

Convection  velocity 

All  former  calculations  of  PFRPA  were  carried  out  for  the  constant 
convection. velocity  JJC  =  0&  U0  .  Our  calculations  show  the  strong 
dependence  of  PFRPA  on  variation  of  this  parameter.  So  this  parameter 
must  be  written  with  more  accurate  definition 


Figure  7.  Convection  velocity  as  a  function  of  longitudinal  wave  number. 
Line:  the  calculation,  according  to  (8). 

^  Experimental  data  of  Blake  [41] 

According  to  Bernard  .  [40]  the  convection  velocity -.determines  the 
turbulence  structure  in  .near- wall  region  of  turbulent  flows.  It  depends  on. 

wave  number  k  x  and  doesn’t  depend,  on  frequency  of  fluctuations. 

And,  may  be,  the  convection,  velocity  is  equal  to  the  velocity  of  eddy 
centre  disposed  in  turbulent  core. 

And  now  the  convection  velocity  is  calculated  as 

Uc/U0  =  ^.5ln(l/kiyB](c.fj2f  (8) 

with  the  restriction  following  from  experimental  data  of  different  authors: 
U\,  <  0.7  O0  •  Here  c-y  is  the  friction  coefficient. 


192 


C.j:  =  2rwfpU^  ,  k1  =  kxv/od  ■  According  to  formula  (8)  the  upper 
limit  is  (Jc  =  UQ  tut  in. real  calculations  (in. the  considered,  region  of 
wave  numbers)  UC<0.9U0 .  The  comparison,  (in.  Fig.  7)  of  this 

calculation  with  experimental  data  of  Blake  [41]  shows  a  suitability  of 
formula  (8). 

Velocity  fluctuation  structure. 

The  former  analysis  [10]  of  compliant  boundary  action. on  near- wall 
turbulence  has  already  showed  ,  the  importance  of  the  correct  taking  into 
account  the  velocity  fluctuation  structure,  namely  the  ratio  of  transversal 
andlongitudinal  components  of  velocity  fluctuation.  Now  this  parameter  is 
discussed  again 


Figure  8.  Dependence  of  PFRPA  of  smooth,  compliant  surface  on.  the 
velocity  fluctuation. structure  (kzJkx  ):  (1)  kz  fkx  *  0,  (2)  kzfkx  =  1/12, 

(3)  kz/kx  =  0.8,  (4)  kzfkx  =  1.0,  (5)  kzfkx  -  1.6;  Re0  =  107 

According  to  Sternberg  model  [11],  B ’y  fay  ~^z/^x  ’  ^  *s  known. 

from  tests  of  Laufer  [42]  at  y+  =  650  that  this  ratio  depends  on.  the 
dimensionless  wave  number  kx  and: varies  from  ~  0.65  for  kx  ~  5xl0‘5  to 
-2.2  for  kx  >  0.04.  The  results  of  PFRPA  calculations  for  different 
values  of  this  ratio  are  shown  ,  in  .  Figure  8.  They  demonstrate  very  strong 
dependence  of  PFRPA  on  k,x  fkx  .-It  turns  out  that  compliant  boundary 
can’t  manage  with.two-dlmensiorial  wave  fluctuations  propagating  in. the 
main. flow  direction.  (  kz/kx  «  0).  But  this  fact  can’t  worry  since  these 
fluctuations  are  absent  in  near- wall  turbulent  flows.  And  .it  shows  that  any 
theory  considering  these  fluctuations  (for  example,  jkx  =  1/12  in 
monoharmonic  theory  [18])  gives  unacceptable  solution  for  comphant 
boundary.  In.  all  calculations  authors  consider  k„  Jkx  =  1  as  the  most 
dangerous  but  real  variant. 

Y.  ON  INFLUENCE  OF  REYNOLDS  NUMBER  AND  SURFACE 
ROUGHNESS 

The  problem  on. influence  of  Reynolds  number  on  drag  reducing 
possibility  of  compliant  coatings  was  considered  ,  formerly  [28,  32].  Here 
the  solutionis  defined  more  precisely.  The  results  are  shown,  in.  Figure  9 
for  smooth  surface. 

Reynolds  number  increase  leads  to  PFRPA  decrease.  Here  it  is 
necessary  to  remind,  that  is  determined,  for  the  beginning  x0  of 
comphant  surface.  And.  these  results  show  the  requirement  to  minimize 
X0  •  And,  please,  note:  the  experimental  data  are  still  absent  for  a  check¬ 
up  of  this  prognosis,  but  they  are  very  necessary. 

All  experimental  attempts  of  drag  reduction,  using  rough,  comphant 
coatings  were  unsuecessfull  (but  systematic  investigations  of  roughness 
influence  are  still  absent).  And.  ah  researchers  try  to  minimize  the 
comphant  surface  roughness  in  spite  of  many  technological  difficulties.  So 
it  is  important  to  estimate  the  roughness  limit.  The  interference  theory 
permits  to  consider  the  influence  of  surface  roughness  for  the  transition. 


zone  of  its  values  (smooth->rough).  In  this  case  the  viscous  sublayer 
becomes  more  thin,  the  logarithmic  profile  of  mean  velocity  is  displaced 
down.  [24]. So  in.  (7):  S+  <  0,  A  <  1.  The  results  of  numerical 
investigations  of  the  dependence  of  PFRPA  on.  compliant  surface 
roughness  (see  Table  D  and. Figure  10)  lead,  to  the  conclusion,  that  the 

reasonable  limit  of  sand,  roughness  is  k*  ~  15.  A  higher  roughness 
liquidates  a  possibility  of  comphant  surface  use  for  drag  reduction. 


Figure  9.  Dependence  of  PFRPA  of  smooth  comphant  surface  on 
Reynolds’number:  (1)  Re0  =  106,  (2)  Re0=2xlO6,  (3)  Re0=4.2xlO6 
(4)Re0=lO7,  (5)Re0=2xl07,  (6)  Re0=4xlO7,  (7)  Re, -10*. 

(8)  Re0=2xlO*;  kt/kx  =  1.0 


Figure  10.  Dependence  of  PFRPA  of  compliant  surface  on  its  sand 
roughness:  (1)^<3,  (2)  k*  =  5,  (3)  £  =  10,  (4)  £  =  15, 

(5)  £  =  20,  (6)  fc*  =  25;  Re0=107;  kt/kx  =  U) 


k* 

S+ 

A 

yl 

5 

-0.55 

0.956 

43.5 

10 

-1.733 

0.860 

37.0 

15 

-2.75 

0.773 

31.1 

20 

-3.6 

0.697 

26.2 

25 

-4.35 

0.626 

21.5 

Table  n.  Parameters  for  calculation  of  mean  velocity  profile  on.  rough 
surface.  Re0  =  107. 


193 


YL  JOINT  USE  OF  COMPLIANT  SURFACE  WITH  OTHER 
DRAG  REDUCING  MEANS 


Figure  11.  Comparison  of  mean  velocity  profile  calculated  according  to 
(7)  for  near-wall  region  of  turbulent  flow  containing  drag-reducing 
polymeric  additives  with,  experimental  data 


Sign 

Refer 

'F* 

S+ 

A 

v 

Line  N 

_ 

here 

0 

0 

1 

46.9 

1 

□ 

[37] 

0.309 

2.8 

1.20 

61 

2 

ik 

[46] 

0.393 

4.8 

1.36 

72.5 

3 

2 

[45] 

0.443 

5.6 

1.42 

79 

4 

JL. 

[37] 

0.686 

14.1 

2.01 

126 

5 

Table  HI.  Data  for  figure  11. 


Figure  12.  Dependence  of  PFRPA  of  smooth,  compliant  surface  on  drag 
reduction,  using  polymer  additives:  (1)  VP=  0,  (2)  VF=0.1, 

(3)  x¥=0.2,  (4)  ¥=0.3;  Re0=6.2xl06 


¥ 

s+ 

A 

yp 

0.1 

1.462 

1.114 

55.13 

0.2 

3.190 

1.244 

64.83 

0.3 

5.277 

1.399 

76.59 

Table  IY.  Parameters  for  calculation  of  mean,  velocity  profile  on. 
smooth,  surface  inflow  with.. drag  reducing  polymeric  additives.  Re0  = 

6.2x1 06 


Figure  13.  Phase-frequency  diagram  for  compliant  surface  with. drag 
reducing  riblets:  (1)  VP=  0,  (2)  ¥=0.05,  (3)  ¥=0.1,  Re0  =  6.2xl06 


¥ 

A 

ytr 

0.05 

0.702 

1.0547 

50.86 

0.1. 

1.462 

1.114 

55.13 

Table  Y.  Parameters  for  calculation,  of  mean,  velocity  profile  on 
surface  with.. drag  reducing  riblets.  Re0"  6,2x10 

The  results  of  the  first  analysis  of  interference  model  [10] 
predicted,  an.  increase  of  PFRPA  for  the  mean,  velocity  profile 
linearization  and  induced  to  search. for  some  means  for  its  realization* 
Apparently  all  means  of  turbulent  drag  reduction  enjoy  this  action*  Two 
means  -  polymer  additives  and  riblets  are  particularly  interesting  since 
they  suppress  only  microeddy  structures  which,  are  not  subject  to 
compliant  surface  managing  long-wave  disturbances.*  So  here  it  is 
necessary  to  take  into  account  only  a  change  of  the  mean  velocity 
profiles  for  interference  analysis. 

According  to  Virk.et  al.  [44]  drag  reducing  polymeric  additives 

lead,  to  “slip”  S+  (the  logarithmic  profile  of  mean  velocity  displaces 
up)  calculated  ,  as:  £+  =  5  -  cf  R  •  So  the  viscous 

sublayer  becomes  more  thick,;  in. (7):  S+  >  0,  A  >1.  The  comparison 
(in  Figure  11)  of  experimental  data  for  mean  velocity  profiles  and.  the 
results  of  calculation  made  according  to  (7)  for  these  variants 
(described  in  Table  IK  )  shows  their  good,  concordance  for  <  0.5. 

Results  of  PFRPA  calculations  shown,  in.  Figure  12  (parameters  are 
shown  in  Table  IY)  lead. to  the  conclusion  that  small  polymer  additives 
in  a  flow  extend  . PFRPA  and  accordingly  the  drag  reduction  possibilities 
of  compliant  coatings. 

The  same  prognosis  follows  from  PFRPA  calculations  for 
compliant  coating  with  drag  reducing  riblets  on.  its  surface  (see  Figure 
13  with. Table  Y).  And,  please,  note  that  a  combination. of  compliant 
surface  and  riblets  must  be  the  fine  variant  of  passive  methods  of 
turbulence  management  realized,  without  additional  energy 
expenditure. 

ACKNOWLEDGEMENTS 

The  work  was  supported  by  the  INTAS  Research  Grant  N  94  -3737. 


*  The  first  experimental  results  of  drag  reduction,  using  compliant 
coatings  and.  polymeric  additives  jointly  showed  fine  outlooks  of  this 
study  [43]. 


194 


REFERENCES 

1.  M.O.  Kramer  “Boundary-  Layer  Stabilization,  by  Distributed. 
Damping”,  J.  Aeron.  Sci.,  1957,  24,  N6,  459-460. 

2.  M.O.  Kramer  “Boundary  Layer  Stabilization  by  Distributed. 
Damping”,  J.Amer.  Soc.  Nav.  Eng.,  1960,  72,  Nl,  25-33. 

3.  M.O.  Kramer  “Boundary  Layer  Stabilization,  by  Distributed. 
Damping”,  Nav.  Eng.  J.,  1962,  74,  N2,341-348. 

4.  BN.  Semenov  “The  Effect  of  Elastic  Covers  on.  a  Turbulent 
Boundary  Layer”,  Investigations  of  Boundary  Layer  Control 
1976,  IT  AN  SSSR,  Novosibirsk,  92-101. 

5.  G.A.  Voropaev  &  V.V.  Babenko  “The  Turbulent  Boundary  Layer 
on. Elastic  Surface”,  Hydromechanics ,  1978,  Naukova  Dumka, 
Kiev,  N3 8,  71-77. 

6.  V.I.  Korobov  &  V.V.  Babenko  “On. a  Mechanism  of  Interaction, 
of  Elastic  Wall  withFlow”,  J.  Eng.  Phys. ,  1983,  44,  N5,  730-733. 

7.  V.M.  Kulik.  “The  Analysis  of  Interaction  of  One-Layer 
Monolithic  Damping  Covers  with  Turbulent  Flow”,  J.  Eng.  Phys., 
1986,  51,  N6,  959-965. 

8 .  V.M.  Kulik,  I.S.  Poguda  &  B  N.  Semenov  “Experimental  Study  of 
the  Effect  of  One-Layer  Viscoelastic  Coatings  on. the  Turbulent 
Friction.and  Pressure  Pulsations  at  the  Wall”,/.  Eng:  Phys.,  1984, 
47,  N2, 189-196. 

9.  BJSI.  Semenov  “Interaction  of  an.  Elastic  Boundary  with,  the 
Viscous  Sublayer  of  a  Turbulent  Boundary  Layer”,  Zh.  Prikl. 
Mekh.  Tekh.  Fiz .,  1971,  N3,  58-62. 

10.  BN.  Semenov  “On.  Interferent  Form  of  the  Influence  of 
Viscoelastic  Boundary  on.  Wall  Turbulence”,  The  Influence  of 
Polymer  Additives  and  Surface  Elasticity  on  Wall  Turbulence, 
1978,  IT.  AN  SSSR,  Novosibirsk,  57-74. 

11.  J.  Sternberg  “A  Theory  for  Viscous  Sublayer  of  a  Turbulent 
Flow”,  Z  Fluid Mech.,  1962, 13,  N2,  241-271. 

12.  V.V.  Skripatchev  “The  Theoretical  Analysis  of  Viscoelastic 
Boundary  Action,  on.  Near-Wall  Turbulence”,  Proc.  Conf  on 
Drag  Reduction,  1978,  Moscow. 

13.  V.V.  Skripatchev  Sc  AP.  Teslo  “The  Drag  of  Plates  and  Tubes 
with.  Elastic  Walls”,  Hidravlika  I  Hidrotekhnika,  1983,  Naukova 
Dumka,  Kiev,  N37,  52-57. 

14.  G.  Schubert  &  G.M.  Corcos  “The  Dynamics  of  Turbulence  Near 
a  Wall  According  to  a  Linear  Model”,  /.  Fluid  Mech.,  19.67,  29, 
Nl,  113-135. 

15.  G.F.  Trifonov  “Theoretical  Investigation,  of  the  Influence  of 
Elastic  Boundary  Characteristics  on  Turbulent  Flow”,  The 

,  Influence  of  Polymer  Additives  and  Surface  Elasticity  on  Wall 
Turbulence ,  1978,  IT  AN  SSSR,  Novosibirsk,  75-85. 

16.  G.F.  Trifonov  “Self-Consistent  Model  of  Interaction,  between 
Turbulent  Flow  and  Deformable  Wall”,  Thermodynamics  of 
Turbulent  Flows,  1986,  IT  AN  SSSR,  Novosibirsk;  5-16. 

17.  G.V.  Kereyko  “Qn.an.Interaction.of  Near-Wall  Turbulence  with. 
Compliant  Surface”,  Izv.  AN  SSSR  MJG ,  1990,  N4,  67-72. 

18.  M.A.  Goldshtik.&  VN.  Shtem  “The  Monoharmonic  Theory  of 
Near- Wall  Turbulence”,  Turbulent  Flows,  1977,  Nauka,  Moscow, 
102-110. 

19.  G.A.  Voropaev  &  V.I.  Popkov  “On. an  Interaction  of  Compliant 
Surface  with. Viscous  Sublayer  of  Turbulent  Boundary  Layer”, 
Hydromechanics,  1988,  Naukova  Dumka,  Kiev,  N57,  32-36. 

20.  M.  Gad-el-Hak  “Compliant  Coatings:  One  Last  Chance?” 
Manuscript  for  the  Workshop  on  Flow  Control :  Fundamentals  and 
Practices ,  1-5  July  1996,  Corsica. 

21.  B.N.  Semenov  “On.Interference  Action.of  Viscoelastic  Boundary 
onNear-Wall  Turbulence”,  Proceedings  of  6th  Nat  Congress  on 
Theor.  and  Appl  Mech.,  1989,  Varna,  3,  330-333. 

22.  BN,  Semenov  “On.  Two  Forms  of  Action,  of  Viscoelastic 
Boundary  on  Near-Wall  Turbulence”,  Abstracts  of  3rd  European 
Turbulence  Conference,  July  1990,  Stockholm,  4.2. 

23.  V.M.  Kulik,  I.S.  Poguda  &  BN.  Semenov  “Experimental 
Investigation,  of  One-Layer  Viscoelastic  Coating  Action,  on 
Turbulent  Friction,  and  Wall  Pressure  Pulsations”,  Recent 
Developments  in  Turbulence  Management,  1991,  Kluwer,  236- 
289. 

24.  J.O.  Hinze  “Turbulence”,  1959,  Me  Graw-Hill. 

25.  BN.  Semenov  “Analysis  of  Deformation  Characteristics  of 
Viscoelastic  Coatings”,  Hydrodynamics  and  Acoustics  of  Near- 
Wall  and  Free  Flows ,  1981,  Nauka,  Novosibirsk,  57-76. 


26.  B.N.  Semenov  “On.  Conditions  of  Modelling  and'  Choice  of 
Viscoelastic  Coatings  for  Drag  Reduction”,  Recent  Developments 
in  Turbulence  Management,  1991,  Kluwer,  241-262. 

27.  E.F.  Blick,  R.R.  Walters,  R.  Smith. &  H.Chu  “Compliant  Coating 
Skin  Friction  Experiments”,  AIAA  Paper ,  1969,  N69-165. 

28.  B.N.  Semenov  “Analysis  of  Four  Types  of  Viscoelastic  Coating 
for  Turbulent  Drag  Reduction”,  Emerging  Techniques  in  Drag 
Reduction,  1996,  MEP,  London  and  Bury  St.  Edmunds,  187-206. 

29.  V.M.  Kulik.  &  BN.  Semenov  “On  the  Certification,  of  Wave 
Properties  of  Viscoelastic  Coatings  Affecting  Wall  Turbulence”, 
Hydrodynamic  Flows  and  Wave  Processes,  1983,  IT.  AN  SSSR, 
Novosibirsk,  117-129. 

30.  V.M.  Kulik.  &  BN.  Semenov  “Two -Parametric  Technique  of 
Measuring  of  the  Viscoelastic  Properties  of  Polymer  Materials”, 
Metrologiya,  1986,  N4,  32-38. 

31.  V.M,  Kuiik  .  &  BN.  Semenov  “The  Measurement  of  Dynamic 
Properties  of  Viscoelastic  Materials  for  Turbulent  Drag 
Reduction”,  Emerging  Techniques  in  Drag  Reduction,  1996,  MEP, 
London  and  Bury  St.  Edmunds,  207 -218. 

32.  B.N.  Semenov  “On.  the  Properties  of  Viscoelastic  Boundary  for 
Turbulent  Friction. Reduction”,  Sib.  Fiz.  Tech.  Zn.,  1993,  Nl,  63- 
73. 

33.  K.-S.  Choi,  X.Yang,  B.R  Clayton,  T.  Glover,  M,  Atlar,  BN. 
Semenov  &  V.M.  Kulik.  “Experiments  on.  Turbulent  Drag 
Reduction.  Using  Compliant  Surface”,  Proceedings  of  1st  Int. 
Conference  on  Flow  Interaction,  1994,  Hong  Kong,  543-546. 

34.  K.-S.  Choi,  X.Yang,  B.R  Clayton,  T.  Glover,  M.  Atlar,  BN. 
Semenov  &  V.M.  Kulik  “Turbulent  Drag  Reduction  Using 
Compliant  Surfaces”,  Proceedings  of  Royal  Society,  A,  1997,  453, 
2229-2240. 

35.  B.N.  Semenov  “Joint  Use  of  Laser  Anemometry  in.a  Flow  and 
Measurements  on.  Compliant  Wall”,  Proceedings  of  7th  Int. 
Conference:  Laser  Anemometry,  Advances  and  Applications , 
1997,  Karlsruhe,  141-148. 

36.  E.M.  Khabakhpasheva  &  B.V.  Perepelitza  “On.  Peculiarities  of 
Near- Wall  Turbulence  in.  Water  Flows  with  Polymeric 
Additives”,/.  Eng- Phys.,  1970, 18,  N6,  1094-1097. 

37.  N.G.  Poznjaja  “A  Model  of  Near- Wall  Turbulent  Flow  of 
Polymeric  Solutions  of  Small  Concentrations”,  Turbulent  Flows, 
1974,  Nauka,  Moscow,  158-165. 

38.  E.M.  Khabakhpasheva  &  E.S.  Mikhailova  “The  Turbulence 
Investigation,  in.  a  Flat  Water  Channel  Flow”,  Experimental 
Investigation  of  the  Near-Wall  Turbulence  and  Viscous  Sublayer 
Structure,  1976,  IT  AN  SSSR,  Novosibirsk;  33-57, 

39.  T,  Mizushina  &  H.  Usui  “Reduction,  of  Eddy  Diffusion  for 
Momentum  and.  Heat  in.  Viscoelastic  Fluid.  Flow  in.  a  Circular 
Tube”,  The  Physics  of  Fluids,  1977,  20,  N10,  pt  II,  S100-S108. 

40.  P.  Bernard.  “Etude  Tridimensionelle  de  la  Sous-Couche  Visque 
Use  Dans  une  Veine  Rectangulaire  par  des  Mesures  de  Transfert 
de  Matiere  inParoi”,  Int.  J.  Heat  and  Mass  Transfer,  1973,  16,  Nl 
129-144. 

41.  W.K.  Blake  “Turbulent  Boundary-Layer  Wall-Pressure 
Fluctuations  on.Smooth.and. Rough.  Walls”,  /.  Fluid  Mech.,  1970, 
44,  N4,  637-660. 

42.  J.  Laufer  “The  Structure  of  Turbulence  in. Fully  Developed.  Pipe 
Flow”,  1954,  NASA  Rep.  1174. 

43.  B.N.  Semenov,  V.M.  Kulik,  V.A.  Lopyrev,  B.P.  Mironov,  I.S. 
Poguda  &  T.I.  Yushmanova  “The  Combined  Effect  of  Small 
Quantities  of  Polymeric  Additives  and  .  Pliability  of  the  Wall  on 
Friction  in.  Turbulent  Flow”,  Fluid  Mech.  -  Soviet  Res.,  1985,14, 
Nl,  143-145. 

44.  P.S.  Virk,E,W.  Merrill,  H.S.  Miskley,  K.A.  Smith.&  E.L.  Mollo- 
Christensen.  “The  Toms  Phenomenon:  Turbulent  Pipe  Flow  of 
Dilute  Polymeric  Solutions”,  J.  Fluid  Mech.,  1967,  30,  N2,  305- 
328. 

45.  E.M.  Khabakhpasheva  &  B.V.  Perepelitza  “Fields  of  Velocities 
and  Turbulent  Fluctuations  for  Small  High-Molecular  Additives  to 
Water”,  /  Eng.  Phys.,  1968, 14,  N4,  598-601. 

46.  E.S.  Mikhailova  &  E.M.  Khabakhpasheva  “Near-Wall 
Turbulence  for  Flow  of  PAA  Dilute  Solution”,  Experimental 
Investigation  of  the  Near-Wall  Turbulence  and  Viscous  Sublayer 
Structure,  1976,  IT.  AN  SSSR,  Novosibirsk,  58-68. 


195 


COMPLIANT  COATINGS:  THE  SIMPLER  ALTERNATIVE 


Mohamed  Gad-el- Hak 

Department  of  Aerospace  &  Mechanical  Engineering 
University  of  Notre  Dame 
Notre  Dame,  IN  46556 
Mohamed.Gad-el-Hak:l  @nd.edu 


Abstract 

Boundary  layer  manipulation  via  reactive  control  strategies  is 
now  in  vogue.  The  payoffs  are  handsome  but  the  difficulties  involved 
are  daunting.  There  are  however  much  simpler  alternatives  to  this 
kind  of  sophisticated  flow  alteration  devices  and  the  present  article 
discusses  one  such  alternative:  passive  compliant  walls.  Much  of  the 
details,  even  the  list  of  cited  references,  are  omitted  here  because  of 
space  limitations  and  the  reader  is  referred  to  the  paper  in  Applied 
Mechanics  Reviews ,  vol.  49,  no.  10,  part  2,  pp.  S147-S157,  1996. 


1  Introduction 

A  compliant  wall,  as  opposed  to  a  rigid  one,  offers  the  potential 
for  favorable  interference  with  a  wall-bounded  flow.  Laminar-to- 
turbulence  transition  may  be  delayed  or  advanced,  boundary  layer 
separation  may  be  prevented  or  triggered,  flow- induced  noise  may 
be  modulated,  and  skin-friction  drag  in  both  laminar  and  turbulent 
flows  may  be  altered.  The  challenge  is  of  course  to  find  a  coating 
with  the  right  physical  properties  to  achieve  a  desired  goal. 

Passive  compliant  coatings  have  been  around  long  before  reac¬ 
tive  flow  control  was  even  contemplated.  For  better  or  worse,  hy- 
drodynamically  speaking,  the  epidermis  of  most  nekton  is  pliable  at 
their  typical  swimming  speeds.  For  close  to  half  a  century  the  sci¬ 
ence  and  technology  of  compliant  coatings  has  fascinated,  frustrated 
and  occasionally  gratified  Homo  sapiens  searching  for  methods  to 
delay  Iaminar-to-turbulence  transition,  to  reduce  skin-friction  drag 
in  turbulent  wall-bounded  flows,  to  quell  vibrations,  and  to  sup¬ 
press  flow-induced  noise.  Compliant  coatings  offer  a  rather  simple 
method  to  delay  laminar-to-turbulence  transition  as  well  as  to  in¬ 
teract  favorably  with  a  turbulent  wall-bounded  flow.  In  its  simplest 
form,  the  technique  is  passive,  relatively  easy  to  apply  to  an  existing 
vehicle  or  device,  and  perhaps  not  too  expensive.  Unlike  other  drag 
reducing  techniques  such  as  suction,  injection,  polymer  or  particle 
additives,  passive  compliant  coatings  do  not  require  slots,  ducts  or 
internal  equipment  of  any  kind.  Aside  from  reducing  drag,  other 
reasons  for  the  perennial  interest  in  studying  compliant  coatings 
are  their  many  other  useful  applications,  for  example  as  sound  ab¬ 
sorbent  materials  in  noisy  flow-carrying  ducts  in  aero-engines,  and 
as  flexible  surfaces  to  coat  naval  vessels  for  the  purposes  of  shielding 
their  sonar  arrays  from  the  sound  generated  by  the  boundary-layer 
pressure  fluctuations  and  of  reducing  the  efficiency  of  their  vibrating 
metal  hulls  as  sound  radiators. 

The  original  interest  in  the  field  was  spurred  by  the  experiments 
of  Kramer  (1957)  who  demonstrated  a  compliant  coating  design 
based  on  dolphin’s  epidermis  and  claimed  substantial  transition 
delay  and  drag  reduction  in  hydrodynamic  flows.  Those  experi¬ 
ments  were  conducted  in  the  seemingly  less-than-ideal  environment 
of  Long  Beach  Harbor,  California.  Subsequent  laboratory  attempts 
to  substantiate  Kramer’s  results  failed,  and  the  initial  interest  in  the 
idea  fizzled.  A  similar  bout  of  excitement  and  frustration  that  dealt 
mostly  with  the  reduction  of  skin-friction  drag  in  turbulent  flows  for 
aeronautical  applications  followed.  Those  results  were  summarized 
in  the  comprehensive  review  by  Bushnell  et  al.  (1977).  During  the 
early  1980s,  interest  in  the  subject  was  rejuvenated  mostly  due  to 


modest  investment  in  resources  by  the  Office  of  Naval  Research  in 
the  United  States  and  the  Procurement  Executive  of  the  Ministry 
of  Defence  in  Great  Britain.  Significant  advances  were  made  during 
this  period  in  numerical  and  analytical  methods  to  solve  the  coupled 
fluid-structure  problem.  New  experimental  tools  were  developed  to 
measure  the  minute  yet  important  surface  deformation  caused  by 
the  unsteady  fluid  forces.  Coherent  structures  in  turbulent  wall- 
bounded  flows  were  routinely  identified,  and  their  modulation  by 
the  surface  compliance  could  readily  be  quantified. 

Careful  analyses  by  Carpenter  and  Garrad  (1985)  and  Willis 
(1986)  as  well  as  the  well-controlled  experiments  reported  by  Daniel 
et  al.  (1987)  and  Gaster  (1988)  have,  for  the  first  time,  provided  di¬ 
rect  confirmation  of  the  transition-delaying  potential  of  compliant 
coatings,  convincingly  made  a  case  for  the  validity  of  Kramer’s  orig¬ 
inal  claims,  and  offered  a  plausible  explanation  for  the  failure  of  the 
subsequent  laboratory  experiments.  There  is  little  doubt  now  that 
compliant  coatings  can  be  rationally  designed  to  delay  transition 
and  to  suppress  noise  on  marine  vehicles  and  other  practical  hy¬ 
drodynamic  devices.  Transition  Reynolds  numbers  that  exceed  by 
an  order  of  magnitude  those  on  rigid-surface  boundary  layers  can 
be  readily  achieved.  Although  the  number  of  active  researchers  in 
the  field  continues  to  dwindle,  new  promising  results  are  being  pro¬ 
duced.  Recent  theoretical  work  by  Davies  and  Carpenter  (1997a) 
and  Carpenter  (1998)  indicates  that  transition  to  turbulence  can  be 
delayed  indefinitely,  at  least  in  principle,  provided  that  optimized 
multiple-panel  compliant  walls  are  used  and  that  the  ffeestream  is 
a  low-disturbance  environment.  There  is  also  recent  evidence  of  fa¬ 
vorable  interactions  of  compliant  coatings  even  for  air  flows  (Lee  et 
al.,  1995)  and  even  for  turbulent  boundary  layers  (Lee  et  al.,  1993a; 
Choi  et  al.,  1997). 

The  present  article  emphasizes  the  significant  compliant  coat¬ 
ing  research  that  took  place  during  the  last  10-15  years  and  sug¬ 
gests  avenues  for  future  research.  The  reader  is  referred  to  prior 
reviews  for  more  classical  work  on  the  subject,  for  example  those 
by  Bushnell  et  al.  (1977),  Gad-el-Hak  (1986a;  1987;  1996),  Riley  et' 
al.  (1988),  Carpenter  (1990),  and  Metcalfe  (1994).  Following  these 
introductory  remarks,  a  somewhat  sketchy  history  of  the  subject, 
particularly  prior  to  1985,  is  recalled.  This  will  help  place  more 
recent  developments  in  proper  perspective. 


2  Subject  Prior  to  1985 

Before  embarking  on  describing  the  recent  accomplishments  in 
the  field  of  compliant  coatings,  we  first  elaborate  on  its  history 
prior  to  1985.  This  seemingly  arbitrary  date  is  chosen  because  it 
demarks  the  time  after  which  tools  for  rationally  designing  a  com¬ 
pliant  coating  to  delay  transition  became  more  readily  available. 
The  victories  and  defeats  of  the  subject  matter  will  become  clear 
through  the  discussion  that  follows.  The  idea  of  using  compliant 
coatings  for  drag  reduction  motivated  much  of  the  earlier  work  in 
this  area  and  was  first  introduced  by  Kramer  (1957)  based  on  his 
earlier  observation,  while  crossing  the  Atlantic  ocean  in  1946,  of 
dolphins  swimming  in  water.  He  advanced  the  concept  that  the 
stability  and  transition  characteristics  of  a  boundary  layer  may  be 
influenced  by  coupling  it  hydroelastically  to  a  compliant  coating.  In 


197 


his  pioneering  paper  and  several  subsequent  publications,  Kramer 
(1960a;  1960b;  1960c;  1961;  1962;  1965;  1969)  reported  substantial 
drag  reduction  for  towed  underwater  bodies  covered  with  compli¬ 
ant  coating  modeled  after  the  dolphin  skin.  He  hypothesized  that 
by  tuning  the  elastic  wall  damping  to  a  frequency  near  that  of  the 
most  unstable  Tollmien-Schlichting  wave,  it  would  be  possible  to 
dissipate  partially  the  instability  waves,  thus  delaying  the  transi¬ 
tion  to  turbulence.  Kramer’s  tests  were  performed  by  towing  a 
test  model  behind  a  motor  boat  in  Long  Beach  Harbor.  Unfortu¬ 
nately,  many  attempts  by  other  investigators  to  repeat  Kramer’s 
experiments  under  more  controlled  conditions  failed  to  yield  simi¬ 
lar  conclusions  (e.g.,  Puryear’s,  1962,  experiment  in  a  towing  tank). 
This  so-called  Kramer  controversy  will  be  revisited  in  Section  4. 

Theoretical  work  by  Benjamin  (1960),  Betchov  (1960),  Landahl 
(1962),  and  Kaplan  (1964)  indicated  that  drag  reduction  by  delay¬ 
ing  transition  is  possible.  However,  the  theoretically  predicted  suc¬ 
cessful  coatings  had  specific  characteristics  that  would  be  extremely 
difficult  to  match  in  practice.  It  is  important  to  stress  that  almost 
all  this  early  work  addressed  the  delay  of  transition  and  ignored 
the  potential  for  reducing  turbulence  skin  friction  with  compliant 
coatings. 

During  the  mid-1960s,  Benjamin  (1966)  explored  the  possibil¬ 
ity  that  a  compliant  coating  may  affect  the  skin-friction  drag  in 
a  fully-developed  turbulent  boundary  layer  without  necessarily  de¬ 
laying  transition.  Dinkelacker  (1966)  conducted  careful  tests  of  a 
compliant  surface  in  a  water  pipe  flow.  He  systematically  attempted 
to  determine  the  repeatability  of  rigid-tube  data,  the  influence  of 
small  steps  in  the  tube  wall,  and  the  possible  occurrence  of  organ 
pipe  acoustic  modes.  Dinkelacker’s  results  seemed  to  indicate  a 
modest  reduction  in  drag  by  using  a  compliant  wall. 

Blick  and  his  co-workers  at  the  University  of  Oklahoma  experi¬ 
mentally  demonstrated  significant  reductions  in  turbulence  skin  fric¬ 
tion  for  compliant  surfaces  in  air  (Fisher  and  Blick,  1966;  Looney 
and  Blick,  1966;  Smith  and  Blick,  1966;  Blick  and  Walters,  1968; 
Chu  and  Blick,  1969).  Subsequent  tests  by  Lissaman  and  Harris 
(1969),  who  attempted  to  substantiate  Blick’s  conclusions,  yielded 
only  extremely  modest  gains.  In  another  study,  McMichael  et  al. 
(1980)  demonstrated  that  the  apparent  reduction  in  turbulence  skin 
friction  in  the  University  of  Oklahoma’s  experiments  could  be  a  con¬ 
sequence  of  experimental  deficiencies  coupled  with  the  improper 
interpretation  of  data.  McMichael  et  al.  concluded  that  drag  re¬ 
duction  via  compliant  coating  in  gaseous  flows  would  not  be  as 
successful  as  in  liquids. 

During  the  1970s  various  compliant  materials  were  tested  in  wa¬ 
ter  at  the  Naval  Ocean  Systems  Center,  the  Naval  Research  Labora¬ 
tory,  the  Naval  Undersea  Systems  Center,  and  the  Advanced  Tech¬ 
nology  Center  of  the  LTV  Corporation,  all  in  the  United  States.  In 
no  case  was  a  statistically  significant  reduction  in  drag  measured. 
Fischer  and  Ash  (1974)  presented  a  general  review  of  concepts  for  re¬ 
ducing  skin  friction,  including  the  use  of  compliant  coatings.  Bush- 
nell  et  al.  (1977),  in  summarizing  the  work  conducted  at  the  NASA 
Langley  Research  Center  and  the  general  status  of  compliant  sur¬ 
face  drag  reduction,  stated  that,  while  it  was  possible  to  increase 
the  transition  Reynolds  number  by  perhaps  a  factor  of  2,  there  was 
no  definitive  reduction  of  drag  for  turbulent  flows  in  air.  They  also 
stated  that  drag  reduction  in  turbulent  flows  in  water  is  potentially 
feasible  and  can  be  accomplished  using  surfaces  that  can  be  prac¬ 
tically  built.  It  is  of  particular  interest  to  note  that  much  of  the 
research  on  compliant  coatings  has  been  based  on  materials  that 
attempt  to  replicate  dolphin  skin.  Yet,  in  the  Russian  book  Nekton 
(Aleyev,  1977)  it  is  indicated  that  the  “wrinkling”  of  the  dolphin 
skin  has  no  hydrodynamic-drag  advantage.  Other  characteristics  of 
the  dolphin’s  skin  may,  however,  be  beneficial.  This  subject  will  be 
revisited  in  Section  5.4. 

Bushnell  et  al.  (1977)  put  forward  the  possibility  of  a  feed¬ 
back  mechanism  in  turbulent  wall-bounded  flows  through  which 
the  quasi-period ic,  coherent  structures  termed  bursts  regenerate. 
Older  bursts  grow,  migrate  away  from  the  wall,  and  interact  to  pro¬ 
duce  a  pressure  field  which  contains  pulses  of  sufficient  duration 
and  amplitude  to  induce  new  bursts  in  the  near-wall  region.  This 
model  is  supported  by  the  measurements  of  Burton  (1974),  who  re¬ 
ported  a  strong  correlation  between  the  occurrence  of  a  burst  and 


the  imposition  on  the  wall  flow  of  a  large  moving  adverse-pressure 
gradient  followed  by  a  favorable  pressure-gradient.*  Bushnell  et  al. 
hypothesized  that  a  successful  compliant  coating  would  modulate 
the  preburst  flow  in  the  turbulent  boundary  layer  by  providing  a 
pressure  field  that  would  tend  to  block  the  feedback  mechanism  and, 
thus,  inhibit  burst  formation.  This  would  result  in  a  reduction  in 
the  number  of  bursts  occurring  per  unit  time  and  also  in  the  skin- 
friction  drag.  Orszag  (1979)  assumed  this  conceptual  model  and 
performed  numerical  calculations  of  wall  boundary  layer  instability 
to  explore  the  effects  of  complaint  surfaces.  His  results,  although 
preliminary,  indicated  that  turbulence  drag  reduction  may  be  pos¬ 
sible  for  certain  classes  of  materials.  He  concluded  that  compliant 
walls  which  support  only  short  wavelengths  may  have  an  appre¬ 
ciable  effect  in  inhibiting  further  bursts  in  a  turbulent  boundary 
layer. 

During  the  U.S.  Navy-sponsored  research  program  conducted 
over  the  period  1980-1985,  the  subject  of  boundary  layer  inter¬ 
action  with  compliant  coatings  has  been  re-examined  to  answer  the 
question:  can  compliant  coatings  delay  transition  and/or  signifi¬ 
cantly  reduce  turbulence  skin  friction  on  bodies  at  high  Reynolds 
numbers?  Several  significant  developments  have  been  achieved  by 
the  many  investigators  participating  in  this  research  program.  Al¬ 
though  unrefutable  experimental  evidence  of  compliant  coating  drag 
reduction  was  still  lacking  by  1985,  our  understanding  of  boundary 
layer  flow  over  a  compliant  surface  has  increased  dramatically  over 
this  period.  That  understanding  proved  crucial  to  the  subsequent 
successes  in  the  field,  a  subject  which  will  be  emphasized  through¬ 
out  the  rest  of  this  paper. 

3  System  Instabilities 

From  a  fundamental  viewpoint,  a  rich  variety  of  fluid-structure 
interactions  exists  when  a  fluid  flows  over  a  surface  that  can  comply 
with  the  flow.  Not  surprisingly,  instability  modes  proliferate  when 
two  wave-bearing  media  are  coupled.  Some  waves  are  flow- based, 
some  are  wall-based,  and  some  are  a  result  of  the  coalescence  of  both 
kind  of  waves.  What  is  most  appealing  about  compliant  coatings  is 
their  potential  to  inhibit,  or  to  foster,  the  dynamic  instabilities  that 
characterize  both  transitional  and  turbulent  boundary  layer  flows, 
and  in  turn  to  modify  the  mass,  heat  and  momentum  fluxes  and 
change  the  drag  and  the  acoustic  properties.  While  it  is  relatively 
easy  to  suppress  a  particular  instability  mode,  the  challenge  is  of 
course  to  prevent  other  modes  from  growing  if  the  aim  is,  say,  to 
delay  laminar-to-turbulence  transition.  FVom  a  practical  point  of 
view,  it  is  obvious  that  an  in-depth  understanding  of  the  coupled 
system  instabilities  is  a  prerequisite  to  rationally  designing  a  coating 
that  meets  a  given  objective. 

There  are  at  least  three  classification  schemes  for  the  fluid- 
structure  waves,  each  with  its  own  advantages  and  disadvantages. 
The  original  scheme  is  due  to  Benjamin  (1963)  and  divides  the 
waves  into  three  classes  according  to  their  response  to  irreversible 
energy  transfer  to  and  from  the  compliant  wall.  Both  class  A 
and  class  B  disturbances  are  essentially  oscillations  involving  con¬ 
servative  energy  exchanges  between  the  fluid  and  solid,  but  their 
stability  is  determined  by  the  net  effect  of  irreversible  processes 
such  as  dissipation  in  the  coating  or  energy  transfer  to  the  solid 
by  non-conservative  hydrodynamic  forces.  Class  A  oscillations  are 
Tollmien-Schlichting  waves  in  the  boundary  layer  modified  by  the 
wall  compliance,  in  other  words  by  the  motion  of  the  solid  in  re¬ 
sponse  to  the  pressure  and  shear-stress  fluctuations  in  the  flow.  T-S 
waves  are  stabilized  by  the  irreversible  energy  transfer  from  the  fluid 
to  the  coating,  but  destabilized  by  dissipation  in  the  wall.  Class  B 
waves  reside  in  the  wall  and  result  from  a  resonance  effect  much  the 
same  as  wind-induced  waves  over  a  body  of  water.  Their  behavior  is 
the  reverse  of  that  for  class  A  waves,  stabilized  by  wall  damping  but 
destabilized  by  the  non- conservative  hydrodynamic  forces.  Essen¬ 
tially  class  B  waves  are  amplified  when  the  flow  supplies  sufficient 
energy  to  counterbalance  the  coating  internal  dissipation.  Finally, 
class  C  waves  are  akin  to  the  inviscid  Kelvin-Helmholtz  instability 
and  occur  when  conservative  hydrodynamic  forces  cause  a  unidi¬ 
rectional  transfer  of  energy  to  the  solid.  The  pressure  distribution 


198 


in  an  inviscid  flow  over  a  wavy  wall  is  in  exact  antiphase  with  the 
elevation.  In  that  case,  class  C  waves  can  grow  on  the  solid  surface 
only  if  the  pressure  amplitude  is  so  large  as  to  outweigh  the  coat¬ 
ing  stiffness.  Irreversible  processes  in  both  the  fluid  and  solid  have 
negligible  effect  on  class  C  instabilities. 

If  one  considers  the  total  disturbance  energy  of  the  coupled  fluid- 
solid  system,  a  decrease  in  that  energy  leads  to  an  increase  in  the 
amplitude  of  class  A  instabilities,  class  B  is  associated  with  an 
energy  increase,  and  virtually  no  change  in  total  energy  accompa¬ 
nies  class  C  waves.  In  other  words,  any  non-conservative  flow  of 
activation  energy  from/to  the  system  must  be  accompanied  by  dis¬ 
turbance  growth  of  class  A/B  waves,  while  the  irreversible  energy 
transfer  for  class  C  instability  is  nearly  zero. 

The  second  classification  scheme  is  due  to  Carpenter  and  Garrad 
(1985;  1986).  It  simply  divides  the  waves  into  fluid-based  (Tollmien- 
Schlichting  instabilities,  TSI)  and  solid-based  (flow-induced  surface 
instabilities,  FISI).  FISI  are  closely  analogous  to  the  instabilities 
studied  in  hydro-  and  aeroelasticity,  and  include  both  the  traveling- 
wave  flutter  that  moves  at  speeds  close  to  the  solid  free- wave-speed 
(class  B)  and  the  essentially  static,  and  more  dangerous,  divergence 
waves  (class  C).  The  main  drawback  of  this  classification  scheme 
is  that  under  certain  circumstances  the  fluid-based  T-S  waves  and 
the  solid-based  flutter  can  coalesce  to  form  a  powerful  new  insta¬ 
bility  termed  transitional  mode  by  Sen  and  Arora  ( 1988) .  Accord¬ 
ing  to  the  energy  criterion  advanced  by  Landahl  (1962),  this  latest 
instability  is  a  second  kind  of  class  C  waves.  In  a  physical  ex¬ 
periment,  however,  it  is  rather  difficult  to  distinguish  between  the 
static-divergence  waves  and  the  transitional  ones. 

The  third  scheme  to  classify  the  instability  waves  considers 
whether  they  are  convective  or  absolute  (Huerre  and  Monkewitz, 
1990).  An  instability  mode  is  considered  to  be  absolute  if  its  group 
velocity  is  zero.  On  the  other  hand,  the  unstable  development  of 
a  disturbance  is  said  to  be  convective  when  none  of  its  constituent 
modes  posses  zero  group  velocity.  Both  classes  A  and  B  are  convec¬ 
tive,  while  class  C  divergence  and  transitional  modes  are  absolute. 
As  Carpenter  (1990)  points  out,  the  occurrence  of  absolute  instabil¬ 
ities  would  lead  to  profound  changes  in  the  laminar-to-turbulence 
transition  process.  It  is  therefore  pointless  to  consider  reducing 
their  growth  rate  or  postponing  their  appearance  to  higher  Reynolds 
number;  nothing  short  of  complete  suppression  would  work.  Fig¬ 
ure  1  combines  and  summarizes  all  three  classification  schemes. 

4  The  Kramer  Controversy 

It  may  be  worth  recalling  in  more  details  the  pioneering  work 
of  Max  O.  Kramer  and  the  controversy  surrounding  it.  The  entire 
field  of  compliant  coatings  became  the  Rodney  Dangerfield  of  fluid 
mechanics  research,  getting  no  respect  from  a  skeptical  community, 
largely  because  of  the  loss  of  credibility  of  Kramer’s  original  exper¬ 
iments.  However  as  will  be  seen  below  the  most  recent  evidence 
resurrects  the  good  name  of  this  ingenious  German-American  and 
with  it  renewed  confidence  in  this  waning  and  waxing  field. 

As  already  mentioned,  Kramer  (1957;  1960a;  1960b;  1960c;  1961; 
1962;  1965;  1969)  conducted  his  original  experiments  by  towing  a 
model  behind  an  outboard  motor  boat  in  Long  Beach  Harbor,  Cal¬ 
ifornia.  His  early  tests  showed  a  drag  reduction  of  more  than  50% 
when  a  dolphin-like  skin  was  used.  A  typical  successful  coating  used 
by  Kramer  consisted  of  a  flexible  inner  skin,  an  outer  diaphragm, 
and  stubs,  all  made  of  soft  natural  rubber.  The  cavity  between  the 
outer  diaphragm  and  the  inner  skin  was  usually  filled  with  a  highly 
viscous  damping  fluid,  such  as  silicone  oil.  which  in  Kramer’s  view 
damped  out  the  Tollmien-Schlichting  waves. 

n  Subsequent  experiments  to  confirm  Kramer’s  findings  were  con¬ 
ducted  in  a  towing  tank,  a  lake,  or  a  water  tunnel  (Puryear,  1962; 
Nisewanger,  1964;  Ritter  and  Messum,  1964;  Ritter  and  Porteous, 
1964).  No  significant  drag  reduction  was  observed  in  any  of  these 
investigations.  Since  then,  many  researchers  have  assumed  that 
Kramer’s  results  were  in  error  and  that  his  observed  drag  reduc¬ 
tion  could  have  come  about  as  a  result  of  favorable  changes  to  the 
form  drag  or  the  accidental  excretion  of  the  silicone  oil  used  as  the 
damping  fluid  during  the  tests.  Surface  discontinuities  could  have 


Figure  1:  Summary  of  all  three  classification  schemes 


favorably  altered  the  pressure  drag,  and  the  released  oil  could  have 
acted  as  a  drag- reducing  polymer  when  released  into  the  boundary 
layer  and  the  ambient  fluid. 

Carpenter  and  Garrad  (1985)  stated  that:  “It  is  probably  no  ex¬ 
aggeration  to  suggest  that  the  credibility  of  Kramer’s  coatings  is 
now  rather  low.”  Acceptance  of  his  results  was  not  granted  by  the 
scientific  community  because  the  rigorous  standards  of  scientific  in¬ 
vestigation  were  not  met  and  the  gradual  improvements  by  Kramer 
to  meet  these  standards  were  not  adequate  (Johnson,  1980).  It  did 
not  help  his  cause  any  that  Kramer’s  explanations  of  his  own  em¬ 
pirical  results,  though  intuitively  appealing,  were  proven  physically 
incorrect.  For  example,  we  now  know  that  damping  in  the  solid 
destabilizes  TSI. 

Almost  30  years  after  Kramer’s  original  investigation,  Carpen¬ 
ter  and  Garrad  (1985)  presented  a  very  careful  analysis  of  his  ex¬ 
periments  (e.g.,  Kramer,  1957)  and  the  subsequent  tests  (Puryear, 
1962;  Nisewanger,  1964;  Ritter  and  Messum,  1964;  Ritter  and  Por¬ 
teous,  1964)  that  attempted  to  provide  independent  evidence  of 
the  drag-reducing  capabilities  of  Kramer’s  coatings.  Based  on  their 
own  rigorous  analysis  of  the  hydrodynamic  stability  of  flows  over 
Kramer-type  compliant  surfaces,  Carpenter  and  Garrad  argue  that 
Kramer’s  coatings  were  only  marginally  capable  of  delaying  transi¬ 
tion.  Any  unfavorable  factor,  such  as  an  adverse  pressure  gradient, 
a  step  where  the  compliant  surface  is  joined  to  a  rigid  surface  or 
an  unusually  high  freestream  turbulence  level,  could  badly  affect 
the  performance  of  the  coating.  Also,  a  particular  coating  was  de¬ 
signed  for  a  restricted  range  of  Reynolds  number  and  was  therefore 
unlikely  to  delay  transition  outside  that  range. 

Carpenter  and  Garrad  (1985)  contend  that  one  or  more  of  the 
above  adverse  factors  may  have  existed  in  the  experiments  con¬ 
ducted  by  Puryear  (1962),  Nisewanger  (1964),  Ritter  and  Messum 
(1964),  and  Ritter  and  Porteous  (1964).  Puryear ’s  (1962)  experi¬ 
ments  were  conducted  using  a  prolate  spheroid  in  a  towing  tank. 
He  did  not  use  Kramer’s  coating  with  the  best  performance,  and 
serious  problems  were  encountered  in  making  a  smooth  joint  be¬ 
tween  the  rigid  and  compliant  surfaces.  Nisewanger’s  (1964)  tests 
were  conducted  by  releasing  a  lighter-than-water  body  of  revolution 
from  the  bottom  of  a  lake.  His  Kramer-like  coating  contained  a  fluid 
with  a  viscosity  below  that  of  the  optimum  fluid  as  determined  from 
Kramer’s  results.  Ritter  and  Messum  (1964),  and  Ritter  and  Por- 


199 


teous  (1964)  conducted  their  experiments  in  a  water  tunnel  using 
either  a  flat  plate  or  a  cylindrical  model  with  an  elliptic  nose.  The 
conventional  flume  had  a  relatively  high  freestream  turbulence  level, 
which  may  render  the  facility  unsuited  for  transition  experiments. 

In  addition  to  these  adverse  effects,  some  evidence  existed  in  the 
tests  conducted  to  confirm  Kramer’s  results  for  the  onset  of  a  hy¬ 
droelastic  instability  in  the  coating.  Such  large-amplitude  waves 
would  certainly  lead  to  drag  increase,  and  their  presence  may  in¬ 
dicate  that  the  boundary  layer  was  already  turbulent.  Based  on 
these  experiments,  Carpenter  and  Garrad  (1985)  concluded  that 
the  results  presented  in  these  tests  should  not  be  taken  as  conclu¬ 
sive  evidence  that  the  Kramer  coatings  are  not  capable  of  delaying 
transition  and  that  “the  case  against  Kramer’s  coating  may  not  be 
so  strong  as  popularly  supposed.” 

Carpenter’s  (1988)  optimization  procedure  described  in  Sec¬ 
tion  5.2,  results  in  a  compliant  coating  that  is  capable  of  delaying 
transition  by  a  factor  of  4-6  in  Reynolds  number.  It  is  therefore 
quite  conceivable  to  design  a  Kramer-type  coating  that  may  lead 
to  a  drag  reduction  of  the  order  reported  by  the  original  inventor 
himself.  The  above  analysis  of  Kramer’s  tests  illustrates  the  impor¬ 
tance  of  carefully  selecting  the  flow  facility  to  conduct  compliant 
coating  experiments.  The  background  turbulence  in  the  facility 
should  particularly  be  monitored  if  transition  delay  is  sought.  This 
is  precisely  what  was  done  in  the  successful  experiments  conducted 
by  Gaster  (1988)  to  confirm  the  theoretical  prediction  of  Carpenter 
and  Garrad  (1985),  both  described  in  more  details  in  the  following 
section. 


5  Transitional  Flows 

5.1  Linear  Stability  Theory 

Both  the  hydrodynamic  and  the  hydroelastic  stability  theories 
have  reached  an  impressive  level  of  maturity  during  the  last  two 
decades.  The  linear  theories  can  be  handled,  for  the  most  part,  an¬ 
alytically,  while  the  nonlinear  stability  theories  are  more  computer 
intensive.  Perhaps  no  one  has  contributed  more  to  the  recent  appli¬ 
cation  of  the  stability  theory  to  compliant  coatings  than  Peter  W. 
Carpenter,  originally  with  the  University  of  Exeter  and  presently 
with  the  University  of  Warwick.  His  list  of  relevant  publications 
includes  65  papers  and  growing;  obviously  only  a  selected  few  will 
be  cited  in  the  present  short  article. 

Within  the  framework  of  the  linear  stability  theory,  two- 
dimensional  small  disturbances  are  assumed  to  be  superimposed 
upon  a  steady,  unidirectional  mean  flow.  The  nonlinear,  partial 
Navier-Stokes  equations  are  then  reduced  to  the  well-known  Orr- 
Sommerfeld  equation  which  is  a  fourth-order,  linear,  ordinary  dif¬ 
ferential  equation.  The  order  of  this  equation  increases  when  addi¬ 
tional  complexities  are  included  in  the  problem.  For  rotating-disk 
flows,  for  example,  Coriolis  and  streamline-curvature  terms  are  in¬ 
corporated  leading  to  a  sixth -order  stability  equation.  The  major 
difficulty  in  integrating  the  Orr-Sommerfeld  equation  is  that  it  is 
highly  stiff  and  unstable,  which  makes  it  virtually  impossible  to 
apply  conventional  numerical  schemes.  Explicit  codes  with  step 
size  that  is  commensurate  with  the  global  behavior  of  the  solution 
lead  to  numerical  instabilities,  and  alternative  routines  have  been 
developed  to  handle  this  stiff  eigenvalue  problem. 

An  added  difficulty  when  the  walls  are  compliant  is  the  interfa¬ 
cial  conditions  which  require  continuity  of  velocity  and  stress.  Those 
boundary  conditions  can  also  be  linearized,  but  special  care  should 
still  be  exercised  in  handling  them.  Appropriate  equations  must 
be  used  for  the  compliant  walls  to  be  able  to  fully  couple  the  fluid 
and  solid  dynamics.  Many  types  of  compliant  surfaces  exist,  so 
that  there  are  numerous  models  for  the  solid.  Those  models  can  be 
either  surface-based  or  volume-based.  The  former  model  reduces 
the  spatial  dimensions  by  one,  and  is  therefore  less  computation¬ 
ally  demanding.  An  example  is  the  thin  plate-spring  model  used  by 
Garrad  and  Carpenter  (1982),  Carpenter  and  Garrad  (1985;  1986), 
Domaradzki  and  Metcalfe  (1987),  Metcalfe  et  al.  (1991),  and  Davies 
and  Carpenter  (1997a;  1997b),  among  others,  to  simulate  Kramer- 
type  coatings.  This  model  is  relatively  simple  yet  contains  charac¬ 


teristics  representative  of  a  broad  range  of  surfaces.  If  a  coordinate 
system  is  chosen  with  the  x-axis  lying  along  the  undisturbed  free 
surface  and  the  y-axis  normal  to  this  surface,  then  the  equation  for 
the  y-component  of  the  momentum  of  the  compliant  coating  reads 


■  V  +  F 


(1) 


d2j]  _  Tt  d2<q  p  dr]  JF  cHy 

dt 2  m  dx 2  dt  m  dx 4  m 

where  rj(x ,  t)  is  the  y-displacement  of  the  surface  from  its  equilib¬ 
rium  state  at  time  t  and  position  xy  Ti  is  the  longitudinal  tension 
and  T  the  flexural  rigidity  of  the  thin  plate,  m  is  the  mass  per  unit 
area,  D  is  the  damping  coefficient,  k  is  the  spring  constant,  and  F 
is  an  external  forcing  term. 

The  volume-based  models  are  based  on  the  Navier  equation  and 
include  single  and  multi-layer  coatings  (Duncan  et  al.,  1985;  Eraser 
and  Carpenter,  1985;  Buckingham  et  al.,  1985;  Yeo,  1988)  as  well 
as  isotropic  and  anisotropic  materials  (Yeo,  1992;  1990;  Duncan, 
1988).  The  equations  describing  the  stability  of  the  coupled  system 
form  a  numerical  eigenvalue  problem  for  the  complex  wavenum¬ 
ber  of  the  disturbance.  Duncan  (1987)  offers  a  useful  comparison 
between  the  results  obtained  from  a  surface-based  model  and  a  cor¬ 


responding  volume-based  one. 

Compliant  walls  do  suppress  the  Tollmien-Schlichting  waves  due 
to  the  irreversible  energy  transfer  from  the  fluid  to  the  solid,  but 
solid-based  instabilities  proliferate  if  the  coating  becomes  too  soft. 
For  the  class  A  T-S  waves,  the  wall  compliance  reduces  the  rate  of 
production  (via  Reynolds  stress)  of  the  disturbance  kinetic  energy. 
Simultaneously,  the  viscous  dissipation  is  increased  and  thus  the 
balance  between  the  energy  production  and  removal  mechanisms  is 
altered  in  favor  of  wave  suppression. 

Experimental  validation  of  the  stability  calculations  is  rather  dif¬ 
ficult  and  requires  well-controlled  tests  in  a  quiet  water  or  wind 
tunnel.  Several  careful  experiments  to  test  the  flow  stability  to  two- 
dimensional  as  well  as  three-dimensional  controlled  disturbances 
have  been  reported  in  the  past  few  years  (Daniel  et  al.,  1987;  Gaster, 
1988;  Lee  et  al.,  1995;  1997).  A  simple  compliant  model  predicts  a 
dramatic  decrease  in  the  instability  of  the  flow,  and  this  prediction 
agrees  well  with  the  experimental  observations  when  a  thick,  soft 
coating  is  covered  with  a  thin,  stiff  layer. 

The  papers  by  Lee  et  al.  (1995;  1997)  report  the  results  of  wind 
tunnel  experiments  and  actually  demonstrate  the  stabilizing  po¬ 
tential  of  compliant  coatings  in  aerodynamic  flows;  a  remarkable 
achievement  that  has  been  deemed  impractical  in  the  past  (Bushnell 
et  al.,  1977;  Carpenter,  1990).  Excellent  agreements  are  reported 
between  the  results  of  the  stability  theory  and  the  hydrodynamic 
experiments  (Willis,  1986;  Daniel  et  al.,  1987;  Gaster,  1988;  Riley 
et  al.,  1988;  Carpenter,  1990;  Lucey  and  Carpenter,  1995).  The 
paper  by  Lucy  and  Carpenter,  in  particular,  applies  the  linear  sta¬ 
bility  theory  to  predict  the  experimentally  observed  evolution  of 
both  Tollmien-Schlichting  waves  and  traveling- wave  flutter  in  wa¬ 
ter  flows.  For  the  wind  tunnel  experiments,  Carpenter  (1998)  has 
conducted  the  corresponding  calculations,  but  his  preliminary  re¬ 
sults  thus  far  are  negative:  the  density  of  an  effective  coating  must 
be  comparable  to  the  fluid  density  otherwise  no  transition  delaying 
benefits  are  observed.  This  theoretical  result  leaves  open  the  ques¬ 
tion  of  explaining  the  positive  experimental  findings  of  Lee  et  al. 
(1995),  Reductions  in  the  maximum  rms-amplitude  of  as  much  as 
40%  are  observed  for  the  softer  coating,  which  may  lead  to  delayed 
transition. 


5.2  Coating  Optimization 

If  a  compliant  coating  is  to  be  designed  for  use  on  an  actual 
vehicle,  a  relevant  question  may  be:  what  are  the  optimum  wall 
properties  to  give  the  greatest  transition  delay?  The  large  number 
of  available  parameters  makes  it  imperative  that  a  rational  (i.e.,  one 
derived  from  first  principles)  selection  process  be  conducted.  For 
obvious  reasons,  the  trial-and-error  empirical  approach  used  in  the 
past  (if  it  is  soft ,  let  us  try  it!)  should  not  even  be  contemplated. 
This  should  be  particularly  true  now  that  rational  optimization  pro¬ 
cedures  are  becoming  readily  available  as  described  below.  A  wall 
that  is  too  compliant  (i.e.,  too  soft)  can  substantially  delay  tran¬ 
sition  via  TSI  by  shrinking  its  unstable  region  in  the  frequency- 


200 


Reynolds  number  plane,  but  rapid  breakdown  can  occur  through 
the  amplification  of  wall-based  instabilities  (Lucey  and  Carpenter, 
1995).  Both  kinds  of  FISI  are  potentially  harmful.  The  diver¬ 
gence  instabilities  are  absolute,  nearly  static,  and  yield  to  whole¬ 
sale  deformations  of  the  surface  which  are  likely  to  trigger  prema¬ 
ture  transition  due  to  a  roughness-like  effect.  Flutter  instabilities, 
though  convective,  are  also  dangerous.  Their  narrow  band  of  unsta¬ 
ble  frequencies  extends  indefinitely  as  Reynolds  number  increases 
downstream.  Thus,  once  these  instabilities  are  encountered  at  some 
downstream  location,  sustained  growth  follows.  This  is  unlike  the 
broad-band  Tollmien-Schlichting  instabilities  which  grow  then  de¬ 
cay  as  the  different  waves  travel  downstream  and  pass  through  the 
lower  and  upper  branches  of  their  neutral-stability  curve. 

A  workable  strategy  for  coating  optimization  suggested  by  Car¬ 
penter  (1988)  is  to  choose  a  restricted  set  of  wall  properties  such 
that  the  coating  is  marginally  stable  with  respect  to  FISI  (both 
flutter  and  divergence).  The  remaining  disposable  wall  parameters 
can  then  be  varied  to  obtain  the  greatest  possible  transition  (via 
TSI)  delay.  For  the  plate-spring,  surface-based  model,  for  example, 
there  are  two  disposable  parameters:  the  wall  damping  and  the  crit¬ 
ical  wavenumber  for  divergence.  The  downstream  location  of  the 
transition  region  is  estimated  from  an  en-criterion,  where  n  is  typ¬ 
ically  chosen  in  the  range  of  7-10.  The  lower  exponent  represents 
the  approximate  limit  of  validity  of  the  linear  stability  theory  for 
a  low-disturbance  environment,  and  provides  a  rather  conservative 
calculation. 

Although  wall  dissipation  destabilizes  Tollmien-Schlichting 
waves,  a  viscoelastic  coating  with  moderate  level  of  damping  leads 
to  greater  delay  in  transition  as  compared  with  purely  elastic 
surfaces.  Apparently  the  stabilizing  effects  of  wall  damping  on 
traveling- wave  flutter  allow  a  softer  wall  to  be  used,  and  thus  more 
than  offset  the  adverse  effects  of  coating  dissipation  on  TSI. 

Coating  optimization  with  respect  to  TSI  growth  rate  is  per¬ 
formed  at  a  rather  narrow  range  of  Reynolds  numbers.  On  a  grow¬ 
ing  boundary  layer,  the  Reynolds  number  increases  monotonically, 
and  a  compliant  coating  will  not  be  optimum  over  the  whole  length 
of  a  vehicle.  Carpenter  (1993)  suggests  that  a  multiple-panel  wall, 
placed  in  series,  with  each  panel  optimized  for  a  particular  range 
of  Reynolds  numbers,  is  likely  to  produce  larger  transition  delays 
than  a  single-panel  wall.  His  calculations  for  a  two-panel,  plate¬ 
spring-type  compliant  wall  indicate  an  additional  performance  im¬ 
provement  of  over  30%  over  an  optimized  single-panel  wall. 

It  seems  reasonable  that  a  large  number  of  panels,  say  10,  in  series 
would  lead  to  superior  performance,  but  of  course  the  calculations 
involved  become  prohibitive  very  quickly.  An  additional  benefit 
from  using  multi-panels  is  that  shorter  panels  are  more  resistant  to 
both  static-divergence  waves  and  traveling- wave  flutter  (Carpenter, 
1993;  Lucey  and  Carpenter,  1993;  Dixon  et  al.,  1994),  thus  allowing 
softer  panels  to  be  used  which  further  suppress  TSI  and  improve  the 
coating  performance. 

In  the  flat-plate  and  similar  boundary  layers  in  low- 
disturbance  environments,  the  quasi-two-dimensional  Tollmien- 
Schlichting  waves  dominate  the  laminar-to-turbulence  transition. 
Various  receptivity  processes  are  responsible  for  generating  2-D  in¬ 
stabilities  which  are  probably  initially  three-dimensional  and  ran¬ 
domly  'distributed.  Low-disturbance  environments  could  be  real¬ 
ized,  for  example,  in  free  flight  and  marine  vehicles.  Very  recently, 
Davies  and  Carpenter  (1997a)  and  Carpenter  (1998)  have  shown 
that  in  such  environment,  complete  suppression  of  the  Tollmien- 
Schlichting  waves  is  possible  provided  that  optimized  multiple-panel 
compliant  .walls  are  used  with  each  panel  tailored  to  suit  its  local 
surrounding.  Assured  by  the  experimental  observations  that  static- 
divergence  waves  are  only  observed  when  the  wall-bounded  flow  is 
turbulent,  Carpenter’s  (1998)  new  assumptions  are  somewhat  less 
conservative  than  those  used  in  earlier  theories  (Carpenter,  1993; 
Dixon  et  al.,  1994).  The  new  finding  raises  the  possibility  of  main¬ 
taining  laminar  flow,  in  situations  where  the  T-S  instabilities  are  the 
primary  cause  of  transition,  to  indefinitely  high  Reynolds  numbers, 
a  very  profound  prospect  indeed. 

Work  on  nonlinear  stability  theory  has  recently  been  in  the  fore¬ 
front  and  confirms  that  transition-delaying  coatings,  optimized  us¬ 
ing  the  linear  theory,  maintain  their  beneficial  effects  into  the  latter 


stages  of  transition  to  turbulence  (Metcalfe  et  al.,  1991;  Joslin  et 
al.,  1992;  Thomas;  1992a;  1992b).  Lee  et  al.  (1997)  studied  exper¬ 
imentally  the  effects  of  a  compliant  surface  on  the  growth  rates  of 
both  the  subharmonic  and  three-dimensional  fluid-based  instabili¬ 
ties  of  a  laminar  boundary  layer  in  air.  Their  results  suggest  that  a 
delay  of  the  excitement  of  the  secondary  instability  can  be  achieved 
by  suppressing  the  growth  of  the  primary  waves  using  surface  com¬ 
pliance. 

5.3  Practical  Examples 

Most  of  the  theoretical  as  well  as  experimental  compliant  coat¬ 
ing  research  has  been  concerned  with  canonical  boundary  layers. 
Nevertheless,  an  attempt  is  made  in  here  to  estimate  the  potential 
benefit  of  applying  the  technique  for  field  applications  where  strong 
three-dimensional  and  pressure-gradient  effects  and,  for  aeronauti¬ 
cal  applications,  compressibility  effects  may  be  present.  The  typical 
Reynolds  numbers,  based  on  vehicle  speed  and  overall  length,  for 
a  hydrofoil,  a  torpedo  and  a  nuclear  submarine  are,  respectively, 
of  the  order  of  10  million,  50  million  and  1  billion.  Applying  an 
en-type  calculations  (with  the  exponent  chosen  conservatively  to 
be  n  =  7)  to  an  optimum  two-panel,  plate-spring-type  compliant 
wall,  Carpenter  (1993)  computes  a  transition  Reynolds  number  of 
13.62  x  106,  as  compared  with  2.25  x  106  for  a  rigid  wall.  This  means 
that  the  laminar  region  that  would  normally  extend  over  23%,  5% 
and  0.2%  of  the  respective  vehicle  lengths  would,  with  the  use  of  an 
optimum  coating,  extend  over  a  larger  length  of  100%,  27%  and  1%. 
Computing  the  corresponding  overall  drag  coefficients  using  stan¬ 
dard  methods  for  a  mixed  laminar-turbulent  boundary  layer  over  a 
flat  plate,  the  potential  reduction  in  skin-friction  drag  using  the  op¬ 
timum  two-panel  compliant  wall  can  be  as  much  as  83%,  19%  and 
0%  for  the  three  respective  vehicles.  Obviously  the  large  submarine 
does  not  benefit,  as  far  as  drag  reduction  is  concerned,  from  the  use 
of  transition-delaying  compliant  coating  but  the  smaller  vehicles  do. 
However,  extending  the  laminar  region  on  a  submarine  even  by  1 
m  can  be  significant  for  sonar  applications  requiring  longer  quiet 
regions  of  the  boundary  layer. 

For  aeronautical  applications,  a  cruising  commercial  jet  aircraft 
has  a  fuselage  Reynolds  number  of  the  order  of  0.5  billion  and  a 
wing  Reynolds  number  of  the  order  of  50  million.  Again,  increasing 
the  transition  Reynolds  number  by  a  factor  of  5  or  so  is  significant 
for  the  wing  but  not  for  the  fuselage.  Skin-friction  reduction  of 
the  order  of  20%  is  achievable  for  the  wings  (whose  skin-friction 
drag  accounts  for  about  50%  of  the  skin  friction  of  the  entire  air¬ 
craft  and  25%  of  the  total  drag).  Finding  a  compliant  coating  that 
would  reduce  the  turbulent  skin-friction  drag  would  of  course  be 
very  beneficial  for  both  the  typical  fuselage  and  long  submarine. 

The  estimates  above  were  made  for  a  simple  plate-spring  model. 
Using  more  than  two  panels  can  provide  further  transition  delay. 
More  complex  compliant  surfaces,  particularly  anisotropic  ones  de¬ 
signed  specifically  to  suppress  the  Reynolds  stress  fluctuations,  can 
conceivably  offer  more  spectacular  savings.  Such  custom-designed 
coatings  can  also  favorably  interact  with  fully-turbulent  flows.  Even 
for  laminar  flows,  the  calculations  involved  when  complex,  wall- 
based  models  are  used,  though  straightforward  in  principle,  are 
quite  demanding  in  practice. 

5.4  The  Dolphin’s  Secret 

The  ability  to  swim  or  to  fly  with  minimum  skin-friction  and 
pressure  drag  is  of  extreme  importance  to  the  Darwinian  survival 
of  certain  nektonic  and  avian  species.  Homo  sapiens  interested  in 
building  the  fastest  submarine  or  the  most  fuel-efficient  aircraft  have 
much  to  learn  about  alternative  drag-reduction  approaches  from 
their  humble  earthlings.  As  Max  O.  Kramer  has  remarked  close  to 
half  a  century  ago,  a  school  of  porpoises,  including  the  young  and 
the  old,  the  weak  and  the  strong,  showing  off  its  seemingly  effortless 
glide  along  a  fast  ocean-liner  is  a  sight  to  behold. 

Cetaceans  appear  to  possess  unusually  low  overall  drag  coeffi¬ 
cients.  This  is  the  basic  for  the  so-called  Gray’s  (1936)  paradox,  in 
which  a  steady-state  energy  balance  based  on  the  anticipated  mus- 


201 


cle  power  of  various  nekton,  including  the  dolphin,  failed  to  explain 
their  unusually  fast  swimming  speeds.  Gray  clocked  bottlenose  dol¬ 
phins,  Tursiops  trucatus ,  swimming  at  speeds  exceeding  10  m/s  for 
a  period  of  7  s.  If  one  assumes  that  cetaceans  power  output  is  equal 
to  that  of  other  mammals  (~  35  W/kg  of  body  weight),  then  such 
speeds  are  reached  under  turbulent  flow  conditions  only  if  dolphins 
can  expend  several  times  more  power  than  their  muscles  can  gen¬ 
erate.  Lang  (1963)  concluded  that  based  on  energy  considerations, 
dolphins  could  not  exceed  a  speed  of  6  m/s  for  periods  greater  than 
2  hours. 

Transition  delay  is  of  course  an  obvious  albeit  arduous  technique 
for  achieving  about  an  order  of  magnitude  lower  skin-friction  drag, 
but  does  the  dolphin  posses  an  exotic  means  by  which  such  difficult 
flow  control  goal  can  be  accomplished?  Obviously  the  dolphin  is 
not  sharing  its  secrets  with  other  fellow  mammals.  Kramer’s  (1957; 
1961)  invention  of  a  compliant  coating  tried  to  mimic  the  dolphin’s 
epidermis  and  claimed  drag  reduction  of  as  much  as  60%.  His  expla¬ 
nation  for  the  dolphin’s  secret  is  that  their  skin,  like  his  successful 
compliant  coating,  is  capable  of  substantially  delaying  laminar-to- 
turbulence  transition.  Kramer’s  work  was  discredited  for  a  while 
but  now  seems  to  be  back  in  vogue  as  remarked  in  Section  4.  The 
calculations  presented  in  Section  5.3  indicate  that  it  is  quite  con¬ 
ceivable  to  design  a  Kramer-type  coating  that  delay  transition  by 
a  factor  of  4—6  in  Reynolds  number  and  that  drag  reduction  of  the 
order  reported  by  Kramer  is  also  quite  possible.  Does  the  dolphin 
or  other  similar  fast  swimmers  posses  such  a  coating? 

In  a  recent  article,  Bushnell  and  Moore  (1991)  quote  the  rele¬ 
vant  energetic  and  controlled  swimming  studies,  but  conclude  by 
supporting  the  explanation  offered  by  Au  and  Weihs  (1980)  that 
dolphins,  which  must  periodically  breath  air,  achieve  high-speed 
swimming  by  simply  porpoising,  i.e.,  momentarily  leaping  out  of  the 
water  thereby  reducing  their  drag  force  by  a  factor  of  800  (density 
ratio  of  air  and  water).  This  more  than  pays  for  the  additional  inter- 
facial  or  wave  drag  and  accounts  for  the  abnormally  low  apparent 
drag-coefficients  inferred  from  the  assumption  of  fully-submerged 
travel. 

The  present  author,  however,  does  not  concur  with  the  above 
final  solution  to  the  Gray’s  paradox.  Dolphins  have  been  clocked 
at  sustained  and  burst  speeds  of  close  to  10  and  20  m/s,  respec¬ 
tively.  Delphinus  delphis  has  a  typical  length  of  2  m.  This  leads  to 
sustained  and  burst  Reynolds  numbers  based  on  the  overall  length 
of  the  order  of  20  million  and  40  million,  respectively.  Carpenter 
(1993)  reports  the  results  of  optimizing  a  rather  simple  plate-spring 
coating.  Using  a  single  panel,  as  compared  with  a  rigid  surface  a 
4.6-fold  increase  in  transition  Reynolds  number  is  estimated,  which 
leads  to  a  drag  reduction  of  36%  at  the  typical  dolphin’s  sustained 
speed  and  20%  at  burst  speed.  Using  a  mere  two-panel  coating, 
the  transition  Reynolds  number  becomes  6.1  times  the  value  for  a 
rigid  surface,  and  the  potential  drag  reductions  for  the  sustained 
and  burst  speeds  are  now  52%  and  30%,  respectively. 

These  lower  levels  of  skin  friction  are  compatible  with  the  avail¬ 
able  muscle  power  for  a  dolphin  of  the  size  used  above.  Admittedly, 
the  above  estimates  were  made  for  a  flat-plate  boundary  layer  and 
may  not  hold  when  pressure-gradient  and  other  shape  effects  are 
taken  into  account.  Additionally,  the  dolphin  has  also  pressure 
drag  on  top  of  the  (much  larger)  skin  friction.  On  the  other  hand, 
cetaceans  have  had  millions  of  years  of  evolutionary  adaptations 
to  hone  their  coatings  for  maximum  speed  and  efficiency,  and  it 
is  quite  conceivable  that  their  epidermis  is  quite  more  complex, 
and  hydrodynamically  beneficial,  than  the  simple  ones  computed 
in  the  examples  above.  Moreover,  each  portion  of  the  skin  could 
have  been  optimized  for  the  appropriate  range  of  local  Reynolds 
numbers.  Therefore,  the  dolphin’s  apparent  success  is  not  incom¬ 
patible  with  having  optimum  compliant  coatings  to  substantially 
delay  laminar-to-turbulence  transition,  and  therefore  to  attain  in¬ 
ordinately  low  coefficients  of  drag. 

Other  fascinating  questions  related  to  the  amazing  swimming 
abilities  of  the  dolphin  include  the  possibility  that  its  excreted 
mucin  is  a  drag-reducing  additive.  Is  there  a  hydrodynamic  advan¬ 
tage  to  the  warm-blooded  cetaceans  because  their  epidermis  tem¬ 
perature  is  higher  than  the  ambient  one  (in  which  case  the  near-wall 
water  viscosity  is  lowered  and  the  turbulent  boundary  layer  may  be 


relaminarized)?  Does  the  dolphin’s  particular  body  shape  during 
coasting  (with  no  attendant  overall  body  deformation)  or  actual 
swimming  (accompanied  by  appropriate  body  oscillations)  offer  ad¬ 
ditional  drag-reducing  advantages?  Also,  what  are  the  potential 
benefits  to  the  porpoise  when  it  uses  ship-generated  bow  waves  for 
body  surfing?  These  subjects,  though  related  to  the  above  discus¬ 
sion,  are  outside  the  scope  of  the  present  brief  and  are  therefore  left 
for  another  circumstance. 

6  Turbulent  Wall-Bounded  Flows 

Unlike  the  laminar  and  transitional  flows  investigated  in  Sec¬ 
tion  5,  compliant  coating  effects  on  turbulent  boundary  layers  are 
rather  difficult  to  study  theoretically.  In  fact  any  turbulent  flow  is 
largely  unapproachable  analytically.  For  a  turbulent  flow,  the  de¬ 
pendent  variables  are  random  functions  of  space  and  time,  and  no 
straightforward  method  exists  for  analytically  obtaining  stochastic 
solutions  to  the  governing  nonlinear,  partial  differential  equations. 
The  statistical  approach  to  solving  the  Navier-Stokes  equations  al¬ 
ways  leads  to  more  unknowns  than  equations  (the  closure  problem), 
and  solutions  based  on  first  principles  are  again  not  possible.  Direct 
numerical  simulations  (DNS)  of  the  canonical  turbulent  boundary 
layer  have  thus  far  been  carried  out  up  to  a  very  modest  momentum- 
thickness  Reynolds  number  of  1410  (Spalart,  1988). 

How  would  one  go  about  rationally  choosing  a  coating  to  achieve 
a  particular  control  goal  for  a  turbulent  boundary  layer?  Analyti¬ 
cal  optimization  procedures  such  as  those  used  to  delay  transition 
(Section  5.2)  would  not  work  for  fully-turbulent  flows.  In  order  to 
analyze  the  full  problem,  direct  numerical  simulations  of  the  turbu¬ 
lent  boundary  layer  should  be  coupled  to  a  finite-element  model  of 
the  compliant  coating,  a  task  that  is  extremely  time  consuming,  ex¬ 
pensive  and  taxes  the  fastest  supercomputer  around.  Modeling  the 
turbulence  by  an  eddy-viscosity  or  even  a  more  sophisticated  closure 
scheme  is  less  computationally  demanding,  but  there  is  no  guaran¬ 
tee  that  turbulence  models  developed  primarily  for  rigid  surfaces 
would  work  for  a  compliant  surface.  In  fact,  it  is  not  difficult  to  ar¬ 
gue  that  closure  models  based  on  mean  quantities  miss  completely 
the  all  important  spectral  contents  of  a  fluid-solid  interaction,  and 
will  therefore  never  work. 

A  turbulent  boundary  layer  is  characterized  by  a  hierarchy  of 
coherent  structures.  Near  the  wall,  the  dynamics  are  dominated 
by  the  quasi-periodic  bursting  events  (Robinson,  1991).  A  crude 
albeit  resourceful  attempt  to  model  a  turbulent  boundary  layer  in¬ 
teraction  with  a  single-layer,  isotropic,  viscoelastic  coating  has  been 
advanced  by  Duncan  (1986).  He  approximates  the  turbulent  flow 
over  the  coating  by  a  potential  flow  with  a  superimposed  pressure 
pulse,  convecting  downstream,  that  mimics  the  pressure  footprint 
of  a  single  bursting  event.  In  order  to  relate  the  problem  to  a  real 
turbulent  flow,  the  pressure  pulse  characteristics  are  taken  from 
actual  boundary  layer  measurements  and  the  potential  flow  is  mod¬ 
ified  to  incorporate  the  reduced  magnitudes  and  phase  shifts  found 
experimentally  in  boundary  layer  flows  over  moving  wavy  walls.  At 
low  flow  speeds  (relative  to  the  transverse- wave  speed  in  the  solid), 
the  coating  response  to  the  pressure  pulse  is  stable  and  primarily 
localized  under  it.  At  intermediate  speeds,  the  response  is  still  sta¬ 
ble  but  includes  a  discernible  wave  pattern  tagging  along  behind 
the  pressure  pulse.  At  the  highest  speed  studied,  large-amplitude, 
unstable  waves  develop  on  the  compliant  surface,  much  the  same  as 
the  FISI  observed  experimentally.  Duncan  and  Sirkis  (1992)  have 
recently  extended  the  above  model  to  anisotropic  compliant  coat¬ 
ings.  They  report  that  certain  anisotropic  surfaces  provide  more 
effective  control  over  the  amplitude  and  angular  extent  of  the  gen¬ 
erated  stable  response  pattern.  Larger  amplitudes  are  generated  as 
compared  with  isotropic  surfaces,  thus  providing  for  greater  poten¬ 
tial  for  modifying  the  turbulence. 

Whenever  the  flow  speed  in  a  turbulent  boundary  layer  becomes 
sufficiently  large  compared  with  the  transverse  free-wave  speed  in 
the  solid,  flow-induced  surface  instabilities  proliferate.  The  pressure 
fluctuations  within  the  flow  are  an  order  of  magnitude  larger  than 
the  normal  and  tangential  viscous  stresses,  and  drive  the  coating 
response.  In  laminar  wall-bounded  flows  it  is  difficult  to  observe 


202 


the  hydroelastic  waves  in  their  unstable  state.  As  soon  as  flutter  or 
divergence  waves  grow,  rapid  breakdown  to  turbulence  takes  place 
in  the  boundary  layer  and  the  flow  is  no  longer  laminar. 

Most  of  the  experimental  studies  concerning  compliant  coating 
effects  on  turbulent  boundary  layers  focused  on  documenting  the 
unstable  flow-induced  surface  instabilities.  When  divergence  waves 
or  flutter  are  unstable,  the  effects,  though  adverse,  are  pronounced 
and  are  somewhat  easier  to  document.  Only  recently  few  hardy 
souls  have  attempted  to  investigate  the  wall-bounded  flows  when 
these  FISI  are  stable  or  neutrally  stable.  Obviously  the  latter  kind 
of  studies  have  to  await  the  development  of  refined  techniques  to 
measure  the  minuscule  surface  deformation  and  the  associated  co¬ 
herent  structure  modulation  when  the  FISI  are  neutrally  stable. 

Both  Gad-el- Hak  (1986)  and  Hess  et  al.  (1993)  introduce  non- 
intrusive  methods  for  the  point  measurement  of  the  instantaneous 
vertical  surface-displacement  of  a  compliant  coating,  while  Lee  et  al. 
(1993b)  offer  an  optical  holographic  interferometer,  in  connection 
with  an  interactive  fringe-processing  system,  to  capture  whole-field 
random  topographic  features.  The  latter  technique  is  more  expen¬ 
sive  to  set  up  but  offers  higher  spatial  resolution,  of  the  order  of  1 
micron,  and  yield  simultaneous  surface  displacement  information  on 
a  large  section  of  the  compliant  coating.  Both  the  local  and  global 
methods  were  initially  employed  to  document  the  unstable  surface 
response  to  the  pressure  fluctuations  in  turbulent  boundary  layers. 
The  holographic  interferometer  was  recently  used  to  record  the  sur¬ 
face  topography  in  the  presence  of  stable  flow-induced  deformations 
(Lee  et  al.,  1993a). 

The  onset  speed  and  wave  characteristics  of  the  solid-based 
class  B  and  C  instabilities  were  systematically  documented  in  a 
series  of  towing-tank  experiments  (Gad-el-Hak,  1986).  Divergence 
waves  were  observed  on  a  single-layer  viscoelastic  coating  made  from 
a  PVC  plastisol.  The  flutter  appeared  on  an  elastic  coating  made 
from  common  household  gelatin,  but,  in  the  absence  of  damping, 
its  threshold  speed  was  consistently  lower  than  that  for  divergence. 
The  damping  in  the  PVC  coating  stabilized  the  traveling-wave  flut¬ 
ter  and  hence  only  divergence  was  observed  there.  For  the  elastic 
coating,  flutter  appeared  first  and  dominated  the  observed  surface 
deformation.  For  both  kind  of  waves,  the  threshold  speed  decreases 
with  coating  thickness,  in  other  words  thin  surfaces  (relative  to  the 
displacement  thickness  of  the  boundary  layer)  are  less  susceptible 
to  hydroelastic  instabilities  than  thick  ones. 

Typical  profiles  of  unstable  class  B  and  C  waves  were  also 
recorded  in  the  same  hydrodynamic  experiments  using  a  laser  dis¬ 
placement  gauge.  The  vertical  displacement  at  a  point  associ¬ 
ated  with  the  slow  moving,  asymmetric,  large-amplitude  diver¬ 
gence  waves  contrasts  the  faster,  more-or-less  symmetric,  smaller- 
amplitude  flutter.  Both  waves  cause  roughness-like  effect,  but  the 
static  divergence  is  the  more  dangerous  instability.  The  phase  speed 
of  the  static-divergence  waves  is  of  the  order  of  1%  of  the  freestream 
speed,  and  their  wavelength  is  about  5-10  times  the  coating  thick¬ 
ness.  The  corresponding  quantities  for  the  flutter  are  40%  and 
1.5-3,  respectively. 

Hess  (1990)  and  Lee  et  al.  (1993a)  also  investigated  compliant 
coating  effects  on  turbulent  boundary  layers.  Both  experiments 
were  conducted  in  the  same  water  tunnel,  but  the  second  paper 
focused  on  the  stable  interaction  between  the  fluid  and  a  single¬ 
layer,  homogeneous,  viscoelastic  coating  made  of  a  mixture  of  sili¬ 
cone  rubber  and  silicone  oil.  Lee  et  al.’s  coating  was  chosen  based 
on  the  criterion  established  by  Duncan  (1986).  In  the  presence 
of  a  stable  wave  pattern  on  the  compliant  surface,  the  flow  visu¬ 
alization  experiments  indicated  low-speed  streaks  with  increased 
spanwise  spacing  (by  as  much  as  80%)  and  elongated  spatial  co¬ 
herence  compared  \yith  those  obtained  on  a  rigid  surface.  More 
significantly,  for  the  particular  compliant  coating  investigated  an 
intermittent  relaminarization-like  phenomenon  was  observed  at  low 
Reynolds  numbers.  Lee  et  al.  (1993a)  also  report  a  slight  thicken¬ 
ing  of  the  buffer  region  and  viscous  sublayer  and  an  upward  vertical 
shift  in  the  compliant  Iaw-of-the-wall.  The  streamwise  turbulence 
intensity,  the  local  skin-friction  coefficient  and  the  Reynolds  stress 
across  the  boundary  layer  were  all  reduced,  indicating  a  possible 
interruption  of  the  feedback  loop  which  allows  the  turbulence  to  be 
self-sustaining.  Thus,  potentially  favorable  interaction  between  a 


compliant  coating  and  a  turbulent  boundary  layer  has  been  demon¬ 
strated  for  the  first  time.  The  more  recent  hydrodynamic  experi¬ 
ments  by  Choi  et  al.  (1997)  provide  additional  evidence  for  favorable 
interaction  and  indicate  a  total  drag  reduction  for  a  long,  slender 
body  of  revolution  of  the  order  of  7%. 

7  The  Future 

The  diminishing  pool  of  researchers  remaining  active  in  the  field 
of  compliant  coatings  includes  teams  from  the  University  of  War¬ 
wick,  University  of  Nottingham,  Johns  Hopkins  University,  Uni¬ 
versity  of  Houston,  University  of  Maryland,  and  the  Institute  of 
Thermophysics  in  Novosibirsk.  A  larger  pool  was  involved  during 
the  early  1980s,  but  the  realities  of  research  funding  combined  with 
the  checkered  past  of  the  field  led  to  the  present  decline. 

Few  suggestions  for  future  research  are  given  in  here.  The  op¬ 
timization  procedures  discussed  in  Section  5.2  have  not  been  vali¬ 
dated  experimentally.  Gaster-type  experiments  should  be  repeated 
using  optimized  coatings,  including  multi-panel  ones.  The  recent 
claims  by  Davies  and  Carpenter  (1997a)  and  Carpenter  (1998)  re¬ 
garding  the  possibility  of  maintaining  laminar  flow  to  indefinitely 
high  Reynolds  numbers  are  very  profound.  Experiments,  partic¬ 
ularly  field  ones  in  low-disturbance  environments,  specifically  de¬ 
signed  to  test  those  claims  would  be  extremely  useful. 

The  results  of  the  transitional-boundary-layer,  wind-tunnel  ex¬ 
periments  reported  by  Lee  et  al.  (1995;  1997)  are  intriguing  and 
fly  in  the  face  of  the  conventional  wisdom.  They  indicate  that 
compliant  coatings  are  capable  of  delaying  transition  even  for  air 
flows.  Past  calculations  using  a  plate-spring  model  and  consid¬ 
ering  the  extremely  large  density  of  typical  walls  compared  with 
the  density  of  air  indicated  that  very  flimsy  coatings  would  be  re¬ 
quired  to  achieve  transition  delay  and  that  the  situation  gets  worse 
as  the  air  speed  increases.  This  led  Carpenter  (1990)  among  oth¬ 
ers  to  conclude  that  the  use  of  wall  compliance  is  impractical  for 
aeronautical  applications.  But  the  plate-spring  results  do  not  ap¬ 
ply  in  any  straightforward  way  to  the  homogeneous,  single-layer 
walls  studied  by  Lee  et  al.  (1995).  Validating  the  recent  favorable 
results  using  both  independent  experiments  and  numerical  simula¬ 
tions  would  open  the  door  for  aerodynamic  applications,  something 
that  was  seriously  considered  but  later  abandoned  by  NASA  and 
the  aerospace  industry.  The  optimization  procedures  developed  by 
Carpenter  (1988)  for  transitional  hydrodynamic  flows  should  be  ex¬ 
tended  to  air  flows.  Experiments  should  be  conducted  using  the 
resulting  optimized  coatings. 

More  complex  coatings  could  potentially  yield  superior  perfor¬ 
mance  as  compared  with  the  relatively  simple  walls  studied  thus 
far.  Multi-panels,  multi-layers,  anisotropic  coatings  and  combina¬ 
tions  thereof  should  be  investigated.  In  any  such  research  program, 
experiments  has  to  be  guided  with  theoretical  results.  As  already 
mentioned,  trying  to  pick  a  compliant  coating  by  trial  and  error 
is  a  very  inefficient  use  of  limited  resources  and  will  perhaps  never 
work. 

Favorably  modulating  a  fully-turbulent  flow,  in  contrast  to 
merely  delaying  transition,  is  also  of  great  practical  importance. 
The  experimental  results  reported  by  Lee  et  al.  (1993a)  are  very 
encouraging,  but  the  coating  used  was  chosen  based  on  a  rather 
simplistic  model  of  the  turbulence  pressure  fluctuations.  In  order 
to  custom-design  compliant  coatings  to  achieve  particular  control 
goals  for  turbulent  wall-bounded  flows,  direct  numerical  simulations 
of  the  coupled  fluid-structure  system  have  to  be  performed.  Tur¬ 
bulence  modeling  via  classical  closure  schemes,  while  sufficient  for 
some  simple  flows  over  rigid  surfaces,  will  perhaps  not  yield  reliable 
results  for  compliant  walls.  DNS,  on  the  other  hand,  requires  ex¬ 
tensive  computer  resources  and  is  quite  expensive  to  carry  out.  The 
bottom  line  is  that  relatively  large  investment  in  resources  are  re¬ 
quired  for  this  task,  but  the  enormous  potential  payoffs  could  easily 
justify  the  expenditure. 

Most  of  the  research  thus  far  has  considered  incompressible,  zero- 
pressure-gradient,  flat-plate  boundary  layers.  Effects  of  compress¬ 
ibility,  pressure  gradient  and  three-dimensionality  on  the  perfor¬ 
mance  of  compliant  coatings  are  largely  unknown.  Such  studies 


203 


will  yield  invaluable  information  for  field  application  of  the  con¬ 
trol  technique  for  both  air  and  water  flows.  Most  practical  aero¬ 
dynamic  flows  are  in  the  moderate-to-high  Mach  number  regime, 
and  compressibility  effects  must  therefore  be  investigated  before 
compliant  coatings  are  used  on  actual  aircraft.  Related  to  the 
pressure-gradient  effects  is  the  question  of  separated  flows:  does 
compliant  coating  affect  separation  favorably  or  adversely?  Other 
stability  modifiers,  such  as  favorable  pressure-gradient,  suction  or 
heating/cooling,  do  delay  transition  as  well  as  prevent  separation. 
It  is  not  known  whether  compliant  coatings  also  have  this  dual 
benefit,  and  it  may  be  beneficial  to  research  the  possibility.  Finally, 
real  flows  are  three-dimensional  and  involve  complex  geometries.  A 
model  problem  for  three-dimensional  flows  is  the  rotating  disk.  Few 
experiments  were  conducted  using  a  rotating  disk  with  a  compliant 
face  (Hansen  and  Hunston,  1974).  More  recently,  Cooper  and  Car¬ 
penter  (1995;  1997a;  1997b;  1997c)  analyzed  the  cross-flow  (type  I; 
inviscid)  as  well  as  the  viscous  (type  II)  fluid-based  instabilities 
which  develop  in  the  same  three-dimensional  flow.  The  preliminary 
results  are  encouraging  and  indicate  that  compliant  coatings  can 
suppress  the  more  dangerous  type  I  instabilities. 

Active  compliant  coatings,  though  bringing  us  back  to  the  com¬ 
plexity  of  reactive  control  systems,  is  an -emerging  area  deserving 
of  further  research.  Energy  expenditure  is  required  to  drive  the 
wall,  but  the  potential  for  significant  net  drag  reduction  is  higher 
than  that  for  passive  coatings.  The  feasibility  of  the  concept  for 
stabilizing  laminar  boundary  layers  has  been  shown  through  nu¬ 
merical  experiments  (Metcalfe  et  al.,  1986).  Active  coatings  could 
also  be  used  to  suppress  the  Reynolds  stress  and  reduce  the  skin- 
friction  drag  in  turbulent  wall-bounded  flows,  but  any  realistic  field 
application  of  the  technique  has  to  await  further  development  of 
reasonably-priced  and  rugged  microfabricated  sensors  and  actua¬ 
tors  (Gad-el-Hak,  1994;  1996b). 

Using  the  subject  of  compliant  coatings  to  make  a  point,  I  would 
like  to  end  this  section  with  a  personal  commentary.  There  is  a 
growing  impatience  among  our  fellow  citizens  with  the  glacial  pace 
of  transferring  knowledge  from  the  laboratories  to  the  factories,  get¬ 
ting  back  the  invested  research  dollars  of  yesterday  in  the  form  of 
stronger  industrial  competitiveness  tomorrow.  In  his  closing  re¬ 
marks  on  the  occasion  of  the  presentation  of  the  1990  American 
Physical  Society  Fluid  Dynamics  Prize,  Lumley  (1992)  lamented 
that  the  United  States  is  a  curiously  unsympathetic  environment 
for  a  theoretician,  or  any  scientist  interested  in  fundamental  work. 
Through  all  its  ups  and  downs,  compliant  coating  research  provides 
a  good  case  study.  Although  in  the  general  scheme  of  things  this 
basic  research  is  but  a  drop  in  the  ocean,  its  triumphs  and  debacles 
are  not  untypical.  The  usual  five-year  cycle  for  academic  research 
is  just  enough  to  get  off  the  ground. 

When  the  compliant  coating  research  program  was  re-ignited 
in  the  early  1980s,  few  veterans  from  the  1960s  and  1970s  were 
around  to  share  their  valuable  experiences,  and  the  newcomers  have 
had  to  climb  the  learning  curve  from  its  bottom.  Nevertheless, 
we  now  know  how  to  carry  out  stability  calculations,  solve  fully 
coupled  fluid-solid  problems,  numerically  simulate  turbulent  flows, 
conduct  well-controlled  experiments  for  both  transitional  and  tur¬ 
bulent  flows,  reliably  measure  surface  deformation,  identify  as  well 
as  quantify  coherent  structures,  optimize  a  coating  for  a  particu¬ 
lar  task  using  first  principles,  ....  In  other  words,  the  compliant 
coating  research  community  has  now  most  of  the  tools  it  needs  for 
significant  further  progress.  Unfortunately,  this  community  has  re¬ 
cently  been  forced  into  an  early  retirement. 

As  amply  illustrated  in  this  paper,  compliant  coating  research, 
despite  its  checkered  history,  offers  the  potential  for  substantial 
transition  delay  and  favorable  interactions  with  turbulent  boundary 
layers.  It  requires  modest  commitment  of  resources,  but  the  payoff 
is  extraordinary.  It  might  be  worth  recalling  that  a  mere  10%  re¬ 
duction  in  the  total  drag  of  an  aircraft  translates  into  a  saving  of 
$1  billion  in  annual  fuel  cost  for  the  commercial  fleet  in  the  United 
States  alone.  Contrast  this  benefit  to  the  annual  cost  of  less  than 
$2  million  for  the  5-year  compliant  coating  research  program  that 
was  sponsored  by  the  U.S.  Office  of  Naval  Research  in  1980.  Pri¬ 
vate  capital  will  not  and  cannot  step  in  place  of  the  government  to 
support  leading-edge  research  with  long-term  promise  but  without 


short-term  return.  Do  we  have  the  will,  desire,  patience  and  re¬ 
sources  to  continue  the  journey  towards  real-life  applications?  In  so 
many  similar  circumstances  in  the  past,  the  answer  was  no.  Scarce 
resources  were  spent  for  five  years  only  to  be  hastily  diverted  to 
newer  areas,  long  before  the  fruits  of  our  labor  have  even  had  a 
chance  of  being  reaped.  But  even  in  these  difficult  times  of  trying 
to  reduce  the  federal  budget  deficit,  one  hopes  for  a  different  road 
to  prosperity — and  I  do  not  mean  for  the  researchers  involved — this 
time  around. 

And  while  we  are  at  it,  cutting  funds  for  basic  research  in  general 
may  be  popular  but  is  certainly  unwise.  Today’s  research  gener¬ 
ates  the  knowledge  from  which  the  future  is  built,  and  a  responsi¬ 
ble  government  must  strike  a  balance  between  near-term  goals  and 
long-term  economic  growth  and  prosperity.  Reducing  spending  on 
current  outlays  is  one  thing,  but  investing  less  in  the  country  future 
is  an  entirely  different  matter.  Fundamental  knowledge  provides 
the  foundation  for  a  nation’s  productivity  and  economic  growth, 
sustains  its  high  standard  of  living,  improves  its  quality  of  health 
and  environment,  and  ensures  its  security.  The  overall  detrimental 
impact  of  reducing  government  funding  for  basic  research  probably 
will  not  be  felt  for  a  generation,  but  it  will  be  felt. 

8  Parting  Remarks 

Passive  compliant  coatings  present  a  much  simpler  alternative 
to  reactive  flow  control  strategies  aimed  at  favorably  interfering 
with  wall-bounded  flows.  The  last  10-15  years  witnessed  renewed 
interest  in  compliant  coatings  as  a  means  to  achieve  beneficial  flow 
control  goals.  Significant  advances  were  made  in  numerical  and 
analytical  techniques  to  solve  the  coupled  fluid-structure  problem. 
Novel  experimental  tools  were  developed  to  measure  the  stable  as 
well  as  the  unstable  surface  deformations  caused  by  the  pressure 
fluctuations  in  the  boundary  layer.  In  turbulent  wall-bounded  flows, 
coherent  structures  were  routinely  identified  and  their  modulation 
by  wall  compliance  could  be  quantified. 

Most  significant  results  in  the  field  thus  far  were  obtained  when 
a  strong  cooperation  existed  between  theory  and  experiment.  Re¬ 
cent  theoretical  work  indicates  that  complete  suppression  of  the 
Tollmien-Schlichting  waves  may  be  possible,  provided  that  opti¬ 
mized  multiple-panel  compliant  walls  are  used.  The  new  finding 
raises  the  possibility  of  maintaining  laminar  flow  to  indefinitely  high 
Reynolds  numbers,  a  very  profound  prospect  indeed.  Recent  exper¬ 
iments  indicate  favorable  compliant  coating  interactions  even  for 
aerodynamic  flows  and  even  for  turbulent  boundary  layers.  More 
research  is  needed,  however,  to  confirm  these  latest  results. 

The  coupled  system  instabilities  are  now  well  understood,  and 
compliant  coatings  can  therefore  be  rationally  designed  to  achieve 
substantial,  perhaps  even  indefinite,  transition  delay  in  hydrody¬ 
namic  flows.  That  recent  shift  from  random  to  rational  search  for 
the  right  kind  of  coating  is  not  unlike  the  great  paradigm  change 
in  synthetic  chemistry  that  took  place  near  the  beginning  of  the 
twentieth  century.  Increased  understanding  of  the  molecular  ge¬ 
ometry  of  organic  compounds  changed  the  scene  from  a  hapless 
alchemist  muddling  around  hoping  to  chance  the  right  combination 
of  ingredients,  heat,  pressure  and  catalysts  to  produce  something 
useful  to  a  professional  chemist  figuring  out  what  she  wants  and 
working  backward  from  the  shape  of  a  desired  molecule  for,  say,  a 
synthetic  hormone.  In  fact,  the  present  analogy  is  apt:  the  fluid 
dynamist  working  with  the  Navier-Stokes  equations  can  tell  the 
chemist  the  exact  properties  of  the  compliant  coating  to  be  synthe¬ 
sized  to  achieve  a  given  goal.  If  the  needed  molecular  structure  is 
too  complicated,  futuristic  nano-scale  machines  can  assemble  the 
required  molecules  directly,  element  by  element. 


204 


DRAG  REDUCTION  OF  THE  OCEAN  SURFACE  BY  THE  SURFACE  WAVES 


Alexander  Y.  Benilov 

Davidson  Laboratory,  Stevens  Institute  of  Technology 
Castle  Point  on  Hudson 
Hoboken,  New  Jersey,  07030,  USA 
abenilov@stevens-tech.edu 

Abstract  -The  experimental  and  theoretical  study,  presented  in  the  paper,  demonstrates  that  the  key  parameter  controlling  the  aerodynamic 
resistance  of  the  ocean  surface  is  the  wave  age.  (1)  For  the  “young”  waves,  the  ocean  surface  behaves  as  a  rough  solid  surface.  The  roughness 
parameter  exceeds  the  thickness  of  laminar  sub-layer  and  the  drag  coefficient  may  be  significantly  greater  than  it  would  be  for  a  smooth  surface. 
The  wind  looses  its  energy  and  momentum  and  the  wave  grows.  (2)  When  the  wind  waves  reach  the  developed  state,  the  ocean  surface  behavior 
becomes  similar  to  the  smooth  solid  surface.  The  fluxes  of  wind  energy  and  momentum  balance  the  losses  which  the  waves  experience  by 
breaking.  (3)  The  ocean  surface  becomes  “oversmoothed”  in  the  case  of  the  “old”  waves.  The  roughness  parameter  becomes  less  than  the  thickness 
of  laminar  sub-layer  and  the  drag  coefficient  becomes  less  than  it  would  be  for  a  smooth  solid  surface  under  the  same  wind  conditions.  In  this  case, 
the  waves  transfer  their  energy  and  momentum  to  the  atmospheric  boundary  layer.  A  comparison  shows  that  the  theoretical  conclusions  have  a 
good  correlation  with  measurements. 


I.  INTRODUCTION 

The  transport  of  momentum,  heat,  humidity,  and  salt  occurs  across 
the  air-sea  interface.  The  character  of  this  transport  is  regulated  by  the 
turbulence  of  the  air-sea  interface.  Influences  of  surface  waves  on  surface 
layers  of  the  atmosphere  and  ocean  have  been  well  noted  by  many 
researchers  [1-12].  These  influences  are  very  complex  and  still  poorly 
understood,  although  there  have  been  numerous  experimental 
investigations  and  analytical  studies.  There  is  not  sufficient  observational 
data  to  specify  completely  the  quantitative  impact  of  surface  waves  on  the 
characteristics  of  air-sea  boundary  layers.  One  of  the  major  difficulties  in 
air-sea  interaction  problems  is  the  correct  description  of  surface-wave 
effects.  Here,  the  distinctive  feature  is  the  oscillation  of  the  air-water 
interface,  so  that  the  standard  methods  of  description  of  turbulence  are 
generally  inapplicable. 

An  important  factor  giving  rise  to  the  boundary  layer  in  the 
atmosphere  above  the  sea  surface  is  the  expenditure  of  momentum  and 
energy  of  the  wind  on  the  generation  of  waves  and  currents  [13-15].This 
constitutes  a  fundamental  difference  of  the  atmospheric  surface  layer  not 
only  from  the  ordinary  layer  above  a  smooth  wall  (solid  surface),  but  also 
from  the  boundary  layers  above  stationary  rough  surfaces.  The  interval  of 
the  atmospheric  boundary  layer  right  above  the  water  surface,  which  is  a 
few  tens  of  meters  thick,  is  called  the  atmospheric  surface  layer.  A 
distinctive  property  of  this  layer  is  that  within  it,  the  vertical  fluxes  of 
momentum,  heat,  moisture,  and  various  types  of  passive  impurities  vary 
little  with  height,  and  they  can  be  taken  as  constants.  This  experimentally 
established  fact  is  important  in  studying  the  turbulent  boundary  layer  above 
the  ocean  and  the  interaction  .of  the  atmospheric  boundary  layer  with  the 
underlying  surface  because  of  the  fluxes  that  completely  define  the 
turbulent  structure  of  the  layer  [16]. 

II.  VERTICAL  STRUCTURE 

It  is  known  that  the  turbulent  boundary  layer  of  the  atmosphere  is 
stratified;  turbulent  processes  within  it  are  influenced  by  buoyancy,  which 
in  turn  results  from  changes  in  air  density  owing  to  fluctuations  in 
temperature  and  humidity.  In  particular,  the  structure  of  the  main  interval 
of  the  atmospheric  surface  layer  at  a  distance  above  sea  level  greater  then  a 
few  times  the  height  of  the  largest  waves  was  described  by  the 
Monin-Obukhov  theory  [4,  7,  10,  11,  16].  This  theory  gives  equations 
relating  the  steady-state  characteristics  of  turbulence  at  various  heights  to 
known  turbulent  fluxes  of  momentum,  heat,  and  humidity  under  particular 
stratification  conditions.  The  important  parameter  of  the  theory  is  the 
Monin  -Obukhov  buoyancy  scale,  which  can  be  used  to  distinguish  two 
sub-layers  within  the  surface  layer.  In  the  lower  sub-layer,  at  heights  less 
than  the  buoyancy  scale,  the  effect  of  stratification  is  small  and  the  laws 
applying  to  a  turbulent  boundary  layer  in  a  fluid  of  uniform  density  are 
applied.  The  mean  wind  velocity  profile,  u  (z) » has  the  classical  form 

Ua(Z)=Vb 

K 

where  z  is  the  distance  from  undisturbed  ocean  surface,  u*  is  the  friction 
velocity,  k  is  the  Karman’s  constant,  Zo  is  the  roughness  parameter.  In  a 
regular  turbulent  flow  over  a  rough  solid  surface,  the  roughness  parameter 
is  associated  with  the  actual  roughness  of  the  surface.  The  situation  is 


totally  different  from  the  ocean  condition  where  the  roughness  parameter  is 
a  result  of  the  wind-wave  interactions.  The  so-called  logarithmic  turbulent 
boundary  layer  is  similar  in  many  respects  to  the  turbulent  boundary  layer 
above  stationary  smooth  or  rough  surfaces.  However,  the  roughness 
parameter  has  tremendous  variability  and  varies  from  0.00001  cm  to  10 
cm.  This  results  in  the  variability  of  the  drag  coefficient  of  the  ocean 
surface  ranging  from  0.0005  to  0.01  [2,  11].  These  experimental  facts 
clearly  demonstrate  that  the  atmospheric  surface  layer  differs 
fundamentally  from  both  the  ordinary  boundary  layer  above  a  smooth  wall 
(  solid  surface)  and  the  boundary  layer  above  a  stationary  rough  surface. 
The  upper  sub-layer  occurs  at  heights  greater  than  the  buoyancy  scale, 
where  the  effect  of  stratification  is  more  important  than  the  effect  of  mean 
wind  shear.  In  unstable  stratification,  the  equations  of  turbulent  convection 
are  applied  in  this  layer.  Conclusions  derived  from  the  Monin  -  Obukhov 
theory  are  the  principal  tool  for  calculating  the  characteristics  of  the 
turbulent  atmospheric  surface  layer. 

Much  valuable  data  on  the  vertical  and  local  structure  of 
turbulence  are  published  in  monographs  [2,  3,  5-8,  10].  The  primary 
conclusion  to  be  drawn  from  this  data  is  that  at  a  sufficient  distance  above 
the  sea  surface  (equal  to  a  few  times  the  height  of  the  highest  waves)  the 
Monin  -  Obukhov  similarity  theory  gives  a  satisfactory  description  of  the 
characteristics  of  turbulence.  Empirical  data  on  the  universal 
characteristics  of  turbulence  in  terms  of  this  theory  were  presented  in  full 
form  by  Kader  and  Yaglom  [17],  who  systematized  measurements  of 
turbulence  in  the  atmospheric  surface  layer  over  land.  There  are  still 
insufficient  measurements  in  the  atmospheric  surface  layer  above  water  for 
such  a  systematization,  but  the  results  that  Kader  and  Yaglom  present  can 
be  used  as  a  substitute  when  making  estimates  for  marine  conditions.  The 
assumption  of  local  equilibrium  of  turbulence  is  valid  in  the  turbulent 
spectra  of  this  part  of  the  surface  layer  above  the  ocean. 

In  the  layer  of  air  between  the  logarithmic  sub-layer  and  the  water 
surface,  however,  the  theory  of  similarity  cannot  be  applied  owing  to  the 
strong  influence  on  dynamic  conditions  exerted  by  the  surface  waves.  An 
example  of  such  influence  in  a  mean  velocity  profile  is  shown  in  Figure  1. 
This  deviations  can  be  presented  in  an  universal  form  (Figure  lb)  where 
atT  (7  \  corresponds  to  the  lower  horizon  Zn,in.  One  can  see  that  the 

deviation  from  the  “logarithm’Maw  is  not  small  and  may  have  a  magnitude 
~0.5  m/s.  The  wave  “age”,  Co/u*,  defines  the  sign  of  the  deviations,  C0  is 
the  phase  velocity  of  the  wave  which  corresponds  to  the  spectral  peak  of 
wind  wave.  The  effect  of  the  wave  factor  is  shown  up  in  all  characteristics 
of  turbulence.  The  effective  mechanism  is  redistribution  of  the  vertically 
invariant  flux  of  momentum  between  the  turbulent  and  wave  components 
of  momentum  [1-3,  5,  6,  8,  10,  18-21].  It  is  known  from  observations  that 
in  the  layer  of  air  about  ten  meters  thick,  waves  make  a  significant 
contribution  to  the  mean  and  fluctuating  fields.  The  waves  increase  the 
intensity  of  the  fluctuations  [3,  6]  and  change  the  nature  of  the  correlation 
between  the  fluctuation  characteristics  [7,  22-25].  The  peaks  produced  by 
waves  are  clearly  distinguishable  in  the  fluctuation  spectra.  The  waves  also 
make  a  considerable  contribution  to  the  total  fluxes  of  momentum,  heat 
and  moisture.  The  mathematical  procedure  for  filtering  stationary  random 
processes  can  be  used  to  reconstruct  the  contributions  of  waves  and 
turbulence  [25], 

Measurements  in  the  air  layer  between  the  crests  and  troughs  of  the 
waves  have  proven  to  be  difficult.  Therefore  little  is  known  about  the 
turbulence  and  the  wave  induced  disturbances  within  this  layer.  Few 
measurements  on  the  laminar  sub-layer  in  the  vicinity  of  the  water  surface 


205 


were  done,  and  a  brief  description  of  results  is  given  in  [7,  9].  The  recent 
findings  [19]  used  Particle  Image  Velocimetery  (PIV)  techniques.  Images 
of  the  flow  using  neutrally-buoyant  20-60pm  diameter  fluorescent  micro¬ 
beads  as  tracers  provided  the  detailed  fluid  velocity  information  in  the 
viscous  sub-layer  beneath  the  waves,  within  the  top  1  mm  of  the  surface. 
The  study  discovered  that  the  mean  tangential  stress  was  significantly  less 
than  wave  form  drag  [18]. 

HI.  TURBULENT  FLUXES 

The  theoretical  approaches  to  the  structure  of  turbulence  and  wave 
disturbances  in  the  atmospheric  surface  layer  require  us  to  specify  the 
vertical  fluxes  of  momentum,  heat  and  moisture.  Thus,  the  models  of  the 
atmospheric  surface  layer  must  identify  the  physical  causes  of  the 
variability  in  the  fluxes  of  momentum,  energy,  heat  and  moisture,  the  laws 
governing  this  variability,  and  the  mechanisms  making  the  principal 
contribution  to  the  variability  of  the  fluxes.  In  the  customary  terminology, 
the  problem  consists  of  determining  the  factors  causing  the  drag  of  the 
ocean  surface  and  the  laws  of  heat  and  mass  transfer  between  ocean  and 
atmosphere. 

The  development  of  detailed  models  that  could  answer  the  above 
questions  is  made  difficult  by  the  important  fact  that  the  fluxes  of 
momentum  and  energy  between  the  atmosphere  and  ocean  are  expended  on 
the  generation  and  maintenance  of  waves,  currents  and  turbulence.  But  the 
question  remains  as  to  how  the  fluxes  are  distributed  between  these  three 
dynamically  different  components  of  motion.  So  far,  no  definitive  answer 
to  this  problem  has  been  found.  The  most  popular  approach  in  practical 
calculations  is  the  simple  hypothesis  that  the  dimensionless  coefficients  of 
drag,  heat  transfer,  and  evaporation  are  constant  and  of  approximately 
equal  magnitude,  roughly  10'3.  The  numerical  estimates  of  the  coefficients 
are  consistent  with  the  mean  values  obtained  by  averaging  all  available 
measurements.  According  to  measurements  taken  by  numerous  researchers 
[2-5,  7,  8,  10,  11,  27],  the  coefficients  of  drag,  heat  transfer  and 
evaporation  range  over  two  orders  of  magnitude,  from  10^  to  10‘2.  The 
physical  basis  for  the  assumption  of  constant  coefficients  is  the  conclusion, 
based  on  an  analysis  of  experimental  data,  that  surface  waves  exert  a  strong 
influence  on  the  aerodynamic  characteristics  of  the  sea  surface.  Since  wind 
waves  are  rapidly  converted  to  equilibrium  waves,  the  accepted  figure  for 
the  coefficients  corresponds  precisely  to  this  case.  A  correction  for 
variations  in  the  interaction  between  the  boundary  layer  of  the  atmosphere 
with  the  ocean  was  made  by  the  researchers  noted  above.  They  employ 
empirical  equations  to  present  the  interaction  coefficients  as  functions  of 
the  wind  speed.  These  equations,  as  one  can  see  in  [1 1],  generally  have  the 
same  level  of  error  as  the  hypothesis,  as  they  are  constant. 

Theoretical  models  of  the  interactions  between  the  turbulent 
boundary  layers  of  the  atmosphere  and  ocean,  developed  from  the  simplest 
models  with  a  constant  turbulent  viscosity  to  k  -  s  turbulent  model,  can  be 
used  to  estimate  the  magnitude  of  interaction,  neglecting  the  energetic  of 
wind  waves.  But  these  calculations  do  not  explain  the  actual  variability  of 
the  interaction  parameters. 

Simple  estimates  of  the  interaction  between  wind  and  waves  indicate 
that  wind  waves  are  very  energy-intensive  and  accumulate  a  considerable 
fraction  of  the  total  momentum  and  energy  of  the  atmospheric  boundary 
layer;  the  flux  of  momentum  to  the  waves  is  comparable  in  magnitude  to 
the  total  flux  of  momentum  to  the  sea  surface,  and  the  influence  of  waves  is 
not  confined  to  the  dynamic  characteristics  of  the  atmospheric  boundary 
layer,  but  also  extends  to  the  rate  of  heat  transfer  between  the  ocean  and  the 
atmosphere. 

The  mutual  adaptation  of  the  wind  and  waves  can  be  studied  directly 
via  the  integral  laws  of  conservation  of  momentum  and  energy  in  the 
atmospheric  boundary  layer  and  in  surface  waves  [11,  14,  28],  using 
integral  methods  that  are  common  in  the  classical  boundary  layer  theory, 
the  main  principles  of  the  theory  of  wind  waves  [  1 ,  29]  and  the  mechanism 
of  wind  wave  breaking  described  by  Longuet-Higgins  [30]. 

The  equations  for  the  wave  momentum  and  energy,  in  the  case  of 
horizontally  uniform  waves,  finally  yield  an  evolutionary  equation  for  the 
phase  velocity  C0(t), 

Pw  “C0d<C0  =  Pau-  -  jy,PwPCo'  (2) 

where  pw  is  the  water  density,  p  is  the  Phillips’  constant,  the  second  term  in 
the  right  hand  side  represents  the  wave  breaking  ,  yi  ~  3x10  ’  4  is  the 
Longuet-Higgins’  constant  in  the  wave  breaking  parameterization.  The 
equations  of  wind  momentum  and  energy  yield  the  equations  on  u*(t)  and 
the  boundary  layer  thickness  8(t), 


d 


Ua,s5 


«Mu;,6 


kU. 


kU 


a, 5 


=  u.2(yuas  +  c0). 


exp 


kU 


(3) 

(4) 


(5) 


where  Ua>5  is  the  known  wind  velocity  at  the  upper  boundary  of 
atmospheric  boundary  layer  z  =  8(t)  ,  y  is  the  dimensionless  dissipation 
constant.  For  developed  waves,  the  wave  equation  (2)  defines  two 
dimensionless  parameters  -  the  root  mean  square  wave  elevation  gan  /  u*  — 
a\  and  the  frequency  of  wave  spectral  peak  o>ou*/g  =  <?2-  Calculated  and 
well  known  experimental  appraisals  conform  with  one  another  better  than 
one  could  expect.  The  asymptotic  analysis  of  (2)  -  (5)  shows  that  the  drag 
coefficient  of  sea  surface  in  the  fully  developed  wave  case  reduces  to  a 
value  which  is  about  the  drag  coefficient  of  smooth  flow. 

The  generation  of  wind  waves  consists  of  the  following  two  main 
stages:  1)  the  generation  of  non-collapsing  waves,  in  which  there  is  little 
collapse  and  the  evolution  of  the  atmospheric  boundary  layer  and  the 
waves  is  not  affected  and  2)  the  concluding  stage,  in  which  effective  wave 
breaking  occurs.  Calculations  indicate  that  the  principal  factor  governing 
the  dynamic  properties  of  the  atmospheric  boundary  layer  above  the  sea 
and  the  state  of  the  underlying  surface  is  the  ratio  of  the  phase  velocity  of 
the  spectral  peak  of  the  wind  waves  to  the  friction  velocity;  this  finding 
corresponds  well  to  numerous  measurements,  and  this  approach  explains 
the  observed  variation  in  the  characteristics  of  the  atmospheric  boundary 
layer(  Figures  2-5),  since  the  surface  waves  are  able  to  adapt  themselves  to 
particular  wind  conditions,  and  it  also  can  be  used  to  derive  numerous 
empirical  equations  for  developed  wind  waves.  Allowing  for  wave 
breaking  makes  it  possible  to  trace  the  evolution  of  the  wind  and  waves  all 
the  way  to  the  equilibrium  steady  state.  The  theory  can  be  used  to  derive 
practically  all  known  empirical  equations  related  with  the  characteristics  of 
the  atmospheric  surface  layer  and  to  find  the  limiting  law  of  drag  of  the  sea 
surface,  which  is  qualitatively  very  similar  to  the  experimental  figures 
obtained  in  1960  for  Hurricane  Donna[4]. 

Several  modified  models  were  developed  to  incorporate  the 
characteristics  of  the  atmospheric  boundary  layer  and  the  sea  waves 
(Gumbatov,  Mamedov,  1983;  Belberov,  1985;  Alchmetov  et  al.,  1987); 
these  models  were  in  agreement  with  measurements. 

The  full  integral  model  (2)  -  (5)  extends  the  previous  results.  The 
following  important  result  from  the  full  model  is  worth  noting:  this  theory 
makes  it  possible  to  calculate  the  flux  of  momentum  to  waves,  the  amount 
of  the  momentum  flux  from  the  wave  breaking  that  is  consumed  in  the 
generation  of  drift  currents,  the  flux  of  energy  to  the  waves,  and  the  amount 
of  the  flux  energy  from  the  wave  breaking  that  is  used  in  the  generation  of 
turbulence  in  the  upper  layer.  This  model  can  also  be  used  to  construct  a 
theory  of  heat  transfer  [1 1]  in  the  course  of  the  development  of  wind  waves 
which  qualitatively  agrees  with  measurements  [24], 

Measurements  were  taken  of  the  dynamic  and  thermodynamic 
characteristics  of  the  surface  layer  above  water  that  govern  its  vertical  and 
local  structure  (see  for  example  [6,  22-24,  31]).  These  studies  indicate  that 
these  quantities  are  highly  dependent  on  the  degree  of  development  of  the 
waves.  Figures  2  shows  the  empirical  dependence,  based  on  these 
observation,  of  the  roughness  length  Zo  as  a  function  of  the  wave  age  Co/u* 
(where  C0  is  typical  phase  velocity  of  surface  waves  customarily  associated 
with  the  maximum  of  the  wave  spectrum,  u.  is  the  friction  velocity) .  With 
a  certain  dispersal,  experimental  points  gather  around  one,  universal 
dependence,  which  in  a  broad  scope  of  parameter  Cq/u*  change  (5  <  Co/u. 
<  90)  can  be  approximated  by  the  second  order  polynomial  [12]: 


-35  +  1.29 


±5, 


(6) 


where  zv  =  0.1 1  v/  u*  is  the  roughness  parameter  of  the  smooth  wall,  v  is 
the  coefficient  of  molecular  viscosity  of  the  air,  k  *=  0.4.  The  same  data 
were  presented  in  the  form  of  the  drag  coefficient  deviation,  8CU  =  Cu  - 
Cu >smooth  ,  where  CUjSmooth  is  the  drag  coefficient  of  “smooth”  wall  (Figure  3). 


206 


The  both  forms  demonstrate  strong  wave  influence  on  the  drug  reduction 
and  the  roughness  of  the  ocean  surface. 

The  equation  (6)  was  applied  for  a  numerical  modeling  of  influences 
of  ocean  waves  on  turbulence  of  the  air-sea  system  [32].  The  model  shows 
good  agreements  with  measurements  of  influences  of  waves  on  wind  and 
geostrophic  drag  coefficients.  It  is  also  possible  to  classify  the  cases  of 
deviation  from  logarithmic  law  for  the  mean  wind  velocity  Ua(z)  [6], 

IV.  DISCUSSION  AND  CONCLUSION 

The  wind-wave  interaction  produces  significant  impact  on  the 
atmospheric  boundary  layer  above  the  ocean  surface.  Three  fundamental 
features  of  this  interaction  are  as  follows: 

1. For  the  “young”  waves,  the  ocean  surface  behaves  as  a  rough  solid 

surface.  The  roughness  parameter  exceeds  the  thickness  of  laminar  sub¬ 
layer  and  the  drag  coefficient  may  be  significantly  greater  than  it  would  be 
for  a  smooth  surface.  This  regime  corresponds  to  the  strong  interaction 
between  the  wind  and  the  surface  waves.  The  wind  looses  its  energy  and 
momentum  and  the  wave  grows.  In  the  presence  of  developing  waves 
(Cq/u*  <  33  5),  momentum  is  transferred  from  the  wind  to  the  waves, 

which  ultimately  causes  large  deviations  from  smoothness  and  gives  rise  to 
"rough"  air  flow  conditions  and  agrees  very  well  with  the  integral  model 
[14]  and  (2)-(5).  One  can  see  that  the  drag  coefficient,  observed  and 
predicted,  reduces  about  ten  times  (Figure  4),  and  that  yields  the  variability 
of  roughness  parameter  /  jj*  ranging  from  10*1  to  10'7  (Figure  5). 

2.  When  the  wind  waves  reach  the  developed  state,  the  ocean  surface 

behavior  becomes  similar  to  the  smooth  solid  surface.  The  fluxes  of  wind 
energy  and  momentum  balance  the  losses  which  the  waves  experience  by 
breaking.  In  this  intermediate  situation  (C0/u*  «  33  5)  and  the  ocean 

surface  is  nearly  aerodynamically  smooth  (z0  ~  Zv),  the  waves  usually  may 
be  treated  as  developed  and  thus  as  largely  unaffected  by  the  wind  (that 
corresponds  an  asymptotic  state  of  interaction  between  wind  and  waves  in 
the  model),  so  that  the  entire  flux  of  momentum  from  the  atmosphere 
ultimately  is  imparted  to  currents  rather  than  to  the  waves  as  a  result  of 
viscous  friction  with  the  underlying  surface  and  the  wave  breaking.  In  this 
case,  according  to  the  recent  measurement  [19],  the  wave  breaking 
mechanism  dominates  in  transmitting  the  momentum  to  the  drift  current. 
Figure  6  shows,  by  the  asymptotic  solution  of  (2)  -  (5)  and  the  data  of  the 
Marine  Hydrophysics  Institute  wind-wave  tank  by  Leikin  and  Rosenberg, 
how  the  equilibrium  state  between  wind  and  waves  establishes  in  terms  of 
the  ratio  Ua  /Q-  One  can  see  that  the  theoretical  prediction  with  y  =  0.5 

and  the  deep  water  data  ( Ua  =  3  m/s)  meet  the  same  limit  value. 

3.  The  “old”  waves  are  not  associated  with  the  local  wind  condition, 

except  propagating  in  the  same  direction  as  the  local  wind.  The  ocean 
surface  becomes  “oversmoothed”.  The  roughness  parameter  becomes  less 
than  the  thickness  of  laminar  sub-layer  and  the  drag  coefficient  becomes 
less  than  it  would  be  for  a  smooth  solid  surface  under  the  same  wind 
conditions.  In  this  case,  the  waves  transfer  their  energy  and  momentum  to 
the  atmospheric  boundary  layer.  When  swells  are  present  or  in  a  situation 
of  slackening  winds  but  with  already  developed  waves(C0/u*  >  33  5),  the 

atmospheric  boundary  layer  receives  additional  momentum  from  the  waves 
and  "oversmoothed"  conditions  of  air  flow  over  the  sea  surface  occur.  This 
means  that  the  waves  play  role  of  a  propulsive  force  with  respect  to  the  air 
boundary  layer. 

V.  REFERENCES 

1.  O.  M.  Phillips,  “The  Dynamics  of  the  Upper  Ocean.  Cambridge 
University  Press”,  1966. 

2.  S.A  Kitaygorodskiy  “The  Physics  of  Air-Sea  Interaction”,  Israel 
Programs  for  Translation,  Jerusalem,  1973. 

3.  A  S.  Dubov  “Transfer  Processes  Near  an  Interface”,  Gidrometeoizdat, 
Leningrad,  240  pp.,1974. 

4.  S.S.  Zilitinkevich,  A  S,  Monin,  And  D.V.  Chalikov  “Interaction 
Between  the  Ocean  and  Atmosphere”,  In:  Oceanology.  Physics  of  the 
Ocean.  Vol.l.  Hydrophysics  of  the  Ocean.  Nauka  Press,  Moscow,  pp. 
208-339,1978. 

5.  E.K.  Byutner  “Dynamic  of  the  Atmospheric  Surface  Layer”, 
Gidrometeoizdat,  Leningrad,  158  pp.,  1978. 

6.  V.V.  Yefimov  “Dynamics  of  Wave  Processes  in  the  Atmospheric  and 
Oceanic  Boundary  Layers”,  Naukova  Dumka  Press,  Kiev,  256  pp.,  1981. 

7.  G.N.  Panin  “Heat  and  Mass  Transfer  Between  a  Water  Body  and  the 
Atmosphere  Under  Natural  Conditions”,  Nauka  Press,  Moscow,  206  pp., 
1985. 


8.  R.S.  Bortkovskii  ”Ar-Sea  Exchange  of  Heat  of  Moisture  During 
Storms”,  D.  Reidel  Pub.Co.  159  pp.,  1987. 

9.  K.N.  Fedorov,  A  I  Ginzburg  “The  Near-Surface  Ocean  Layer”, 
Gidrometeoizdat,  Leningrad,  1988. 

10.  G.L  Geemaert  and  W.L.  Plant,  (Ed.)  “Surface  Waves  and  Fluxes, 
Volume  1  -  Current  Theory”,  Kluwer  Academic  Publishers,  336  pp.,  1990. 

11.  B.A  Kagan  “Ocean  -  Atmosphere  Interaction  and  Climate 
Modeling”,  Cambridge  University  Press,  377  pp. ,  1995. 

12.  AY.  Benilov  “Influence  of  Surface  Waves  on  the  Atmosphere 
Turbulent  Boundary  Layer”,  In:  Numerical  methods  in  laminar  & 
turbulent  flow,  vol.  9,  Pineridge  Press,  Swansea,  U.K.,  pp.  960-971,  1995. 

13.  B.  Benjamin  “Shearing  Flow  Over  a  Wavy  Boundary”,  J.Fluid  Mech., 
v.66,  1959. 

14.  AY.  Benilov,  A  I.  Gumbatov  et  al.  “Nonsteady  -  State  Model  of  the 
Development  of  the  Turbulent  Boundary  Layer  above  the  Sea  with 
Generation  of  Surface  Waves”,  Izv.Ac.Sci.USSR,Atm.Ocean.Phys.,  v.  14, 
No.l  1,1978. 

15.  AY.  Benilov  “Dynamic  Structure  of  the  Upper  Ocean  Including  The 
Effects  of  Surface  Waves  and  Breaking”,  TR-SIT-DL  Project  No.  5540, 
Stevens  Institute  of  Technology,  Hoboken,  NJ,  53  pp.,  1997 

16.  AS.  Monin  and  AM.  Yaglom  “Statistical  Fluid  Mechanics: 
Mechanics  of  Turbulence.  Vol.l  -2”,  MIT  Press,  1987. 

17.  V.  Kader  and  A  M.  Yaglom  “Mean  Fields  and  Fluctuation  Moments 
in  Unstably  Stratified  Turbulent  Boundary  Layers”,  J.  Fluid  Mechu,v.  212, 
pp.  637-662,1990. 

18.  M.L.  Banner  “The  Influence  of  Wave  Breaking  on  the  Surface 
Pressure  Distribution  in  Wind-Wave  Interactions”,  J.Fluid  Mech.,  v.2 11, 
463-495,  1990. 

19.  M.L.  Banner  and  W.L.  Peirson  “Aerodynamic  Roughness  of  the  Sea 
Surface”.  Johns  Hopkins  Conference  in  Environmental  Fluid  Mechanics, 
pp.  13-14,  1998. 

20.  D.V.  Chalikov  “Numerical  Simulation  of  the  Boundary  Layer  Above 
Waves”,  Boundary  Layer  Meteorology,  v.  43,  No.  1,  pp.  63-98,  1986. 

21.  D.V.  Chalikov  “The  Parameterization  of  the  Wave  Boundary  Layer”, 
Journal  of  Physical  Oceanography,  v.25,  No.6,  Part  1,  pp.  1333-1349, 
1995. 

22.  Y.A  Volkov  “Spectra  of  Velocity  and  Temperature  Fluctuations  of 
the  Air  Flow  Above  a  Surface”.  Izv.  Ac.  Sci.  USSR,  Atm.  Ocean  .Phys., 
v.5.  No.  12,  pp.1251-1265,  1969. 

23. V.I.  Makova  “Characteristics  of  the  Dynamic  Regime  of  Turbulence  in 
the  Atmospheric  Surface  Layer  in  Various  Stages  of  Wave  Development”, 
Izv.  AC.  Sci.  USSR,  Atm.  Ocean.  Phys.,  v.  11,  No.  3,  pp.297-307,  1975. 

24.  AS.  Aliyev,  S.  L.  Zubko vskiy,  and  L.  R.  Tsvang  “Universal 
Functions  for  Atmospheric  Turbulence  Above  the  Sea”,  In:  Atmospheric 
Physics  and  the  Problem  of  Climate,  Nauka  Press,  Moscow,  pp.  194-2 15, 
1980. 

25.  AY.  Benilov,  O.A.  Kuznetsov,  and  G.N.  Panin  “On  the  Analysis  of 
Wind  Wave-Induced  Disturbances  in  the  Atmospheric  Turbulent  Surface 
Layer”,  Boundary  Layer  Meteorology,  v.  6,  No.  1-2,  pp.  269-285,  1974. 

26.  M. A  Donelan  “The  dependence  of  aerodynamic  drag  coefficient  on 
wave  parameters”.  In:  Proceedings  of  the  First  International  Conference  on 
Meteorology  and  Coast  Zone,  Boston,  MA,  Amer.Meteorol.Soc.  381-387, 
1982. 

27. G.L.  Geemaert,  G  L,  K  Katsaros,  and  K  Richer  “Variation  of  the  drag 
coefficient  and  its  dependence  on  sea  state”,  J.Gephys.Res.,  v.91, 
7667-7679,  1986. 

28.  AY.  Benilov  “On  the  Interaction  of  the  Wind  Field  with  Waves  on  a 
Shallow  Sea”,  In:  Interaction  of  the  Atmosphere,  Hydrosphere  and 
Lithosphere  in  the  Coastal  Zone  of  the  Sea.  The  Kamchiya  -79  Experiment, 
Sofia,  Bulgarian  Academy  of  Sciences,  pp.  175-184,  1983. 

29. V.E.  Zaharov  and  M.  M.  Zaslavskii  “Kinetic  Equation  and 
Kolmogorov  Spectra  in  the  Weakly  Turbulent  Theory  of  Wind  Waves”, 
Izv.  Ac.  Sci.  USSR,  Atm.  Ocean.  Phys.,  v.  18,  No.  9,  pp.970-979,  1982. 

30. M.S.  Longuet-Higgins  “  On  Wave  Breaking  and  the  Equilibrium 
Spectrum  of  Wind-Generated  Waves.  Proc.  Roy.  Soc.,  A  310,  No.  1501, 
pp.  151-159,  1969. 

31.  AY.  Benilov,  A  I.  Gumbatov  et  al.  “Interpretation  of  Measurements 
of  the  Mean  Wind  Speed  in  the  Atmospheric  Surface  Layer”,  Izv.  Ac.  Sci. 
USSR.,  Atm.  Ocean.  Phys.,  v.  12,  No  10,  pp.  1011-1019,  1976. 

32. L.N.  Ly  and  P.  Luong  “A  mathmatical  coastal  ocean  circulation  system 
with  breaking  waves  and  numerical  grid  generation”.  Applied 
Mathematical  Modeling,  v.  10,  No.  10,  633-641,  1998. 


207 


Figure  1.  Deviation  of  mean  velocity  profiles  from  the  “logarithm’Maw  in  the  interaction  sub-layer. 


Figure  2.  Aerodinamical  features  of  the  ocean  surface 


10  20  30 


Figure  3.  Sea  surface  drag  reduction  in  terms  of  Figure  5.  Roughness  of  the  ocean  surface, 

the  drag  coefficient  deviation,  8Q,  =  Cu  -  Q  moo*  ,  theory  and  observation, 

as  a  function  of  the  wave  age,  Cq/u.  . 


Cuxl03 


u. 


Figure  4.  Drag  reduction  of  the  ocean 
surface  —  theory  and  observation. 


it 

Q 

u, 

x  3  m/s ,  deep  water 
0  5  m/s ,  shallow 

•  8  m/s ,  shallow 

A  1 1  m/s ,  shallow 

1  -y=  1/2  , 
2-y*l/4, 

3  -y  =  0 


Figure  6.  Phase  velocity  of  the  surface  wave 
spectral  peak  in  the  generation  regime,  theory 
and  measurement  (  the  data  of  the  Marine 
Hydrophysics  Institute  wind-wave  tank  by 
Leykin  and  Rosenberg ) 


209 


BLUBBER  AND  COMPLIANT  COATINGS  FOR  DRAG  REDUCTION  IN  FLUIDS: 

V.  DRIVING  POINT  SHEAR  IMPEDANCE  MEASUREMENTS  ON  COMPLIANT  SURFACES 


Edwin  R.  Fitzgerald 
Johns  Hopkins  University 
3400  N.  Charles  St. 
Baltimore,  MD  21218 


James  W.  Fitzgerald 
Kildare  Corporation 
1  Spar  Yard  St. 

New  London,  CT  06320 


Abstract  -  An  automated  dynamic  mechanical  measurement  system  for  complex  shear  compliance,  J*  «  J'  -  iT,  and  shear  modulus, 
G*  *  G'  +  iG*  =  1/J*,  from  2  to  10,000  Hz  has  been  used  to  obtain  these  viscoelastic  parameters  for  excised  samples  of  dolphin  blubber 
and  skin  at  21°C  from  2  to  1000  Hz  as  previously  described.  This  measurement  system  has  been  modified  to  allow  determinations  of 
complex  driving  point  shear  impedance  (force Arclocity)  on  compliant  surfaces,  including  living  animal  tissues.  Shear  impedance 
measurements  are  reported  for  compliant  polymer  gel-foam  composite  coatings  with  viscoelastic  properties  close  to  those  of  dolphin 
blubber  for  small  wafer-shaped  samples  with  vibrational  shearing  forces  across  their  entire  faces,  and  for  extended  sheets  where  the  shear 
force  vibrator  acts  on  only  a  portion  of  the  sheet  surface.  This  later  type  of  in  situ  shear  impedance  measurement  has  been  made  on 
compliant  coatings  of  several  discs  used  for  rotating  disc  drag  measurements  which  show  a  drag  reduction  and  a  delay  in  the  onset  of 
turbulence  compared  to  drag  measurements  of  an  uncoated,  rigid  disc  of  the  same  dimensions.  These  results  are  in  accord  with  the 
matched  shear  impedance  explanation  of  low  dolphin  drag,  and  suggest  the  possibility  of  in  situ  surface  shear  impedance  measurements 
on  live  dolphins  to  get  improved  values  of  their  viscoelastic  properties  and  increased  drag  reduction. 


L  INTRODUCTION 

The  matched  shear  impedance  explanation  of  low  dolphin  drag 
requires  viscoelastic  properties  of  the  skin  and  blubber  so  that  they 
act  as  a  compliant  layer  load  of  shear  impedance,  7^ ,  which  matches 
the  effective  shear  impedance,  Zq  ,  of  incipient  boundary  layer 
turbulence  acting  as 'an  equivalent  shear  force  generator.  With 
matched  impedances,  maximum  power  transfer  and  energy 
absorption  in  the  blubber  dampens  the  incipient  turbulence, 
maintains  laminar  flow,  and  provides  drag  reduction  [1,  2]. 
Measurements  from  2  to  1000  Hz  of  complex  shear  compliance  and 
modulus,  J*  =  V  -  iT  and  G*  =  G'  +  iG",  on  excised  blubber 
samples  vs.  time  after  death  allow  extrapolation  to  0  hours  to  get 
"live"  values  as  illustrated  in  Fig.  1  for  blubber  and  skin  from  a 
stranded  harbor  seal  for  which  rescue  efforts  failed  [3];  similar 
measurements  on  excised  samples  of  blubber  from  a  stranded 
dolphin  gave  the  frequency  dependences  of  the  elastic,  J',  G'  ,  and 
viscous,  V,  G",  components  of  compliance  and  modulus  for  "live" 
dolphin  blubber  as  shown  in  Fig.  2.  Also  shown  in  Fig.  2  are  the 
corresponding  elastic  and  viscous  compliance  and  modulus 
components  for  two  polymer  gel-foam  composites  that  match  closely 
the  dolphin  blubber  viscoelastic  properties  [4,5].  An  equivalent 
mechanical  circuit  representation  of  turbulent  flow  over  a  compliant 
surface  suggests  that  the  dolphin  load  impedance  depends  chiefly  on 
the  blubber,  but  also  on  a  parallel  terminal  impedance  from  the 
dolphin  muscle  and  skeleton  [2].  In  order  to  get  direct  measurements 
of  driving  point  shear  impedance  on  live  dolphins,  a  mobile 
automated  measurement  system  has  been  designed.  The  present 
system  for  small,  wafer-  shaped  samples  has  been  modified  also  to 
make  driving  point  shear  impedance  measurements  on  extended 
surfaces  such  as  the  compliant  coatings  on  large  discs  used  for 
rotating  drag  measurement,  and  to  allow  in  situ  surface  impedance 
measurements  on  live  animal  tissues. 

II.  MEASUREMENT  METHOD 

An  automated  dynamic  mechanical  measurement  system  for  the 
elastic  and  viscous  components  of  complex  shear  compliance, 
modulus,  loss  tangent,  J7J'  =  G7G',  and  shear  wave  velocity  and 
attenuation  was  used  to  get  the  frequency  dependence  of  compliance 
and  modulus  for  the  dolphin  blubber  and  the  compliant  coating 
composites  shown  in  Fig.  2.  In  this  system  a  rigid  plate,  with  fine  wire 
embedded  flat  coils  suspended  transversely  to  permanent  magnetic 
fields,  Blt  B2  Js  used  to  vibrate  the  surfaces  of  a  pair  of  small  wafer- 
shaped  samples  clamped  between  the  plate  and  fixed  outer  blocks. 
An  oscillating  electric  current,  l\  through  one  of  the  coils  of  length, 
tx ,  produces  a  vibrating  force,  F*t  =  B^I^  ,  which  moves  the  plate 
and  a  second  coil  of  length,  €2 ,  with  velocity,  v*,  so  that  a  motional 
emf,  E*2  =  B2€2v*  is  generated  in  tne  second  coil.  The  impedance 


TIME  AFTER  DEATH  -Hrs 


Figure  1.  Time  after,  death  variation  of  shear  compliance  elastic  (J') 
and  viscous  (J")  components  for  harbor  seal  blubber  and  skin; 
extrapolations  to  0  hours  give  "live"  tissue  values. 


211 


(force/velocity)  of  the  plate,  without  samples,  is, 

Zmp*  =  Fj*  /  v2*  =  B,^BA  It*  /  E*‘  (1) 

With  a  pair  of  samples  clamped  against  the  plate  the  impedance  is, 

ZMr*  =  BlflB2€2Il'*/E2'*,  (2) 

and  the  sample  impedance  is  Z^*  -  Z -  Z^*  •  For  samples  of 
cross  sectional  area,  2A,  and  thickness,  h,  the  shear  compliance  for 
sinusoidal  current  and  force  at  frequency,  f,  is, 

J*  =  (  "i  Yms*  2A/h  )  /2irf,  (3) 

where  Y^*  =  1  /  Z^*.  The  mechanical  parameters  are  thus  found 
in  terms  of  an  electrical  transfer  admittance,  Y12*  =  Ix*  /  Ej*.  The 
system  has  a  range  from  2  to  10,000  Hz  at  temperatures  from  -50  to 
150°C  A  complete  description  is  given  in  several  publications  [6,7]. 

Sample  pairs  of  dimensions  1.25  in.  x  1.25  in.  x  .125  in.  thick,  or 
smaller  and  thinner,  have  been  measured  in  the  standard 
electromagnetic  transducer  shown  in  schematic  cross  section  in  Fig. 
3A,  but  a  small,  offset  extension  at  the  end  of  the  drive  plate  is 
needed  for  the  driving  point  shear  impedance  determinations  as 
depicted  in  Fig.  3B.  The  area  in  contact  with  the  surfaces  measured 
is  0.7  x  0.6  in.  giving  an  area  of  0.42  in2,  (  2.71  cm2).  In  order  to 
make  certain  that  slipping  is  not  present,  measurements  are  made  at 
current/force  values  varied  by  a  factor  of  two;  if  measured  impedance 
values  are  unchanged,  slipping  is  absent,  and  the  force-deformation 
response  can  be  considered  as  linear. 


DRIVE  PLATE  a>  t 


DRIVE  B 

PLATE 
EXTENSION 


u  u 


Figure  3.  A.  Schematic  cross  section  of  transducer  drive  plate  with 
force  coil  1  in  magnetic  field  Bx  and  velocity  coil  2  in  field  B2.  The 
entire  inner  faces  of  the  sample  pair  are  subject  to  the  vibrating 
shear  force.  B.  Modifided  drive  plate  with  an  extension  to  measure 
driving  point  shear  impedance  of  a  portion  of  a  surface. 


Figure  2.  Frequency  variation  of  shear  compliance  and  modulus, 
J*,  G*,  for  "live"  dolphin  blubber  (dashed  lines)  matched  by  10:1 
(circles)  and  5:1  (triangles)  polymencuring  agent  polydimethyl 
siloxane  (PDMS)  gel-foam  composites. 


III.  DRIVING  POINT  SHEAR  IMPEDANCE  OF  COATED  DISCS 

Surface  shear  impedance  measurements  were  made  at  eight 
equally  spaced  locations  around  each  face  of  20-cm  diameter  discs 
coated  with  0.5  and  1.0  cm  thick  layers  of  polymethyl  siloxane  gel- 
polyurethane  foam  composites  as  shown  in  Fig.  4.  Mean  values  of 
the  8  complex  impedance  components  (Z^*  =  Rmd  *  ^md) 
measured  for  each  side  of  the  disc  were  found,  and  are  displayed  in 
the  logarithmic  plot  of  Fig.  5.  From  this  figure  it  is  evident  that  the 
impedance  is  essentially  the  same  for  the  disc  with  1.0  cm  thick 
coating  and  the  disc  with  the  0.5  cm  thick  coating. 

The  disc  coatings  were  built  up  from  0.125  in.  thick  gel-foam 
layers  cemented  together  and  cured  at  1206C  for  1  hour  under 
moderate  pressure.  After  completion  of  the  in  situ  impedance 
measurements,  several  layers  of  gel-foam  were  removed  and  cut  into 
sheets  2  in.  x  3  in.,  2  in.  x  2  in.,  and  1  in.  x  2  in.  and  thicknesses  of 
.115  in.  and  .205  in.  Driving  point  shear  impedances  were  again 
found  to  be  independent  of  thickness,  but  increased  some  as  the 
sheet  size  increased. 

Samples  of  the  gel-foam  coating  of  the  same  size  as  the  0.7  in. 
x  0.6  in.  contact  face  of  the  drive  plate  extension  gave  values  of 
complex  compliance  from  2  to  400  Hz  calculated  by  Equation  3  that 
closely  matched  the  values  of  sample  pairs  measured  in  the 
unmodified  transducer.  The  shear  impedance  in  this  case,  measured 
for  two  different  sample  thicknesses,  was  inversely  proportional  to 
thickness  for  the  same  sample  area  as  expected  from  Equation  3. 
The  dynamic  mechanical  measurements  of  samples  where  the  entire 
sample  face  is  subject  to  the  shear  force  give  absolute  compliance 
values,  J,  that  vary  from  J  =  10.5  to  8  Mpa*1  at  20eC  compared  to 
"live"  dolphin  values  of  23  to  19  MPa*1  (10*7  cm2  /  dyne)  at 
frequencies  from  2  to  1000  Hz  at  21°C.  The  compliant  coatings  on 
these  discs,  therefore  did  not  match  the  "live"  dolphin  blubber 
viscoelastic  properties  as  well  as  the  polymer  gel-foam  composites  of 
Fig.  2.  However,  the  match  was  close  enough  to  reduce  drag,  and  to 
delay  the  onset  of  turbulencce  from  210  rpm  to  260  rpm  compared 
to  a  rigid,  uncoated  disc  as  shown  in  Fig.  6.  This  corresponds  to  a 
Reynold’s  No.  transition  delay  from  Re  =2.2  x  105  to  2.7  x  105. 


212 


Figure  4.  Schematic  top  and  side  views  of  the  modified  drive  plate 
of  Fig-  3B  in  position  to  measure  driving  point  shear  impedance  at 
1  of  8  places  along  the  edge  surfaces  (top  and  bottom)  of  compliant 
coatings  on  discs  used  for  rotating  disc  drag  measurements. 


IV.  DRIVING  POINT  SHEAR  IMPEDANCE  OF  THIN  SHEETS 
The  modified  driving  plate  with  a  0.6  in.  x  0.7  in.  vibrator 
surface  was  used  to  get  some  preliminary  information  on  the  effect 
of  sheet  size  and  thickness;  the  sheets  were  taken  from  the  compliant 
coatings  on  the  discs  used  for  rotating  drag  measurements. 

Table  I.  Size  effects  on  20°C  driving  point  shear  impedance 
of  polymer  gel-foam  sheets  .115  and  .205  in.  thick  . 


Sheet  Thickness 

Vibration 

Area 

Shear  Impedance  Magnitude 

Size 

LxW 

in. 

Direction 

Ratio* 

Zm  104  dyne 
2  Hz  to 

-sec/cm 

300  Hz 

2.2x2.2 

.110 

2.2 

11.5 

140 

3.30 

2.2x3.0 

.110 

3.0 

15.7 

170 

4.13 

2.2x2.2 

.205 

2.2 

11.5 

151 

2.90 

2.2x3.0 

.205 

3.0 

15.7 

165 

3.44 

2.2x2.2 

.205 

2.2 

11.5 

151 

2.90 

3.0x2.2 

.205 

2.2 

15.7 

168 

3.09 

♦Sheet  /vibrator 

From  Table  I  some  very  tentative  conclusions  can  be  stated: 
(1)  Impedance  increases  with  size  of  the  sheet  relative  to  the  area 
acted  on  by  the  force  vibrator;  (2)  the  impedance  is  independent  of 
thickness  for  sheet/vibrator  area  ratios  greater  than  10;  (3)  If  the 
vibrating  force  acts  over  the  entire  sample  area,  impedance  depends 
directly  on  sample  area,  and  inversely  on  thickness. 


3 


S 

<o 

i 

Q 


FIGURE  5.  Frequency  variation  at  20°C  of  resistive  (  RM  )  and  reactive  (  XM  )  components  of  driving  point  shear 
impedance  of  0.5  cm  (circles,  crosses),  and  1.0  cm  thick  (triangles,  daggers)  polymethyl  siloxane  gel-polyurethane 
foam  coatings  measured  in  place  on  20-cam  diameter  discs  used  for  rotating  disc  drag  measurements  of  Figure  6. 


213 


Figure  6.  Drag  torque  vs  revolutions  per  minute  (rpm)  for  a  rigid  reference  disc  (open  circles),  and  for  a  coated  disc 
with  a  .485  cm  thick  polymethyl  siloxane  gel-polyurethane  foam  and  a  smooth  .015  cm  thick  natural  rubber  latex 
cover,  (filled  circles).  The  rigid  disc  has  a  laminar  to  turbulent  flow  transition  at  210  rpm,  but  the  0.5  cm  thick 
polymer  gel-foam-latex  coated  disc  transition  is  delayed  to  260  rpm.  This  corresponds  to  a  Reynold’s  No.  transition 
delay  from  2.2x10s  to  2.7x10s.  Results  for  a  1.0  cm  thick  coating  are  similar  with  a  260  rpm  transition. 


V  CONCLUSIONS  REFERENCES 

Drag  reduction  and  delayed  laminar  to  turbulent  flow  in  water  1.  E.R.  Fitzgerald  and  J.W.  Fitzgerald  "  Blubber  and  Compliant 

have  been  found  for  10  cm  radius,  4.5  cm  thick,  rotating  discs  coated  Coatings  for  Drag  Reduction  in  Fluids  I. "  Proc.  2nd  Inti  Conf.  Intel. 

with  a  polymer  gel-foam  composite  with  viscoelastic  properties  close  Mt’ls.  510-522,  1994;  Mils.  Sci.  &  Engr.  2  209-214, 1995 

to  those  measured  for  "live"  dolphin  blubber.  Preliminary  2.  J.W.  Fitzgerald,  E.R.  Fitzgerald,  W.M.  Carey,  and  W.A.  Von 

measurements  are  reported  of  driving  point  shear  impedance  on  Winkle  "Blubber  and  Compliant  Coatings  for  Drag  Reduction  in 

portions  of  surfaces  on  polymer  gel-foam  coated  drag  discs,  and  on  Fluids  II."  Proc.  2nd  Int’l.  Conf.  Intel.  Mt’ls.  523-533,  1994;  Mils.  Set. 

small  sheets  of  the  same  composites.  These  measurements  were  &  Engr.  C  2  215-220, 1995 

made  with  a  modification  of  the  present  automated  system  for  3.  E.R.  Fitzgerald  "Dynamic  Mechanical  Measurements  of  Marine 

dynamic  mechanical  measurements  on  small,  wafer-shaped  samples  Mammal  Tissues"  J.  Acoust.  Soc.  Am.  101  2163,  1997 

where  the  entire  sample  surfaces  are  subject  to  a  vibrational  shear  4.  E.R.  Fitzgerald  and  J.W.  Fitzgerald  "Blubber  and  Compliant 

force.  Prior  measurements  were  made  on  excised  blubber  from  a  Coatings  for  Drag  Reduction  in  Fluids  III."  3rd ICIM/ECSSV6  SPIE 

stranded  dolphin  for  which  rescue  efforts  failed;  extrapolation  to  0  vol  2779  83-88,  1996 

hours  of  shear  compliance  vs  time  after  death  was  needed  to  get  5.  J.W.  Fitzgerald,  E.R.  Fitzgerald  and  J.E.  Martin  "Blubber  and 

"live"  tissue  values.  Surface  shear  impedance  measurements  made,  in  Compliant  Coatings  for  Drag  Reduction  in  Fluids  IV."  4th  ECSSV8 

situ  on  live  dolphins  will  give  more  information  on  their  viscoelastic  (Proc.  to  be  published) 

properties  that  could  lead  to  improved  drag  reduction  in  sea  water.  6.  E.R  Fitzgerald  "Automated  Measurement  System  For  Dynamic 

“  r  Mechanical  Properties"  Proc.  Am.  Chem.  Soc.  Div.  Polymeric  Mater. 

Sci.  60  573-578,  1989;  7.  U.S.  Patent  No.  5,081,872,  1992 


214 


BLUBBER  AND  COMPLIANT  COATINGS  FOR  DRAG  REDUCTION  IN  FLUIDS: 

VI.  ROTATING  DISC  APPARATUS  FOR  DRAG  MEASUREMENT  ON  COMPLIANT  LAYERS 


James  W.  Fitzgerald,  James  E.  Martin,  and  Eugene  F.  Modert 
The  Kildare  Corporation;  One  Spar  Yard  Street,  New  London,  CT  06320 

Abstract  -  The  “Matched  Shear  Impedance  Hypothesis  for  Compliant  Layer  Control  of  Boundary  Layer  Turbulence”  requires  that  the  shear  impedance 
of  the  compliant  layer  match  that  of  the  turbulent  boundary  layer,  which  is  viewed  as  a  fluctuating  shear-force  generator.  Under  matched  conditions, 
energy  is  transferred  from  the  incipient  turbulence  into  the  compliant  layer  and  absorbed  by  viscous  losses  .  .  .thus  delaying  the  onset  of  turbulence. 
The  dolphins  thick  blubber,  not  it’s  thin  skin,  is  viewed  as  such  a  matched  load.  Previous  efforts  in  these  continuing  studies  have  developed  candidate 
compliant  materials  that  have  complex  dynamic  shear  compliances  (  J*  =  J’  -  U”)  close  to  those  of  blubber.  The  rotating  disc  apparatus  of  this  study 
was  developed  to  measure  the  torque  (drag)  of  these  materials.  Initial  measurements  reported  herein  indicate  that  blubber-like  compliant  materials  do, 
indeed,  delay  the  onset  of  turbulence.  Harder  materials  appear  to  have  no  effect,  whereas  softer  materials  develop  surface  “ripplings”  that  increases 
drag.  These  preliminary  results  appear  to  confirm  the  matched  impedance  hypothesis. 


I.  INTRODUCTION 

After  some  40  years  of  extensive  investigations,  the  issue  of  whether 
or  not  compliant  surfaces  can  reduce  hydrodynamic  drag  remains  unresolved 
[1].  Based  on  Kramer’s  [2,  3]  initial  identification  of  the  dolphin’s  skin  as 
the  basic  mechanism,  most  of  the  past  work  has  concentrated  on  thin 
(-0.3cm)  compliant  coatings.  The  various  proposed  hydrodynamic  models 
[4,  5,  6]  suggest  that  the  compliant  surface  deflects  in  some  preferred 
manner  and  interacts  with  the  boundary  layer  Tollmein-Schlicting  waves  so 
as  to  reduce  their  stability,  therby  delaying  the  transition  from  laminar  to 
turbulent  flow.  Surprisingly,  in  spite  of  the  extensive  past  work  by  many 
investigators,  in  most  cases  the  compliant  surface  being  studied  has  not  been 
adequately  characterized  by  measurement  of  its  dynamic  complex 
viscoelastic  properties . 

The  “Matched  Shear  Impedance  Hypothesis  for  Compliant  Layer 
Control  of  Boundary  Layer  Turbulence”  takes  a  completely  different 
approach  to  the  problem,  more  akin  to  “acoustics”  then  “hydrodynamics” 
(Figure  I).  This  model’s  [7,  8,  9,  10]  basic  postulates  are: 

The  turbulent  boundary  layer  (TBL)  is  viewed  as  a  fluctuating 
“shear  stress  generator”  coupled  to  the  “compliant-layer  load” 
through  the  viscous  “inner  boundary  layer”. 

To  transfer  appreciable  “fluctuating”  energy  (power)  from  the 
TBL  shear-stress  generator  to  the  compliant-layer  load,  the  shear 
impedance  of  the  load  must  be  “matched”  to  the  shear 
impedance  of  the  TBL  generator. 

Under  matched  load  conditions,  the  build-up  of  the  fluctuating 
energy  of  incipient  turbulence  is  reduced  by  energy  flow  into  the 
compliant  layer  where  it  is  dissipated  by  losses  in  the 
viscoelastic  compliant  layer  material,  thus  delaying  the  onset  of 
turbulence. 

Dolphin  blubber  represents  just  such  a  matched-load  with  the 
required  high  loss  tangent. 

Figure  2  shows  an  equivalent  circuit  representation  of  the  Matched  Shear 
Impedance  Hypothesis. 

fl.  ROTATING  DISC  APPARATUS 

Most  of  the  preceding  investigations  of  hydrodynamic  flow  over 
compliant  surfaces  have  been  deficient  in  one  or  more  of  the  following  areas: 

Concentration  on  the  thin  skin  of  the  dolphin  rather  than  the 
thick  blubber. 

Not  characterizing  the  compliance  of  the  surface  by 
measurements  of  the  dynamic  complex  shear  compliance 
(J*  =  J’  -  U”)  and,  hence,  the  driving-point  shear  impedance. 

Lack  of  a  convenient  laboratory  method  of  measuring  the  drag, 
with  sufficient  precision  and  under  controlled  conditions. 

The  rotating  disc  apparatus  of  this  paper  addresses  the  last  of  these 


deficiencies. 

Pioneering  work  utilizing  rotating  disc  apparatus  tor  studying  flow 
over  compliant  surfaces  was  done  by  Hansen  &  Hunston  [11,12].  Their 
apparatus  used  thin  discs  -0.98  cm  thick  by  -20.9  cm  diameter,  and 
covered  the  range  of  Re- 10  4  to  Re  =5  x  105  .  The  compliant  coatings 
were  thin  (-0.34  cm)  soft  plastisols  (|  J*  |  ~  3  x  KT4  cm?  /  dyne)  that 
developed  surface  instabilities,  accompanied  by  a  marked  increase  in  torque 
(drag)  in  the  vicinity  of  -  Re  ^  5  x  104.  Another  set  of  rotating  disc 
experiments  were  made  by  Chung  &  Merrill  [13]  on  thin  coatings  of  a  soft 
silicone  rubber  with  a  diluent  silicone  oil.  Again,  a  pronounced  rippling  of 
the  surface  was  accompanied  by  a  marked  increase  in  drag  as  turbulence 
developed  in  the  vicinity  of  Re  «  104. 

The  isometric  sketch  of  Figure  3  show's  the  rotating  disc  apparatus  of 
this  study.  It  consists  of  a  variable  speed  motor  connected,  by  means  of  a 
pulley-belt  drive,  to  a  shaft-mounted  disc,  rotating  in  a  water  bath.  The 
drive-shaft  has  an  in-line  torque/rpm  sensor  whose  outputs  are  read  by 
digital  meters.  The  equipment  measures  both  torque  (0-1001b-in)  and 
rotational  speed  (0-1 0,000  rpm).  Both  analogue  (±  5  volt)  and  digital  (RS- 
252-C)  outputs  are  available,  in  addition  to  the  panel  meters. 

Figure  4  shows  the  design  of  the  rotating  discs.  The  basic  rigid 
(aluminum)  reference  disc  is  20  cm  in  diameter  and  4.5  cm  thick,  with 
edges  having  a  radius  of  -0.16  cm.  The  molded  compliant  layered  discs 
have  the  same  outside  dimensioas  and  surface-smoothness  as  the  rigid- 
reference  discs;  but,  three  different  thicknesses  of  compliant  layers:  viz.  0.5 
cm,  l  .0  cm,  and  2.0  cm.  The  effect  of  the  surface  compliance  (i.e.,  the 
driving  point  impedance),  if  any,  will  be  the  difference  between  the  torque 
of  the  rigid-reference  disc  and  that  of  the  compliant-layered  disc.  Significant 
differences  in  drag  (torque)  as  small  as  a  few  percent  can  be  determined. 

In  summary,  the  rotating  disc  apparatus  has  the  following 
measurement  capabilities: 

Rotating  speed  range;  60  rpm  to  2250  rpm 
Torque  range;  0-100  lb-in 
Compliant  layer  thickness;  0.5, 1 .0,  &  2.0  cm 
Rotating  discs,  4.5  cm  thick  x  20  cm  diameter 
Reynold’s  number  range;  5  x  104  to  2.25  x  106 
Drag  (torque)  measurement  precision;  -  ±0.5% 

Measurements  at  room  temperature,  only 

ffl.  APPARATUS  CALIBRATION 

One  of  the  problems  resulting  from  the  required  thickness  of  the 
rotating  discs,  particularly  at  the  higher  rotational  speeds,  is  that  the  rotating 
disc  “stirs”  the  bath  (30"  D  x  24"  H)  into  a  general  rotating  water  mass.  As 
a  result  of  the  rotating  water  mass,  the  relative  velocity  of  rotating  disc 
through  the  water  is  reduced,  accompanied  by  a  reduction  in  torque  (drag). 
The  Himmelstein  Precision  Torque  Meter  Readout  (Model  66042)  and  In 
Line  Torque  Sensor  (Model  MCRT  290 IT)  has  an  A  -  D  conversion  time  of 
only  30  microseconds.  Stability  is  achieved  after  one  second,  the  same  time 
base  upon  which  the  instrument  output  is  gated.  Sampling  occurs  as  an 
integration  of  the  output  over  each  second.  Measurements  of  torque  vs  time 
indicated  that  even  at  the  highest  rotational  speeds,  the  torque  remained 
substantially  constant  in  a  2-4  .second  window  and  then  begins  to  decay  as 
the  water  mass  rotation  sets  in.  In  effect,  the  disc,  driven  by  the  2  hp 
electric  motor,  reaches  its  terminal  rotating  speed  in  -1  second. 
Measurements  made  in  the  2-4  second  period  following,  represents  the  true 


215 


rotational  speed  and  torque  through  quiescent  water.  We,  therefore, 
adopted  the  “2nd -second”  measurement  method  throughout  our  studies. 

Table-1  shows  a  series  of  torque  measurements  made  on  the  rigid- 
reference  disc,  using  the  “2nd-second”  method.  It  should  be  noted  that  these 
are  completely  independent  measurements  starting  with  a  non-rotating  disc 
in  quiescent  water.  The  mean  of  the  10  runs  wfas  T  =  19.33  lb-in,  with  a 
standard  deviation  of  o  =0.068.  The  maximum  spread  was  only  0.20  Ib-in, 
or  ~±  0.5%.  This  represents  a  measurement  precision  not  often  encountered 
in  hydrodynamic  drag  measurements. 

TABLE-I:  REPEATABILITY 


RPM 

TOROUE  (lb.-in) 

STATS 

1000 

19.3 

19.33  Mean 

1000 

19.2 

0.0675  Std  Dev 

1000 

19.3 

19.4  Max 

1000 

19.3 

19.2  Min 

1000 

19.4 

0.200  Spread 

1000 

19.3 

1000 

19.4 

1000 

19.4 

1000 

19.3 

1000 

19.4 

The  customary  dimensionless  torque  coefficient  is: 

Cr=  T  (I) 

(p/2)  a)2  R5 

and  Reyonold’s  number  for  the  rotating  disc  is: 

Re=  (R  2)  ( to)  (2) 

t> 

Where:  C  T  =  torque  coefficient;  T  =  measured  torque;  p  =  density  of  water; 
(a  =  rotational  speed;  R=  disc  radius;  Re=  Reynold's  number  and  u  = 
kinematic  viscosity  of  water. 

Figure  5  shows  the  torque  vs.  rpm  calibration  of  the  rigid  disc. 
Transition  from  laminar  to  turbulent  flow  occurs  at  co  «  210  rpm,  which 
corresponds  to  a  peripheral  speed  of  v  **  4.3  knots.  Figure  6  show's  a 
corresponding  rigid  disc,  drag  coefficient  vs.  Reynolds  No.,  with  laminar-to- 
turbulent  flow  at  Re'--  2.2  x  1 05. 

IV.  REPRESENTATIVE  MEASUREMENTS 

Figure  7  shows  the  shear  compliance  \  J*  |  vs  frequency  for  some 
representative  compliant  materials  from  a  companion  study  [14].  The 
materials  are  identified  as  follows: 

PDMS  - 10:1  polymerxuring  agent  polydimethyl  siloxane  gel 
BLB  -  dolphin  blubber 

PMS  -  polymethyl  siloxane  gel  /  polyurethane  foam  composite 
1 5SILR  -  Shore  A  1 5  durometer  silicone  rubber 
35NEOR  -  Shore  A  35  durometer  Neoprene  rubber 
55NEOR  -  Shore  A  55  durometer  Neoprene  rubber 

Rotating  discs  measurements  on  the  Neopreme  rubbers  showed  no 
perceptible  drag  differences  from  the  drag  measurements  on  the  reference 
rigid  discs.  The  molded  1 5-durometer  silicone  rubber  discs  also  showed  no 


perceptible  delay  of  turbulence,  but  surface  flaws  may  have  masked  any 
effect,  Mid  this  sample  will  have  to  be  remolded  and  rerun.  No  rotating  disc 
samples  have  yet  been  made  with  the  PDMS  (polydimethyl  silicone  gel), 
but  with  a  complex  shear  module  of  |  J*  |  -  2  x  1 0‘5  cm  /  dyne,  surface 
deflections  can  be  expected  to  increase  the  drag. 

Figure  8  shows  the  comparison  of  the  transition  from  laminar  to 
turbulent  regimes  for  the  rigid  reference  disc  and  the  PMS  (polymer  gel- 
foam)  coated  disc.  The  transition  takes  place  at  o  “  210  rpm, 
corresponding  to  Re  - 2.2  x  105,  for  the  rigid  disc.  The  traasition  is  delayed 
to  co  “  260  rpm,  corresponding  to  Re  -  2.7  x  10s,  for  the  PMS  disc.  These 
preliminary'  measurements  were  made  with  a  gel-foam  compliant  layer  not 
fully  matched  to  blubber.  .  .  |  J*  |  -  10  x  l(r7  cnf  /  dyne  for  PMS  as 
compared  to  |  J*  j  -  20  x  KT7  cnf  /  sc  for  BLB.  Moreover,  the  surface 
roughness  of  the  gel-foam  was  excessive  and  sample  preparation  techniques 
will  have  to  be  improved. 

V.  CLOSING  REMARKS 

The  gel-foam  sample  transition  from  the  laminar  to  the  turbulent 
regime  at  co  -260  rpm  corresponds  to  a  peripheral  velocity  of  v  -5.8  knots. 
A  fully  matched,  smooth  sample  could  be  expected  to  extend  this  delay  of 
the  onset  of  turbulence  even  further.  Operational  dolphins  typically  cruise 
at  “10  knots  [15].  If  we  assume  that  this  represents  an  “energy  conserving” 
speed  corresponding  to  the  laminar-turbulent  transition,  a  smooth  fully 
matched  compliant  coated  disc  might  be  expected  to  extend  the  transition 
to  0)  “  448  rpm,  or  Re  -  4.7  x  105 

These  preliminary7  rotating  disc  measurements  appear  to  support  the 
“Matched  Shear  Impedance  Hypothesis  for  Compliant  Boundary  Layer 
Control  of  Boundary  Layer  Turbulence” 


VI.  REFERENCES 

1 .  Gad-el-Hak,M.,  Applied  Mechanics  Review  (1986)  39,  51 1-523 

2.  Kramer,  M Journal  of  Aeronautical  Science  (1957)  24,  459-460 

3.  Kramer,  M.,  Advances  in  Hydroscience  (1 965)  2, 111-130 

4.  Purhouse,  M.,  Cambridge  Unversity  Ph.D.  Thesis ,  (1977) 

5.  Schlichting,  H.,  Boundary  Layer  Theory,  McGraw-Hill  (1979) 

6.  Carpenter,  D.  &  Garrad,  A.,  Journal  of  Fluid  Mechanics  (1985),  1 55 

7.  Fitzgerald,  J.,  Laminar  &  Turbulent  Boundary  Layers  (1984)  ASME,  9 1 

8.  Fitzgerald,  J.,  et  al,  American  Chemical  Soc.  Mtg.  Chichago,  IL  (1985) 

9.  Fitzgerald,  J.,  Final  Technical  Report,  SBIR  Contr.  H66604-87-C-1742 
(1988) 

10.  Fitzgerald,  J.,  et  al,  2nd  hit.  Conf  on  Intelligent  Materials  (1994) 

1 1 .  Hansen,  R.  &  Hunston,  D.,  Journal  of  Sound  &  Vibration  j  1 974)  34 

12.  Hansen,  R.  &  Hunston,  D Journal  of  Sound  &  Vibration ,  (1976)_46 

13.  Chung,  K.  &  Merrill,  E.,  Compliant  Coaling  Drag  Reduction  Rev.  ONR 
(1984) 

14.  Fitzgerald,  J.,  et  al,  4th  ECSS  (1 998)  -  to  be  published 

1 5.  Fitzgerald,  J.  Naval  Institute  Proceedings,  p.  12-13  (Dec.  1 997) 


216 


MATCHED 


IMPEDANCE 

HYPOTHESIS 


COMPLIANT 


Not  twiytkiny  thi  6omz  to  evcAi fbody 

(Non  omrtta  eadon  aegue  omrubviLa) 
Vtaiitub ,  A&om/ufl  (c  200BC  | 


Pa  -  TBL  Shear  Force  Generator  Zf  »  Terminal  Impedance 

Iy  m  Rotational  Inertia  of  Vorticea  Zg  ■  Impedance  'Looking  Into*  TBL  (Generator 

Internal  Impedance) 

Ry  m  Viscous  Losses  in  Fluid  Z^  »  Impede  nee  ’Looking  Into’  Compliant  Layer 

(Load  Impedance) 

Rj  a  Viscous  Lasses  in  Boundary  Sub-layer  UQ  *  Fluctuating  Component  of  Flow  Velocity 

M  »  Unit  Mass  of  Compliant  Layer  Uj  *  Fluctuating  Velocity  Component  in  Boundary 

Sublayer 

J‘  m  Elastic  Compliance  of  Compliant  Layer  ■  Fluctuating  Velocity  m  Compliant  Layer 
1*  »  Loss  Compliance  of  Compliant  Layer  Fj  »  Shear  Force  Applied  to  Compliant  Layer 


Figure  2:  Equivalent  Circuit 


CONTROL  OF 


BOUNDARY 


Figure  5:  Rigid  Disc  Torque  vs.  tpm  Figure  6:  Rigid  Disc  Drag  Coefficient  vs.  Reynolds  No. 


FREQUENCY  Hz 


Figure  7:  Shear  Compliance  of  Representative  Compliant 
Materials  (see  text) 


50  100  200  500  1000 


Revolutions  Per  Minute  RPM 


Figure  8  Comparison  of  the  transition  from  laminar  to  turbulent 
regimes  for  the  Rigid  Reference  Rotating  and  a  Polymer 
Gel-Foam  Coated  Disc 


218 


INTERFACE  WAVES  ON  A  COMPLIANT  COATING  BOUNDED  BY  A  FLUID  FLOW 
AND  THEIR  EXCITATION  BY  ACOUSTIC  RESONANCE 


Herbert  Uberall 
Department  of  Physics 
Catholic  University  of  America 
Washington,  DC  20064 


Walter  Madigosky 
Vector  Research  Division 
A  &  T,  Inc. 
Rockville,  MD  20852 


Abstract  -  The  stability  of  interface  waves  on  a  compliant  coating,  attached  to  a  rigid  substrate  and  exposed  to  a  laminar  or 
turbulent  fluid  flow,  has  been  the  subject  of  several  theoretical  studies,  and  of  experimental  investigations  in  which  the  onset  and 
growth  of  instability  waves  was  determined.  In  the  original  experiments  of  Kramer,  he  attempted  to  retard  the  onset  of  the  flow 
instability,  for  increasing  values  of  flow  speed,  on  a  flow  boundary  that  imitated  a  dolphin  skin.  Of  the  large  number  of  subsequent 
experiments,  some  could,  or  could  partly  confirm  Kramer’s  results  which  had  indicated  a  substantial  instability  retardation  and  drag 
reduction  by  such  a  surface;  other  experiments  could  not.  Exhaustive  surveys  of  the  experimental  and  theoretical  literature  on  the 
subject  can  be  found  in  two  British  PhD  theses  by  Willis  and  by  Yeo,  and  we  shall  give  an  overview  of  this  literature.  Solutions 
of  the  characteristic  equation  of  the  problem  have  been  obtained  by  us,  which  furnish  dispersion  curves  and  stability  information 
for  the  interface  waves.  It  is  shown  that  the  excitation  of  these  interface  waves  by  incident  inhomogeneous  acoustic  signals  can 
occur  in  a  resonant  fashion,  thus  permitting  an  experimental  determination  of  the  dispersion  curves,  of  the  onset  of  instability,  and 
of  the  growth  properties  of  interface  waves. 


L  INTRODUCTION 

Seawater  drag  arises  from  the  onset  of  flow  instabilities  above 
a  limiting  value  of  flow  velocity  along  a  surface,  for  both  rigid 
and  compliant  surfaces  but  in  a  different  fashion  for  each.  Drag 
reduction  then  consists  in  retarding  the  onset  of  the  instability  by 
a  suitable  choice  of  the  surface  parameters.  After  presenting  an 
overview  of  the  experimental  situation  and  its  analysis,  we  note 
that  the  onset  of  instabilities  arises  in  a  resonant  fashion  by  a 
coincidence  of  the  flow  velocity  with  the  speed  of  the  boundary 
waves  which  is  governed  by  the  dispersion  of  the  latter.  We 
propose  a  method  of  experimental  determination  of  the  boundary 
wave  dispersion  curves  by  acoustic  resonance  experiments  using 
inhomogeneous  incident  sound  waves.  Knowledge  of  the 
dispersion  curves  in  their  dependence  on  the  surface  wave 
properties  thus  allows  the  control  of  the  onset  of  instability,  and 
of  the  grow  of  the  interface  waves. 

The  problem  of  flow  instabilities  along  compliant  surfaces  goes 
back  to  the  experiments  of  Kramer  [1].  In  these,  he  attempted  to 
retard  the  onset  of  the  flow  instability  for  increasing  values  of 
flow  speed  by  coating  a  rigid  flow  boundary  with  a  compliant 
layer  bonded  to  the  rigid  surface  with  stubs,  the  space  between 
the  stubs  containing  a  viscous  liquid.  This  surface  was  supposed 
to  model  the  skins  of  dolphins  which  had  been  thought  to  possess 
instability-retarding,  and  hence  drag-reducing  qualities  [2,3].  Of 
the  large  number  of  subsequent  experiments,  some  could,  or 
could  partly  confirm  Kramer’s  results  which  had  indicated  a 
substantial  instability  retardation  and  drag  reduction  by  such  a 
surface;  other  experiments  could  not.  In  spite  of  considerable 
existing  literature,  there  still  seems  to  reign  a  certain  amount  of 
confusion  due  to  the  dependence  of  the  problem  on  a  large 
number  of  variables.  Exhaustive  surveys  of  the  experimental  and 
theoretical  literature  on  the  subject  can  be  found  in  two 
comprehensive  British  PhD  theses  by  Willis  [4]  and  by  Yeo  [5], 

The  following  variables  enter  the  problem  and  can  be 
independently  altered: 

A.  For  the  fluid  flow:  -  (1)  the  fluid  can  be  viscous  or  inviscid; 
the  flow  velocity  can  be  constant,  or  depend  on  the  distance  y 
away  from  the  boundary  (thus  forming  a  boundary  layer);  (3)  the 
flow  can  be  a  laminar  or  potential  flow  (flow  speed  everywhere 
parallel  to  the  surface),  in  particular  a  Blasius  boundary  layer 


flow;  or  it  can  be  a  turbulent  flow. 

B.  For  the  wall:  (1)  the  boundary  may  be  rigid;  or  else  the 
walls  may  be  compliant,  i.e.  the  wall  material  may  be  elastic  or 
viscoelastic;  (2)  the  wall  may  be  a  half-space,  a  single  (visco) 
elastic  layer  bonded  to  a  rigid  boundary,  or  it  may  consist  of 
multiple  layers;  (3)  these  layers  may  be  homogeneous  or 
inhomogeneous  (in  particular,  be  given  by  the  Kramer  model);  (4) 
the  layers  may  be  isotropic  or  anisotropic  (e.g.,  consist  of  a  fiber- 
reinforced  material). 

With  such  an  enormous  amount  of  possibilities  to  choose 
from,  it  is  clear  that  it  will  be  quite  hard  to  systematize  the 
subject  matter  to  be  studied.  In  the  literature,  individual 
investigations  have  thus  always  chosen  selected  cases;  their 
results  still  need  to  be  reviewed  and  categorized  in  a  systematic 
fashion. 

II.  THE  FLOW  STABILITY  PROBLEM 

With  a  boundary  layer,  the  flow  velocity  is  measured  by  its 
asymptotic  value  U^  (at  transverse  distances  y  ->  co).  At  any  U*, 
disturbance  waves  may  develop  along  the  wall  boundary,  having 
the  form 

u  -  <[>(y)exp[i(ax+pz)-icot]  (1) 

where  x  is  the  flow  direction,  and  y  the  direction  normal  to  the 
wall.  This  disturbance  is  referred  to  as  three-dimensional  [5]; 
however,  most  studies  were  made  for  two  -dimensional 
disturbances  where  p  a  0,  and  co  =  acp  where  cp  is  the  phase 
velocity  of  the  disturbance  wave.  If  lma>0  the  disturbance  wave 
decays  and  the  flow  is  one  of  "spatial  stability",  co  being  taken  as 
real.  Alternately,  one  may  look  for  real  a  and  complex  co;  in  that 
case,  lmco<0  leads  to  "temporal  stability"  (the  two  cases  can  be 
related  to  each  other).  If  the  opposite  is  true,  the  disturbance  will 
grow  either  spatially  or  temporally,  and  instability  will  take  place 
with  undesirable  consequences  (turbulent  flow,  hydrodynamical 
drag  being  generated).  Instability  will  set  in  if  U*  exceeds  a 
certain  value  termed  "onset  flow  velocity",  or  "critical  velocity". 

If  a  boundary  layer  exists,  one  has  <J>(y)*  const  and  <|>(y)  can  be 
obtained  by  solving  the  "Orr-Sommerfeld"  equation.  Satisfying 
the  boundary  condition  at  the  wall  leads  to  an  eigenvalue 
equation  and  to  corresponding  normal-mode  solutions  for  4>(y). 


219 


The  way  how  to  formulate  the  boundary  conditions  on  a  flexible 
moving  wall  was,  incidentally,  shown  by  Benjamin  [6-8],  see  also 

P]. 

The  complex  eigenvalues  co  determine  the  temporal  stability; 
an  instability  region  is  defined  by  positive  values  of  Imco.  This 
is  typically  presented  as  in  Fig.  1  [4],  e.g.  for  a  rigid  wall,  R 
being  the  Reynolds  number,  proportional  to  the  flow  velocity;  — 
is  the  Imco  =  0  (or  neutral  stability)  contour,  and  —  are  contours 
of  instability  corresponding  to  Imco  =  0.002,  0.004,..,  .  Similar 
diagrams  of  (real)  ©  vs.  R,  at  constant  values  of  Im  a,  can  be 
drawn  for  spatial  instability.  The  curves  depend,  of  course,  on  all 
other  parameters  of  the  problem  (e.g.,  elastic  modulus  E  of  the 
wall,  viscoelastic  parameters  of  fluid  and  wall  material,  etc.),  as 
well  as  on  the  geometry. 

The  idea  is,  of  course,  to  "retard"  the  onset  of  instability  by 
finding  a  combination  of  geometrical  and  material  parameters 
such  that  the  region  of  instability  becomes  as  small  as  possible, 
or  moves  into  a  region  of  the  (a,R)  plane  where  it  can  do  the 
least  harm.  The  mentioned  studies  [4,5]  claim  significant 
progress  in  the  direction  of  delaying  the  onset  of  instabilities,  and 
hence  of  drag  reduction. 

In  the  history  of  the  problem,  several  mainly  theoretical  studies 
stand  out.  These  are  the  work  of  Benjamin  [6-8]  who  discovered 
and  classified  three  basic  types  of  instabilities;  the  work  of 
Landahl  [10]  and  Kaplan  [11]  who  introduced  a  physical 
explanation  (in  terms  of  energies  of  flow  and  wall)  for 
stabilization  dependence  on  material  -  parameters  (although  their 
numerical  results  are  invalid);  and  ‘the  work  of  Carpenter  and 
Garrard  [12,13]  who  studied  the  stability  problem  of  Kramer-type 
compliant  surfaces  in  great  detail  by  solving  the  Orr-Sommerfeld 
equation.  Similar  extensive  studies  are  those  of  Willis  [4]  and  of 
Yeo  [5]  which  extended  the  Orr-Sommerfeld  solution  to  walls 
containing  isotropic  and  anisotropic  multiple  layers,  and  even 
included  three-dimensional  disturbances  [5].  However,  other 
studies  showed  [9,14]  that  useful  results  (e.g.,  the  classification  of 
instabilities  [13])  can  already  be  obtained  with  quite  simple 
models  of  flow  and  wall. 

Benjamin’s  classification  of  unstable  disturbances  [8]  resulted 
in  three  basic  types  of  instabilities,  to  which  Carpenter  and 
Garrad  [13]  have  added  a  fourth,  as  follows: 

1)  Tollmien-Schlichting  instabilities.  These  correspond  to 
unstable  disturbance  waves  on  a  rigid  wall  (see  Fig.  I)  where  they 
can  exist  for  a  viscous  flow.  If  the  wall  is  made  compliant  (and 
the  flow  may  then  be  inviscid),  these  disturbance  waves  continue 
existing  in  modified  form,  and  were  designated  "Class  A"  by 
Benjamin  [8],  or  TSI  elsewhere.  They  are  found  to  be  stabilized 
by  changing  the  wall  from  rigid  to  compliant,  and  increasing  its 
compliance  (i.e.  the  instability  region  of  Fig.  1  shrinking),  but  to 
be  destabilized  (i.e.,  the  instability  region  becoming  larger  again) 
if  wall  damping  is  introduced  and  increased. 

2)  Compliance-induced  flow  instabilities,  termed  "Class  B"  by 
Benjamin.  They  appear  in  addition  to  the  TSI  if  the  wall  is  made 
compliant,  and  can  occur  even  with  inviscid  fluid  flow.  The 
terminology  of  Yeo  [5],  "compliance-induced  flow  instabilities" 
(CIFI),  is  preferable  for  these  instabilities  rather  than  Carpenter 
and  Garrad’s  [13]  term  "flow-induced  surface  instabilities"  (FISI). 
This  instability  is  essentially  a  resonance  instability;  it  occurs 
when  the  flow  speed  is  close  to  the  natural  speed  of  surface 
waves  in  the  wall  [4]. 

Diagrams  such  as  Fig.  1  can  be  drawn  for  compliant  walls, 
indicating  both  TSI  and  CIFI.  Typically,  they  look  as  shown  in 
Fig.  2.  Changes  in  compliance  and  wall  damping  are  found  to 
have  the  opposite  effect  on  CIFI  as  they  do  on  TSI:  the  CIFI 
instability  region  grows  if  the  wall  becomes  more  compliant,  and 
it  shrinks  if  wall  damping  is  increased.  This  can  be  understood 


from  energy  considerations  [10],  or  simply  from  the  fact  that  the 
disturbance  waves  that  cause  TSI  reside  mainly  in  the  fluid,  while 
those  that  cause  CIFI  reside  mainly  in  the  wall.  An  optimal 
instability-retarding  wall  will  thus  be  one  that  minimizes  the 
combined  TSI  and  CIFI  instability  regions;  minimizing  just  one 
of  these  leads  to  an  increase  in  the  other. 

3)  Kelvin-Helmholtz  instability,  termed  "Class  C"  by  Benjamin 
[8].  This  instability  arises  out  of  a  coalescence  of  Class  A  and 
Class  B  waves,  as  will  be  discussed  below. 

4)  Static  Divergence  (SD),  the  fourth  instability  classified  by 
Carpenter  and  Garrad  [13].  It  has  been  observed  [15]  in  the  form 
of  very  slow-moving  (speed  ~  some  %  of  UJ,  large  amplitude 
waves  causing  a  dramatic  increase  in  drag. 

All  these  modes  can  lead  to  (traveling  wave  or  standing  wave) 
"flutter"  [13]  if  the  group  velocity  of  the  instability  waves  falls  to 
zero,  this  being  an  absolute  instability  that  is  not  convected  away. 
As  to  their  excitation,  it  is  observed  [15]  that  no  significant 
interactions  between  a  boundary  layer  flow  and  a  compliant 
surface  will  occur  for  flow  speeds  below  the  transverse  wave 
speed  of  the  solid. 

Theoretical  studies  considered  the  types  of  instability  and  their 
onset  in  a  qualitative  fashion.  Duncan  et  al  [14]  assumed  an 
elastic  or  viscoelastic  layer  bonded  to  a  rigid  half-space,  and  a 
potential  flow  using,  like  Ref.  [9],  Benjamin’s  pressure  boundary 
condition  on  a  moving  surface.  They  extended  the  approach  to 
include  turbulent  or  laminar  boundary-layer  flow  by  modifying 
the  pressure  boundary  condition  to  allow  for  a  reduced  magnitude 
and  a  phase  change,  taking  these  data  from  experiments  on 
turbulent  flow  [16],  or  from  calculations.  Dispersion  curves  of 
disturbance  waves  were  obtained  from  the  characteristic  equation 
which  resulted  from  satisfying  the  boundary  conditions  [9]. 
These  dispersion  curves  contain  downstream  and  upstream 
branches,  which  will  be  continued  here  to  be  called  that  way  even 
though  a  sufficient  increase  in  LL  converts  the  upstream-traveling 
waves  of  the  upstream  branch  into  downstream-traveling  waves. 

Reference  [14]  found  a  static  response  (SD)  for  a  viscoelastic 
wall  due  to  the  inclusion  of  a  reduced  magnitude  and  a  pressure 
phase  change.  As  to  the  other  types  of  instabilities,  we  here 
present  two  examples  of  dispersion  curves  obtained  in  Ref.  [14] 
(Fig.  3  for  an  elastic,  and  Fig.  4  for  a  viscoelastic  wall)  where 
three  instabilities  (Class  A,  Class  B  and  Kelvin-Helmholtz,  C)  are 
visible.  Recall  that 

a  =  co/Cp,  (2) 

and  a  complex  wavenumber  a=  ar  +  icq  may  be  expressed  by  a 
complex  phase  velocity  cp  =  cr  +  ics ;  instability  corresponds  to 
aj<0  and  hence  to  c>0. 

From  Landahl’s  energy  analysis  of  the  instability  classes  [10], 
the  upstream  (downstream)-propagating  waves  on  the  upstream 
(downstream)  branches  of  the  dispersion  curves  are  Class  B. 
However,  the  downstream-propagating  portion  of  the  upstream 
branch  is  Class  A,  as  indicated.  For  larger  wavenumbers  a,  there 
is  a  coalescence  of  dispersion  curves  with  the  simultaneous 
appearance  of  cs  *  Im  cp  in  the  form  of  a  complex  conjugate 
phase  velocity  pair  cp  =  cr  ±  icj ,  classified  as  a  type  C  (Kelvin- 
Helmholtz)  instability.  The  effect  of  wall  damping  (Fig.  4)  shows 
that  the  B-type  waves  have  changed  from  neutrally  stable  to 
decaying  (Cj<0),  while  the  A-wave  has  become  destabilized  (c>0). 
The  Kelvin-Helmholtz  instability  has  become  even  more  unstable 
(the  positive  branch  of  Cj  has  increased  in  magnitude).  With  this 
simple  model  (not  requiring  solution  of  the  Orr-Sommerfeld 
equation),  Duncan  et  al.  [14]  have  been  able  to  explain  in  a  rather 
quantitative  fashion  the  experimental  values  of  the  onset 
velocities  of  instabilities  with  laminar  and  turbulent  flows 


220 


obtained  by  Hansen  et  al.  [17]  and  by  Gad-el-Hak  et  al.  [18]. 

III.  ACOUSTIC  EXCITATION  OF  INTERFACE  WAVES 

This  topic  has  been  investigated  by  us  in  a  theoretical  study 
[19],  with  the  result  that  the  dispersion  curves  of  the  interface 
waves  on  a  wall  bounded  by  a  fluid  flow  can  be  determined  by 
experiments  resonantly  exciting  these  waves  with  an  incident 
inhomogeneous  signal.  Obtaining  these  dispersion  curves  gives 
us  access  to  a  control  of  the  flow  instabilities,  and  hence  to  drag 
reduction.  (Earlier  experiments  achieved  excitation  with  a 
mechanical  shaker). 

We  consider  a  viscoelastic  layer  of  thickness  d  with  rigid 
backing,  bounded  by  an  inviscid  compressible  fluid,  extending  the 
approach  of  Pierucci  [20]  (which  considered  an  elastic  layer  and 
outgoing  sonic  disturbances  exp  ikx+imy  only)  to  also  include 
incident  signals.  Using  the  Navier-Stokes  equations  for  the  flow, 
and  the  proper  boundary  conditions  at  both  the  surfaces  of  the 
elastic  layer  and  its  backing,  taking  p  =  0  in  Eq.  (1),  a 
characteristic  equation  is  obtained.  Its  solutions,  Fig.  5  for  a 
nonviscous  rubber  layer,  show  real  and  imaginary  parts  of  cp  for 
the  lowest  interface  wave  mode  at  kd  =  10,  with  both  downstream 
and  upstream  branches.  The  Im  cp>0  causes  an  instability  due  to 
exponential  growth  of  the  interface  wave,  and  the  merger  of  the 
two  cp  branches  denotes  the  onset  of  this  CIFI  instability.  For  a 
viscous  rubber  layer,  Fig.  6,  changes  of  the  dispersion  curves  due 
to  viscosity  are  evident. 

With  an  incident  acoustic  signal  expi(kx-my)  added,  the 
outgoing  disturbance  has  amplitude  A  of  the  form 

A  =  (E  +  iF)/(E  -  iF)  (3) 

where  E  -  iF  =  0  is  the  former  characteristic  equation,  and  the 
normal  displacement  uz  on  the  interface  is 

Uj,  ~  1 2mF/(E-iF)  | ,  (4) 

giving  rise  to  resonant  behavior  when  cp  approaches  an 
eigenvalue.  In  Fig.  7  is  shown  uz  at  UJCj  ~  1 .79  (left,  just  before 
the  merger  of  downstream  and  upstream  branches),  and  at  U^/c-r 
=  1.80  (right,  just  after  the  merger),  indicating  the  observable 
resonant  behavior  which  leads  to  a  possible  experimental 
determination  of  interface  wave  dispersion  curves  and  flow 
instabilities. 

IV.  RECOMMENDATIONS  FOR  FURTHER  WORK 

Advanced  British  theories  (involving  solutions  of  the  Orr- 
Sommerfeld  equation)  compare  favorably  with  experiments 
[4,5,12,13]  while  more  straightforward  US  models  [9,14]  also 
compare  semiquantitatively  with  experiments  [15-18],  A  first 
investigation  should  be  carried  out  in  order  to  reconcile  the  two 
theoretical  approaches,  and  to  understand  why  the  simpler  picture 
also  leads  to  reasonable  results,  in  order  to  justify  its  use  for  the 
predictions  of  further  experiments.  If  found  accurate,  it  could  be 
employed  to  cases  of  more  complicated  advanced  coatings  (e.g. 
multilayer)  where  it  might  more  readily  lead  to  useful  results. 
Other,  more  specific  recommendations  can  be  listed  as  follows: 
A-  General  topics:  (1)  parametric  studies  for  multiple-layer 
walls;  (2)  replacing  rigid  wall  backing  by  an  air-backed  metal 
layer;  (3)  suppression  of  certain  instabilities  by  restricting  wall 
motion  via  placement  of  inextensible  sheets. 

B.  Resonance  formalism:  to  be  developed  for  the  excitation  of 
CIFI  waves  which  occurs  when  the  flow  speed  approaches  the 
natural  speed  of  surface  waves  in  the  wall  [4], 


C.  Wall  design:  (1)  Investigation  of  the  effects  of  periodicity  of 
multilayer  walls,  and  its  possible  generation  of  stop  bands  that 
may  retard  transitions;  (2)  effects  of  wall  anisotropy,  e.g. 
continuously  changing  parameters,  or  fiber-reinforced  walls. 

REFERENCES 

1.  M.  0.  Kramer,  "Boundary  layer  stabilization  by  distributed 
damping,"  J.  Aero.  Sci.  24,  459  (1957);  J.  Am.  Soc.  Naval  Engrs. 
72,  25  (1960);  74,  341  (1962). 

2.  J.  Gray,  "Studies  in  animal  locomotion  VI:  The  propulsive 
powers  of  the  dolphin,"  J.  Expt.  Biol.  13,  192  (1936);  "How  fish 
swim,"  Scientific  American  197,  48  (1957). 

3.  M.  O.  Kramer,  "The  dolphins’  secret,"  New  Scientist  7,  1118 
(1960). 

4.  G.  J.  K.  Willis,  "Hydrodynamic  stability  of  boundary  layers 
over  compliant  surfaces,"  PhD  thesis,  University  of  Exeter, 
England ,  1986. 

5.  K.  S.  Yeo,  "The  stability  of  flow  over  flexible  surfaces,"  PhD 
thesis,  Cambridge  University,  Cambridge,  England ,  1986. 

6.  T.  B.  Benjamin,  "Shearing  flow  over  a  wavy  boundary,"  J. 
Fluid  Mech.  6,  161  (1959). 

7.  T.  B.  Benjamin,  "Effects  of  a  flexible  boundary  on 
hydrodynamic  stability,"  J.  Fluid  Mech.  9,  513  (1960). 

8.  T.  B.  Benjamin,  "The  threefold  classification  of  unstable 
disturbances  in  flexible  surfaces  bounding  inviscid  flows,"  J. 
Fluid  Mech.  .16,  436  (1963). 

9.  C.  A.  Evrensel  and  A.  Kalnins,  "Response  of  a  compliant  slab 
to  inviscid  incompressible  fluid  flow,"  J.  Acoust.  Soc.  Am.  78, 
2034  (1985). 

10.  M.  T.  Landahl,  "On  the  stability  of  a  laminar  incompressible 
boundary  layer  over  a  flexible  surface,"  J.  Fluid  Mech.  13,  609 
(1962). 

11.  M.  T.  Landahl  and  R.  E.  Kaplan,  "Effect  of  compliant  walls 
on  boundary  layer  stability  and  transition,"  Agardograph  97,  363 
(1965). 

12.  P.  W.  Carpenter  and  A.  D,  Garrad,  "The  hydrodynamic 
stability  of  flow  over  Kramer-type  compliant  surfaces.  Part  1. 
ToIImien-Schlichting  instabilities,"  J.  Fluid  Mech.  155,  465 
(1985). 

13.  P.  W.  Carpenter  and  A.  D.  Garrad,  "The  hydrodynamic 
stability  of  flow  over  Kramer-type  compliant  surfaces.  Part  2. 
Flow-induced  surface  instabilities,"  J.  Fluid  Mech.  170,  199 
(1986). 

14.  J.  H.  Duncan,  A.  M.  Waxman  and  M.  P.  Tulin,  "The 
dynamics  of  waves  at  the  interface  between  a  viscoelastic  coating 
and  a  fluid  flow,"  J.  Fluid  Mech.  158,  177  (1985). 

15.  See,  e.g.,  M.  Gad-el-Hak,  "Compliant  coatings  research:  A 
guide  to  the  experimentalist,"  J.  Fluid  Struct.  \,  55  (1987). 

16.  J.  M.  Kendall,  "The  turbulent  boundary  layer  over  a  wall 
with  progressive  waves,"  J.  Fluid  Mech.  14,  259  (1970). 

17.  R.  Jf.  Hansen  et  al.,  "Hydrodynamic  drag  and  surface 
deformations  generated  by  liquid  flows  over  flexible  surfaces,"  in 
Viscous  Flow  Drag  Reduction ,  Prog.  Astro.  Aero.  72,  439  (1979). 

18.  M.  Gad-el-Hak,  R.  F.  Blackwelder,  and  J.  J.  Riley,  "On  the 
interaction  of  compliant  coatings  with  boundary  layer  flows,"  J. 
Fluid  Mech.  HO,  257  (1984). 

19.  M.  Talmant,  H.  Uberall  and  W.  Madigosky,  "Interface  waves 
on  a  compliant  coating  bounded  by  a  fluid  flow,  and  their 
excitation  by  acoustic  resonance,"  J.  Acoust.  Soc.  Am.  94,  2793 
(1993). 

20.  M.  Pierucci,  "Surface  waves  on  an  elastic  medium  in  the 
presence  of  an  inviscid  flow  field,"  J.  Acoust.  Soc.  Am.  60,  965 
(1977). 


221 


(Cp/CT) 


Fig.  5.  Phase  speed  cp  of  interface  waves  versus  flow  velocity 

(both  normalized  by  cT),  for  flow  over  nonviscous  rubber 
layer:  real  and  imaginary  parts  of  the  lowest  mode  at  kd 
«  10. 


Fig.  6.  Same  as  Fig.  5  but  for  a  viscous  rubber  layer  and  kd  =  5. 


01  .  .V— ..  .  -i  ■  .  I  01  r— t— r-r  ,  i-*-  *  i  ill  «  I 

0.00  0.20  0.40  0.60  0.80  1.00  1.20  1.40  0.00  0.20  0.40  0.60  0.80  1.00  1.20  1.40 


Cp/CT  Cp/CT 

Fig.  7.  Normal  displacement  uz  at  the  interface  of  a  nonviscous  rubber  layer,  indicating  acoustic  resonant  excitation  of  modes  at  kd  -  10, 
(left)  Excitation  of  the  branches  of  the  first  and  second  mode  at  ujc-r  =  1.79;  (right)  at  U«/cT  -  1.80. 


223 


ANALYSIS  OF  EVOLUTION  OF  DISTURBANCES  IN 
CHANNEL  FLOW  OVER  A  WAVY  WALL 


D.N.  Riahi 

Department  of  Theoretical  and  Applied  Mechanics 
216  Talbot  Laboratory,  University  of  Illinois  at  Urbana-Champaign 
104  S.  Wright  Street,  Urbana,  Illinois  61801  U.S.A. 
d-riahi@uiuc.edu 

Abstract  Perturbation  and  scaling  analyses  at  high  Reynolds  number  are  applied  to  study  evolution  of  finite  amplitude  disturbances  in  channel  flow  over  a 
wavy  wall.  Using  the  governing  flow  system  for  the  incompressible  fluid,  fundamental  evolution  equations  are  derived  which  provide  an  initial  value 
problem  for  the  basic  flow  composed  of  a  mean  flow  plus  a  quasi-modal  harmonic  structure.  The  solution  to  this  basic  flow  system  is  slightly  perturbed  by 
disturbances  in  the  form  of  vortices  which  have  spanwise  structure  but  vary  weakly  with  respect  to  both  streamwise  and  time  variables.  These 
disturbances  can  strongly  destabilize  the  flow  in  the  case  of  channel  flow  bounded  by  flat  and  smooth  walls.  However,  in  the  case  of  channel  flows  over 
wavy  walls,  certain  wavy  boundaries  can  modify  the  basic  flow  and  superimpose  longitudinal  vortices  whose  structures  and  scales  are  due  to  the  wavy 
walls. 


I  INTRODUCTION 

For  shear  flows  bounded  by  smooth  and  flat  walls,  Benney  [1] 
developed  a  so-called  meanflow-first  harmonic  interaction  theory 
which  concerns  about  three-dimensional  instability  of  parallel  shear 
flows  with  respect  to  disturbances  in  the  forms  of  longitudinal  roll 
vortices  and  involved  interactions  between  first  harmonics  of  waves 
and  the  mean  shear  flows.  At  high  values  of  Reynolds  numbers  such 
interactions  were  nonlinear  and  took  place  on  a  fast  time  scale. 
Instability  to  spanwise  disturbance  rolls  was  then  detected  in  several 
cases.  Benney  speculated  that  such  instability  may  explain  the  well- 
known  experimental  observations  of  Klebanoff  et  al.  [2].  These 
experiments  showed  clearly  the  evidence  for  spanwise-periodic 
streamwise  vortices  maintained  by  the  wave  motion  and  provided  proof 
that  three-dimensional  waves  can  dominate  the  nonlinear  shear  flow 
regime.  In  the  present  study  wavy  wall  formulation  developed  by  Riahi 
[3]  and  the  Benney  theory  [1]  are  employed  to  analyze  shear  flow  in  a 
channel  flow  over  a  wavy  wall.  We  found  some  interesting  results.  In 
particular,  we  found  that  certain  wavy  walls  can  lead  to  birth  of 
longitudinal  vortices  whose  structures  are  imposed  by  the  wavy  wall 
structure.  This  result  indicates  possible  procedure  for  shear  flow 
control  and,  in  particular,  application  to  seawater  drag  reduction. 

II  ANALYSIS  AND  RESULTS 

We  consider  problem  of  an  incompressible  fluid  flow  in  a  channel  of 
average  depth  d  bounded  above  by  a  flat  and  smooth  boundary  and 
bounded  below  by  a  wavy  surface  which  varies  with  respect  to  both 
time  and  space  variables.  We  use  a  cartesian  system  of  coordinates 
with  origin  on  the  average  location  of  the  wavy  wall.  Our  model  is 
based  on  the  non-dimensional  forms  of  the  Navier-Stokes  and 
continuity  equations.  The  boundary  conditions  for  the  velocity  vector  u 
of  the  flow  are 


X(<5h)m  dmu 
ml  dym 

m~  1 


at  y  =  0, 


0) 


u  =  0  at  y  =  1,  (2) 

where  y  is  the  transverse  variable,  8  is  the  magnitude  of  the  amplitude 
of  the  wavy  wall,  which  is  assumed  to  be  small  (8«1),  h {x,z,t)  is  the 
wavy  wall  shape  function,  x  is  the  streamwise  variable,  z  is  the 
spanwise  variable  and  t  is  the  time  variable.  The  terms  in  the  right- 
hand-side  of  (1)  arise  simply  by  the  contributions  of  the  higher  order 
terms  in  a  Taylor-series  expansion  about  y=  0  of  u (x,8h,z,t). 

Next,  we  consider  the  following  expansions  for  the  dependent 
variables 

(M,v,w,j?)  =  (woJ0,0,0)  +  5(M1,t;o  +  +wj,p1)  +  c.c.  +  ...,  (3) 

where  u  is  the  streamwise  velocity,  X)  is  the  transverse  velocity,  w  is  the 
spanwise  velocity,  p  is  the  pressure,  and  all  the  coefficients  are 
assumed  to  be  functions  of  xs ,  y,  z  and  ts,  where  xs  and  ts  are  slow 
variables  defined  by 

xs  =  Sx,ts  =  8t.  (4) 

In  addition,  c.c.  in  (3)  indicates  complex  conjugate.  The  wavy  wall 
shape  function  h  is  assumed  to  have  the  following  simple  form 

h  =  A(xs,z,ts)QxpU(axs  ~0)ts)/8]  + 

<5'A^os(/?z).exp(/a'Xy  -  co'ts)  +  c.c.,  (5) 


where  i-  4-1 , CL  and  a'  are  streamwise  wave  numbers  of  the  wavy 
wall,  p  is  spanwise  wave  number  of  the  wavy  wall,  CO  and  CO'  are 
frequencies  of  the  wavy  wall.  A'  is  a  constant  and  5'  is  another  small 
parameter  (8«8'«1). 

To  zeroth  order  in  6',  (5)  leads  to  dependence  for  the  first 
harmonics  ( iq  ,/?j  )  on  x  and  t  of  the  form 


(  U\ ,V\,w\,p\  )=(  «i , V\ , , pi  )exp(i’ax-i  CO  t ),  (6) 

where  ( uj,Vi,Wi,pi )  are  functions  of  xs,y,  z  and  ts.  Using  (3)-(6)  for  the 
order  5  in  the  governing  fluid  flow  system  lead  to  base  flow  system  for 
the  combined  mean  flow  variables  (uo  ,Vo  ,Wo  ,po)  and  the  first  harmonic 
coefficients  (u},  w i,  pi)-  The  only  non-zero  boundary  condition  for 


this  system  is  that  due  to  Uj  where 


ui=-A  ^~at  y=0. 


(7) 


Due  to  8'  term  in  (5),  the  solution  found  for  the  above  system  is  then 
perturbed  by  disturbance  rolls  whose  xs,  z  and  ts  dependence  is  of  the 
fonn  given  by  the  second  term  in  the  right-hand-side  of  (5).  This  leads 
to  preference  of  particular  flow  which  contains  longitudinal  vortices 
whose  flow  characteristics  and  structure  are  closely  linked  to  those  of 
the  wavy  wall.  We  extended  these  results  to  the  case  where  the  8' 
term  in  (5)  is  represented  by  a  continuous  spectrum  of  rolls  modes  [4], 
and  we  found  essentially  the  same  results  as  those  described  above. 
Presently  we  are  investigating  stability  of  three-dimensional  basic  flow 
which  is  essentially  superposition  of  the  above  two-dimensional  basic 
flow  and  the  longitudinal  vortex  flow,  and  the  results  will  be  reported 
elsewhere.  We  plan  to  extend  the  present  model  to  turbulence  regime, 
using  Reynolds  and  Hussain  [5]  approach,  and  then  apply  to  seawater 
drag  reduction  research.  Some  level  of  numerics  plus  some  use  of 
basic  flow  data. will  be  expected  to  carry  out  stability  investigation  of 
the  flow  adjacent  to  wavy  walls,  and  the  subsequent  drag  calculation 
and  optimization  procedure  versus  different  types  of  wavy  walls  will 
then  follows. 

REFERENCES 


[1]  D.J.  Benney  "The  evolution  of  disturbances  in  shear  flows  at  high 
Reynolds  numbers",  Stud.  Appl.  Math  70,  1-19  (1984). 

[2]  P.S.  Klebanoff,  K.D.  Tidstrom  and  L.M.  Sargent  "The  three- 
dimensional  nature  of  boundary-layer  instability",  J.  Fluid  Mech  12, 
1-34  (1962). 

[3]  D.N.  Riahi  "Effects  of  roughness  on  nonlinear  stationary  vortices  in 
rotating  disk  flows",  Mathl.  and  Comput.  Modelling  25,  71-82  (1997). 

[4]  D.N.  Riahi  "Modal  package  convection  in  a  porous  layer  with 
boundary  imperfections",  J.  Fluid  Mech.  318,  107-128  (1996). 

[5]  W.C.  Reynolds  and  A.K.M.F.  Hussain  "The  mechanics  of  an 
organized  wave  in  turbulent  shear  flow,  part  3.  Theoretical  models 
and  comparison  with  experiments,  J.  Fluid  Mech.  54,  263-288(1972). 


225 


Turbulent  Drag  Reduction 
Methods:  Span  wise  Fluid 
Motion  &  Wall  Motion 


227 


THE  MECHANISM  OF  TURBULENT  DRAG  REDUCTION 
WITH  WALL  OSCILLATION 


Kwing-So  Choi  and  Brian  R.  Clayton 

Department  of  Mechanical  Engineering 
The  University  of  Nottingham 
Nottingham  NG7  2RD,  United  Kingdom 
kwing-so.choi@nottingham.ac.uk 


Abstract  -  An  extensive  study  of  the  turbulence  structure  in  the  near-wall  region  of  the  boundary  layer  with  spanwise-wall  oscillation  was  conducted 
in  a  wind  tunnel  by  hot-wire  measurement  and  flow  visualisation.  This  is  to  experimentally  confirm  the  results  of  recent  studies  and  to  understand  the 
mechanisms  involved  in  the  drag  reduction  of  turbulent  boundary  layer  when  the  wall  is  oscillated  in  a  spanwise  direction.  Measurement  of  the 
stream  wise  development  of  skin-friction  coefficient  over  the  oscillating  wall  surface  shows  that  there  are  as  much  as  45%  reductions  in  skin-friction 
drag.  The  logarithmic  velocity  profiles  are  shifted  upwards,  the  turbulence  intensities  reduced,  the  velocity  skewness  and  kurtosis  increased  in  the  near¬ 
wall  region,  suggesting  that  the  viscous  sublayer  is  thickened  as  a  result  of  drag  reduction  with  wall  oscillation.  The  flow  visualised  pictures  suggest  that 
the  streamwise  vorticity  of  alternate  signs  generated  by  the  periodic  Stokes  layer  over  the  oscillating  wall  is  tilted  into  the  spanwise  direction,  creating 
a  net  spanwise  component  of  the  vorticity.  This  seems  to  have  reduced  the  velocity  gradient  near  the  wall  as  observed  in  the  previous  study.  It  is  also 
found  that  the  realignment  of  the  longitudinal  vortices  in  the  near-wall  region  into  spanwise  direction  weakens  the  near-wall  burst  activity,  leading  to 
a  reduction  in  turbulent  skin-friction. 


I.  INTRODUCTION 

Akhavan  and  her  colleagues  [1]  at  the  University  of  Michigan  recently 
conducted  a  direct  numerical  simulation  (DNS)  study  of  turbulent  channel 
flow,  demonstrating  for  the  first  time  that  the  skin-friction  drag  of  a  channel 
flow  can  be  reduced  by  oscillating  one  of  the  walls  in  a  spanwise  direction. 
Their  results  show  that  a  40%  reduction  in  turbulent  skin-friction  drag  can 
be  obtained  by  a  spanwise-wall  oscillation  only  after  five  periods  of 
oscillation  with  the  non-dimensional  period  set  at  100.  The  logarithmic 
velocity  profile  of  the  boundary  layer  is  shifted  upwards,  suggesting  that  the 
viscous  sublayer  is  thickened  as  a  result  of  the  spanwise-wall  oscillation.  It 
is  also  shown  that  the  intensities  of  velocity  fluctuations  are  reduced  by  up 
to  30%.  The  basic  findings  of  this  investigation  were  later  confirmed  by 
Baron  and  Quadrio  [2]  in  their  DNS  study. 

These  numerical  simulations  were  followed  by  an  experimental 
investigation  by  Laadhari  et  al  [3],  who  demonstrated  that  the  mean  velocity 
gradient  of  the  boundary  layer  is  reduced  near  the  oscillating  wall.  The 
reductions  in  the  turbulence  intensities  across  the  boundary  layer  were  also 
demonstrated,  suggesting  that  the  skin-friction  drag  of  the  turbulent 
boundary  layer  may  be  reduced  by  the  spanwise-wall  oscillation.  Choi  [4] 
suggested  a  possible  mechanism  of  turbulent  drag  reduction  by  spanwise- 
wall  oscillation,  arguing  that  the  sequence  of  turbulence  events  can  be 
disturbed  if  the  wall  moves  quickly  by  more  than  the  spanwise  correlation 
distance  of  near-wall  turbulence,  leading  to  a  reduction  in  the  energy 
production  of  the  boundary  layer.  In  other  words,  the  spatial  coherence 
between  the  longitudinal  vortices  and  low-speed  streaks  may  be  disrupted  by 
oscillating  a  wall  in  a  spanwise  direction  [2]. 

The  objective  of  the  present  investigation  is  firstly  to  confirm  the 
results  of  these  studies,  particularly  the  amount  of  turbulent  drag  reduction 
by  a  spanwise-wall  oscillation.  This  was  achieved  by  measuring  the 
streamwise  development  of  skin-friction  coefficient  over  the  oscillating  wall 
surface.  The  probability  density  functions  and  the  higher-moment  turbulence 
statistics  of  velocity  fluctuations  were  documented  over  an  oscillating  wall 
and  they  were  compared  with  those  without  wall  oscillation.  In  order  to 
understand  the  mechanism  of  turbulent  drag  reduction  by  spanwise-wall 
oscillation,  an  extensive  study  of  near-wall  structure  of  the  boundary  layer 
modified  by  the  wall  oscillation  was  carried  out  using  the  hot-wire 
anemometry  and  flow  visualisation  technique.  The  phase  averaged  velocity 
profiles  were  then  obtained  over  a  period  of  wall  oscillation,  and  the 
conditional  averaged  burst  signatures  were  studied  in  order  to  investigate  the 
effect  of  spanwise-wall  oscillation  on  the  near-wall  turbulence  activities. 

II.  EXPERIMENTS 

The  experiments  [5]  were  performed  in  an  open-return,  low-speed 
wind  tunnel  at  the  University  of  Nottingham  (Fig.  1).  The  boundary  layer 
was  tripped  at  the  inlet  of  the  working-section  to  ensure  a  fully-developed 
turbulent  boundary  layer  over  the  test  surface.  The  freestream  velocity  of  the 
present  investigation  was  U„.  =  2.5m/s  with  a  corresponding  Reynolds 
number  of  =  1190  based  on  the  momentum  thickness.  The  pressure 
gradient  along  the  length  of  the  working  section  was  nearly  zero,  with  the 


shape  factor  of  the  boundary  layer  H  =  1.44  at  the  trailing  edge  of  the 
oscillating  plate.  The  sinusoidal  oscillation  was  produced  by  a  crank-shaft 
system,  with  oscillation  frequencies  up  to  7  Hz  and  peak-to-peak  amplitudes 
of  up  to  70mm. 

The  streamwise  velocity  measurements  were  made  with  Dantec  56C 
CTA  system  using  a  single,  miniature,  hot-wire  probe  (Dantec  55P15).  This 
sensor  has  a  5pm-diameter  sensing  element,  1.2mm  long,  which  is  operated 
at  a  constant  temperature  mode  with  an  over-heat  ratio  of  1.8.  Measurements 
of  spanwise  velocities  were  made  with  a  subminiature  X-wire  probe 
specially  made  by  Dantec,  which  has  a  2.5pm-diameter  sensing  element, 
0.5mm  long.  The  total  length  of  the  gold  plated  wires  is  1 .5mm  with  a  space 
of  0.5mm  between  the  two  wires.  The  X-wire  probe  was  operated  at  an 
overheat  ration  of  1.5  to  reduce  the  noise  due  to  thermal  cross  talk,  but  with 
a  sufficient  sensitivity  to  the  velocity.  The  data  from  the  anemometer  were 
sampled  at  a  rate  of  2kHz  through  IOTech  ADC  488/8S  analogue-to-digital 
converter.  The  Preston  tubes  used  for  the  skin-friction  measurements  were 
connected  to  a  differential  pressure  transducer  (Furness  Control  FC0510) 
with  0.001  Pa  resolution,  accurate  to  0.25%  of  reading.  Flow  visualisation 
was  performed  at  a  freestream  velocity  of  1.5  m/s  using  a  smoke-wire 
technique  [6].  A  pulsed  copper-vapour  laser  with  a  power  output  of  15W  at 
a  pulse  rate  of  10kHz  was  used  as  a  light  source,  which  was  fanned  out  with 
a  cylindrical  lens  to  produce  a  light  sheet  at  7.5  wall  units  from  the  wall.  Still 
photographs  with  a  smoke  wire  placed  at  y+  =  4  were  taken  using  a  Nikon 
F-801  camera  with  a  simultaneous  video  recording  by  a  Sony  CCD-V800E 
Hi8-colour  camcorder.  The  high-speed  video  recording  was  also  made  with 
a  Kodak  Ektapro  Motion  Analyzer,  with  a  shutter  speed  of  1/500  sec  at  500 
fps. 


Figure  1.  Experimental  facility. 


229 


III.  RESULTS  AND  DISCUSSIONS 

The  mean-velocity  profiles  from  the  present  study  are  shown  in  Fig.  2 
in  a  log-law  plot,  where  all  the  profiles  were  non-dimensionalised  using  the 
friction  velocity  for  each  oscillating  condition.  The  curves  drawn  through  the 
data  [7]  cover  the  entire  region  of  the  boundary  layer  including  the  viscous 
sublayer,  which  seem  to  fit  all  the  profiles  very  well.  The  logarithmic 
velocity  profiles  are  shifted  upwards  with  an  increase  in  oscillation 
frequency,  suggesting  that  the  skin-friction  drag  is  reduced  by  the  spanwise- 
wall  oscillation.  When  the  outer-scaled  velocity  profiles  are  plotted  in  linear 
coordinates  (Fig.  3),  it  is  clear  that  the  mean  velocity  gradient  in  the  near¬ 
wall  region  is  significantly  reduced  with  wall  oscillation.  This  reduction  in 
the  mean  velocity  gradient,  which  is  also  seen  in  the  experimental  results  of 
Laadhari  et  al  [3],  clearly  demonstrates  that  the  wall-shear  stress  of  the 
turbulent  boundary  layer  is  reduced  by  the  spanwise-wall  oscillation.  The 
inner-scaled  velocity  profiles  (Fig.  4)  show,  on  the  other  hand,  that  the 
extent  of  linear  region  of  the  viscous  sublayer  is  increased  from  y+  «  2.5  [8] 
to  y+  ~  10  at  the  maximum  oscillation  frequency  (7Hz)  of  the  present 
experiment. 


Figure  2.  Logarithmic  velocity  profiles  of  the  boundary  layer  10mm 
downstream  from  the  trailing  edge  of  the  oscillating  plate,  for  different 
frequencies  of  wall  oscillation  (Az  =  70mm). 


Figure  3.  Outer-scaled  velocity  profiles  in  the  near- wall  region  of  the 
boundary  layer  10mm  downstream  from  the  trailing  edge  of  the  oscillating 
plate,  for  different  frequencies  of  wall  oscillation  (Az  =  70mm). 


5  10  15  20 


y+ 

Figure  4.  Inner-scaled  velocity  profiles  in  the  near-wall  region  of  the 
boundary  layer  10mm  downstream  from  the  trailing  edge  of  the  oscillating 
plate,  for  different  frequencies  of  wall  oscillation  (Az  =  70mm). 


Figures.  Turbulent  intensity  profiles  of  the  boundary  layer  10mm 
downstream  from  the  trailing  edge  of  the  oscillating  plate,  for  different 
frequencies  of  wall  oscillation  (Az  =  70mm). 


Frequency  [Hz] 


Figure  6a.  Energy  spectra  of  velocity  fluctuations  at  y+  =  1.5: 
—  with  wall  oscillation,  —  without  wall  oscillation. 


230 


Energy  Energy 


Figure  6b.  Energy  spectra  of  velocity  fluctuations  at  y+  =  4: 
—  with  wall  oscillation,  —  without  wall  oscillation. 


Figure  6c.  Energy  spectra  of  velocity  fluctuations  at  y+  =  20: 
—  with  wall  oscillation,  —  without  wall  oscillation. 


The  turbulence  intensities  of  the  boundary  layer  are  plotted  in  Fig.  5 
against  the  non-dimensional  distance  y+  from  the  wall,  where  large 
reductions  in  the  intensity  values  are  evident  within  the  inner  region  when 
the  wall  is  oscillated  in  a  spanwise  direction.  The  experimental  results  by 
Laadhari  et  al  [3]  as  well  as  numerical  data  by  Jung  et  al.  [1]  and  Baron  and 
Quadrio  [2]  exhibit  a  similar  behaviour.  The  reductions  in  turbulence 
intensities  are  also  demonstrated  in  the  energy  spectra  taken  at  y+  =  1.5,  4 
and  20  (Figs.  6a,  6b  and  6c,  respectively).  It  seems  that  the  turbulence 
energy  is  dramatically  reduced  at  low  frequencies,  say  below  50Hz  while  the 
energy  at  higher  frequencies  is  increased.  This  suggests  that  there  is  a 
transfer  of  energy  from  the  large-scale  turbulence  eddies  to  small-scale  ones 
by  the  periodic  Stokes  layer  developed  over  an  oscillating  wall. 


The  skewness  and  kurtosis  of  the  velocity  fluctuations  (Figs.  7  and  8, 
respectively)  are  increased  with  wall  oscillation  within  the  near-wall  region, 
agreeing  very  well  with  the  DNS  results  by  Baron  and  Quadrio  [2].  These 
increases  in  higher  moments  can  be  interpreted  as  a  manifestation  of  the 
increase  in  the  viscous  sublayer  thickness  by  the  spanwise-wall  oscillation 
[6,  9],  which  have  been  observed  in  several  drag-reducing  flows.  The 
probability  density  functions  of  velocity  fluctuations  at  y+  =  1.5  (Fig.  9a)  and 
at  y+  =  4  (Fig.  9b)  over  an  oscillating  wall  exhibit  long  tails  of  positive 
probability,  reflecting  the  increases  in  the  skewness  and  kurtosis  within  the 
viscous  sublayer.  They  also  show  that  the  velocity  signal  has  predominantly 
positive,  spiky  excursions  in  this  region  of  the  boundary  layer.  The 
probability  density  function  at  y+  =  20  (Fig.  9c)  still  show  a  sign  of  increase 
in  skewness  and  kurtosis  with  a  long  tail  of  positive  probability,  but  the 
difference  is  not  as  great  at  this  location  of  the  boundary  layer  as  within  the 
viscous  sublayer  (Figs.  9a  and  9b). 


Figure  7.  Skewness  profile  of  the  boundary  layer  10mm  downstream  from 
the  trailing  edge  of  the  oscillating  plate,  for  different  frequencies  of  wall 
oscillation  (Az  =  70mm). 


Figure  8.  Kurtosis  profile  of  the  boundary  layer  10mm  downstream  from 
the  trailing  edge  of  the  oscillating  plate,  for  different  frequencies  of  wall 
oscillation  (Az  =  70mm). 


231 


Normalised  deviation 


The  streamwise  variation  of  skin-friction  coefficient  of  the  boundary 
layer  is  given  in  Fig.  10,  showing  that  the  skin-friction  coefficient  over  the 
oscillating  wall  begins  to  reduce  just  upstream  (about  two  boundary  layer 
thicknesses)  of  the  leading  edge  to  reach  a  maximum  level  of  drag  reduction 
somewhere  near  the  middle  of  the  plate.  The  present  data  clearly  indicate 
that  there  are  as  much  as  45%  reductions  in  the  skin-friction  coefficient 
compared  with  that  without  wall  oscillation,  which  is  in  close  agreement 
with  the  results  of  direct  numerical  simulations  [1,  2].  The  skin-friction 
coefficient  then  seems  to  revert  back  gradually  towards  the  level 
corresponding  to  the  condition  without  wall  oscillations  in  the  downstream 
of  the  oscillating  plate.  Nearly  20%  reduction  in  Cf  is  still  evident  after  more 
than  two  boundary  layer  thicknesses  from  the  trailing  edge  of  the  oscillating 
plate,  indicating  that  the  relaxation  process  is  rather  slow. 


Figure  9a.  Probability  density  functions  of  velocity  fluctuations  at  y+  =  1 .5: 
—  with  wall  oscillation,  —  without  wall  oscillation.  . 


Normalised  deviation 


Figure  9b.  Probability  density  functions  of  velocity  fluctuations  at  y+  =  4: 
—  with  wall  oscillation,  —  without  wall  oscillation. 


Figure  10.  Downstream  variation  of  skin-friction  coefficient  Cf  with  a 
spanwise-wall  oscillation  (/'  =  5Hz,  A z  =  50mm),  as  a  ratio  to  the  skin- 
friction  coefficient  Cp  without  oscillation.  The  leading  edge  of  the  500mm 
long  oscillating  plate  is  located  at  x  =  0. 


Normalised  deviation 


Figure  9c.  Probability  density  functions  of  velocity  fluctuations  at  y+  =  20: 
—  with  wall  oscillation,  —  without  wall  oscillation. 


When  a  flat  plate  is  oscillated  tangentially  in  still  fluid,  a  thin  layer  of 
periodic  shear  flow  called  the  Stokes  layer  is  formed  over  the  plate  as  a 
result  of  viscous  diffusion  from  its  surface.  In  other  words,  the  Stokes  layer 
over  an  oscillating  wall  is  a  constant  source  of  vorticity  of  alternate  signs  as 
the  wall  moves  back  and  forth  [10]  in  a  spanwise  direction.  If  there  is  a 
stream  of  uniform  flow  across  an  oscillating  wall  surface,  the  vortex  sheets 
produced  by  the  periodic  Stokes  layer  will  be  convected  by  the  boundary 
layer.  Figure  1 1  shows  the  theoretical,  laminar  velocity  profiles  of  the  Stokes 
layer  over  the  oscillating  wall  in  still  fluid  (i.e.  without  boundary  layer  flow) 
at  different  phase  of  wall  oscillation.  The  experimental  data  obtained  with 
an  X-wire  probe  are  phase  averaged  over  a  period  of  wall  oscillation,  and  are 
also  shown  in  this  figure.  It  is  observed  that  the  measured  velocity  profiles 
are  very  similar  to  the  theoretical  profiles  of  laminar  Stokes  layer  in  both 
their  shape  and  phase  relationship,  although  their  magnitude  seems  to  be 
slightly  less  than  that  of  theoretical  values.  It  should  be  noted  here  that  the 
thickness  of  the  Stokes  layer  over  an  oscillating  wall  is  similar  to  that  of  the 
viscous  sublayer  under  the  experimental  conditions  where  the  turbulent  drag 
reductions  are  observed.  Also,  the  Reynolds  number  of  the  Stokes  layer  is 
well  below  the  critical  value,  so  that  the  Stokes  layer  remains  laminar  [11- 
13].  These  are  considered  to  be  important  conditions  in  obtaining  the 
turbulent  drag  reduction  with  spanwise-wall  oscillation,  since  the 
modification  of  the  near-wall  structure  seems  to  result  from  an  interaction 
of  the  Stokes  layer  with  the  viscous  sublayer  of  the  turbulent  boundary  layer 
where  the  majority  of  the  energy  production  takes  place. 


232 


The  streamwise  velocity  profiles  are  also  phase  averaged  over  a  period 
of  wall  oscillation,  and  are  shown  in  Fig.  1 1 .  There  are  no  noticeable 
changes  in  these  profiles  at  different  phase  of  wall  oscillation  outside  the 
viscous  sublayer.  Examining  the  phase  averaged  velocities  within  the 
viscous  sublayer  closely,  however,  it  is  observed  that  the  streamwise  velocity 
profiles  exhibit  a  cyclic  change  with  the  change  in  wall  velocity  during  the 
oscillation.  In  other  words,  the  velocity  signal  is  modulated  by  the  periodic 
Stokes  layer  at  a  frequency  twice  that  of  the  wall  oscillation,  which  can  be 
seen  in  the  phase-averaged  velocity  signal  over  one  period  of  wall  oscillation 
(Fig.  12).  From  this  figure,  the  streamwise  velocity  profile  at  y+  =  1 .5  seems 
to  be  nearly  in  phase  with  the  spanwise  wall  velocity  but  with  perhaps  a 
slight  phase  lag.  At  y+  =  4,  the  streamwise  velocity  is  lagged  nearly  k/2 
behind  the  wall  velocity.  No  clear  phase  relationship  between  the  streamwise 
velocity  and  the  wall  velocity  is  observed  at  y+  =  20. 


Figure  12.  Phase  averaged  wall  velocity  —  and  streamwise  velocity 
profiles:  a)  at  y+  =  1.5,  b)  at  y+  =  4  and  c)  at  y+  =  20. 


20 

15 

t  to 

i  5 
0 


-5  0 


/-V  rv  i 

•  -  . •*' 

Phase  =  ft 

- v  Y  0~ir^nno=0-0  |  O— 

fr  10  20 

— o - |— 

30 

40 

y+ 


Figure  11.  Velocity  profiles  in  the  Stokes  layer:  —  theory  (spanwise 
velocity  profiles),  o  phase  averaged  experimental  data  (w+),  — -  Dean’s 
formula  (streamwise  velocity  profiles),  •  phase  averaged  experimental  data 
(u+). 


Figures  13a  and  13b  are  the  flow-visualised  pictures  of  the  turbulent 
boundary  layer  showing  the  modified  near-wall  structure  when  a  wall  is 
oscillated  in  a  spanwise  direction.  As  the  oscillating  wall  moves  upwards 
(Fig.  1 3a)  the  streamwise  vorticity  of  the  vortex  sheet  generated  by  the 
periodic  Stokes  layer  is  titled  upwards  as  shown  by  an  arrow  indicating  the 
vorticity  vector  Q.  As  a  result,  a  positive  spanwise  component  of  the 
vorticity  is  created  in  the  near-wall  region  of  the  boundary  layer.  When  the 
oscillating  wall  moves  downwards  (Fig.  13b),  on  the  other  hand,  the  vorticity 
vector  Q  is  titled  downwards  as  shown  by  an  arrow  in  the  figure.  Here,  the 
vortex  sheet  produced  by  the  downward  movement  of  the  oscillating  wall 
has  a  negative  vorticity  as  compared  with  the  positive  vorticity  during  the 
upward  motion.  Therefore,  the  downward  motion  of  the  oscillating  wall 
again  creates  a  positive  spanwise  component  of  vorticity.  This  means  that  a 
net  spanwise  vorticity  is  created  in  a  turbulent  boundary  layer  during  upward 
as  well  as  downward  motion  of  the  oscillating  wall.  The  numerical  study 
carried  out  by  Baron  and  Quadrio  [2]  indeed  shows  the  existence  of  the  local 
intensity  maximum  of  the  spanwise  vorticity  fluctuations  at  y+  =  15,  which 
can  be  considered  as  the  location  of  the  net  spanwise  vorticity  created  by  the 
Stokes  layer  over  the  oscillating  plate. 


t 


Leading  edge  of 
oscillating  plate 


Figure  13a.  Row  visualisation  of  the  near-wall  region  of  the  boundary  layer 
with  wall  oscillation  (f  =  5Hz,  Az  =  50mm).  The  leading  edge  of  the 
oscillating  plate  is  visible  near  the  centre  of  the  picture.  The  flow  is  from  left 
to  right  and  the  oscillating  plate  on  the  right  is  moving  upwards. 


233 


0.15 


t 


Leading  edge  of 
oscillating  plate 


Figure  13b.  Flow  visualisation  of  the  near-wall  region  of  the  boundary  layer 
with  wall  oscillation  (f  -  5Hz,  A z  =  50mm).  The  leading  edge  of  the 
oscillating  plate  is  visible  near  the  centre  of  the  picture.  The  flow  is  from  left 
to  right  and  the  oscillating  plate  on  the  right  is  moving  downwards. 

A  conceptual  model  for  the  turbulent  boundary  layer  over  an  oscillating 
wall  is  shown  in  Fig.  14  to  demonstrate  the  effects  of  the  net  spanwise 
vorticity  created  by  the  wall  oscillation  at  the  edge  of  the  viscous 
sublayer.  Using  this  model,  it  can  be  expected  that  the  mean  velocity 
gradient  in  the  near- wall  region  (y+  <  15)  will  be  reduced  by  the  induction 
of  the  spanwise  vorticity.  The  mean  velocity  will  be  increased  outside  the 
viscous  sublayer  (y+  >  15),  on  the  other  hand,  shifting  the  logarithmic 
velocity  profile  upwards.  These  behaviours  affecting  the  boundary  layer 
profiles  are  clearly  demonstrated  in  the  present  experimental  results  given 
in  Fig.  3  and  Fig.  2,  respectively.  Indeed,  the  measured  changes  in  the 
boundary  layer  profiles  due  to  wall  oscillation  (Fig.  15)  agree  very  well  with 
the  prediction  using  the  conceptual  model  (Fig.  14).  The  crossover  point  of 
the  measured  velocity  profiles  is  located  at  y+  ~  25,  which  is  quite  consistent 
with  the  present  conceptual  model.  It  must  be  emphasised  here  that  the  net 
spanwise  vorticity  Qz  does  not  seem  to  induce  any  inflection  points  in  the 
boundary  layer  profile  as  shown  in  Fig.  4.  Therefore,  no  increases  in  the 
level  of  the  burst  activity  are  expected  as  a  result  of  the  velocity  induction  by 
the  spanwise  vorticity. 


UOO 


Figure  14.  Conceptual  model  for  a  turbulent  boundary  layer  over  an 
oscillating  wall,  showing  a  spanwise  vorticity  Qz  created  by  the  periodic 
Stokes  layer. 


Figure  15.  Velocity  reductions  Am  in  the  boundary-layer  profiles  10mm 
downstream  from  the  trailing  edge  of  the  oscillating  plate,  for  different 
frequencies  of  wall  oscillation  (Az  =  70mm). 


The  results  of  flow  visualisation  in  the  near-wall  region  of  the 
boundary  layer  also  show  that  the  pairs  of  longitudinal  vortices  move 
downstream  in  a  sinuous  form  as  the  test  plate  oscillates  in  a  spanwise 
direction.  Figure  13a  shows  the  near- wall  boundary  layer  structure  over  the 
oscillating  plate  as  it  moves  upwards,  where  the  longitudinal  vortices  in  the 
viscous  sublayer  are  twisted  by  the  Stokes  layer  realigning  themselves  into 
the  direction  of  an  arrow  shown  in  the  figure.  When  the  oscillating  plate 
moves  downwards,  the  longitudinal  vortices  are  twisted  into  the  opposite 
direction  as  shown  by  an  arrow  in  Fig.  13b.  As  a  result,  the  streamwise 
vorticity  associated  with  the  longitudinal  vortices  is  reduced  in  the  near-wall 
region  of  the  boundary  layer. -Indeed,  it  is  found  in  the  DNS  results  [2]  that 
the  intensity  of  streamwise  vorticity  fluctuations  is  nearly  halved  across  the 
entire  thickness  of  the  boundary  layer  as  the  wall  oscillates  in  a  spanwise 
direction.  As  a  consequence,  the  near-wall  burst  [6]  activity  is  weakened 
leading  to  a  reduction  in  turbulent  skin-friction  drag  as  observed  in  the 
present  experiment.  Here,  the  near-wall  bursts  are  associated  with  the 
downwash  of  high-momentum  fluid  towards  the  wall  as  a  result  of  induction 
by  the  pairs  of  longitudinal  vortices  as  they  stretch  into  the  streamwise 
direction.  Therefore,  the  strength  of  the  downwash  during  the  near-wall  burst 
is  reduced  as  the  vorticity  of  the  pairs  of  longitudinal  vortices  is  reduced.  It 
should  be  noted  that  the  tilting  of  the  longitudinal  vortices  will  only  affect  the 
streamwise  component  of  vorticity,  since  the  spanwise  realignment  of  the 
vortices  takes  place  in  alternate  directions  with  the  wall  oscillation. 

Figure  16a  shows  the  conditionally  sampled  signature  of  the  near- wall 
burst  using  the  VITA  technique  at  y+  =  1.5  over  the  oscillating  wall.  The 
change  in  the  burst  signature  is  remarkable  in  the  near-wall  region  of  the 
boundary  layer,  where  the  duration  of  the  burst  is  reduced  to  nearly  one  third 
of  that  without  wall  oscillation.  A  similar  reduction  in  burst  duration  is 
observed  at  y+  =  4  (Fig.  16b).  Even  outside  the  viscous  sublayer  at  y+  =  20 
(Fig.  16c)  the  effect  of  wall  oscillation  on  the  burst  signature  is  still 
significant,  with  the  burst  duration  nearly  a  half  of  that  without  wall 
oscillation.  Note  that  the  vertical  scale  of  the  burst  signatures  (Figs.  16a,  16b 
and  16c)  is  normalised  to  allow  a  comparison  of  the  behaviour  of  the 
velocity  fluctuations  be  made.  It  has  been  observed  that  the  turbulence 
intensity  of  the  boundary  layer  is  reduced  with  wall  oscillation  (Fig.  5), 
reducing  the  intensity  of  the  near-wall  bursts. 


234 


Velocity  (normalised) 


*8 

> 


Figure  16a.  Conditionally  sampled  near- wall  burst  signatures  at  y+  =  1.5: 
—  with  wall  oscillation,  —  without  wall  oscillation. 


Figure  16b.  Conditionally  sampled  near-wall  burst  signatures  at  y+  =  4: 
—  with  wall  oscillation,  —  without  wall  oscillation. 


IV.  CONCLUSIONS 

A  wind  tunnel  study  of  the  turbulent  boundary  layer  with  a  spanwise- 
wall  oscillation  was  carried  out,  where  the  skin-friction  reductions  as  much 
as  45%  were  observed  when  the  oscillation  frequency  and  amplitude  were 
adjusted  to  give  an  optimum  speed  of  wall  oscillation.  With  the  logarithmic 
velocity  profiles  of  the  boundary  layer  shifted  upwards  and  the  turbulence 
intensities  reduced  by  the  spanwise-wall  oscillation,  the  present  results 
convincingly  confirmed  the  basic  conclusions  of  the  recent  direct  numerical 
simulations.  It  was  also  shown  that  the  skewness  and  kurtosis  of  the  velocity 
fluctuations  within  the  near-wall  region  are  increased  with  a  wall  oscillation, 
agreeing  very  well  with  the  boundary  layer  profiles  of  the  DNS  results. 

It  is  believed  that  the  mechanism  of  drag  reduction  by  a  spanwise-wall 
oscillation  strongly  relates  to  the  net  spanwise  vorticity  generated  by  the 
periodic  Stokes  layer,  which  reduces  the  mean  velocity  gradient  of  the 
boundary  layer  within  the  viscous  sublayer.  At  the  same  time,  the 
longitudinal  vortices  are  realigned  into  the  spanwise  direction  by  the  Stokes 
layer  over  the  oscillating  wall,  reducing  the  streamwise  vorticity  in  the  near¬ 
wall  region  of  the  boundary  layer.  As  a  result,  the  near-wall  burst  activity, 
which  is  associated  with  the  downwash  of  high-momentum  fluid  near  the 
wall,  is  weakened  leading  to  a  reduction  in  turbulent  skin-friction  drag. 

Although  the  present  study  was  carried  out  in  a  wind  tunnel,  the  basic 
findings  from  this  research  are  applicable  to  fresh  water  as  well  as  seawater 
environment.  Indeed  the  author  has  recently  carried  out  an  experiment  study 
of  a  turbulent  pipe  flow  using  water  where  a  section  of  the  pipe  was 
oscillated  in  a  circumferential  direction  [14].  The  results  indicated  that  the 
skin-friction  factor  of  the  pipe  is  reduced  by  as  much  as  25%  as  a  result  of 
active  manipulation  of  near-wall  turbulence  structure  by  circular-wall 
oscillation. 

The  work  was  supported  by  EPSRC  Research  Grants,  GR/J06917  and 
GR/K27780.  The  subminiature  X-wire  probes  used  in  this  investigation  were 
made  available  from  Rolls-Royce. 

V.  REFERENCES 

1.  Jung,  W.J.,  Mangiavacchi,  N.,  and  Akhavan,  R.,  “Suppression  of 
Turbulence  in  Wall-bounded  Flows  by  High  Frequency  Spanwise 
Oscillations,”  Phys.  Fluids ,  Vol.  A4,  No.  8,  1992,  pp.  1605-1607. 

2.  Baron,  A.,  and  Quadrio,  M.,  “Turbulent  Drag  Reduction  by  Spanwise 
Wall  Oscillations,”  Appl.  Sci.  Res.,  Vol.  55,  1996,  pp.  311-326. 

3.  Laadhari,  F.,  Skandaji,  L.,  and  Morel,  R.,  “Turbulence  Reduction  in 
a  Boundary  Layer  by  a  Local  Spanwise  Oscillating  Surface,”  Phys.  Fluids, 
Vol.  A6,  No.  10,  1994,  pp.  3218-3220. 

4.  Choi,  K.-S.,  “Turbulent  Drag  Reduction  Strategies,”  in  Emerging 
Techniques  in  Drag  Reduction,  edited  by  K.-S.  Choi,  K.K.  Prasad,  and 
Truong,  MEP,  London,  1996,  pp.  77-98. 

5.  Choi,  K.-S.,  DeBisschop,  J.-R.,  and  Clayton,  B.R.,  “Turbulent 
Boundary-Layer  Control  by  Means  of  Spanwise-Wall  Oscillation”,  to  appear 
in  AIAA  J.,  1998. 

6.  Choi,  K.-S.,  “Near-wall  Structure  of  Turbulent  Boundary  Layer  with 
Riblets,”  J.  Fluid  Mech.,  Vol.  208,  1989,  pp.  417-458. 

7.  Dean,  R.B.,  “A  Single  Formula  for  the  Complete  Velocity  Profile  in  a 
Turbulent  Boundary  Layer,”  Trans.  ASUE  J.  Fluids  Engineering,  Vol.  98, 
No.  4,  1976,  pp.  723-727. 

8.  Durst,  F.,  et  ai,  “LDA  Measurements  in  the  Near-wall  Region  of  a 
Turbulent  Pipe  Row,”  J.  Fluid  Mech.,  Vol.  295,  1995,  pp.  305-335. 

9.  Pal,  S.,  Deutsch,  S.,  and  Merkle,  C.L.,  “A  Comparison  of  Shear  Stress 
Ructuation  Statistics  Between  Microbubble  Modified  and  Polymer  Modified 
Turbulent  Boundary  Layers,”  Phys.  Fluids,  Vol.  Al,  No.  8,  1989,  pp.  1360- 
1362. 

10.  Sherman,  F.S.,  Viscous  Flow,  McGraw-Hill,  New  York,  1990. 

1 1 .  Sarpkaya,  T.,  “Coherent  Structures  in  Oscillatory  Boundary  Layers,” 
J  Fluid  Mech.,  Vol.  253,  1993,  pp.  105-140. 

12.  Akhavan,  R.,  Kamm,  R.D.,  and  Shapiro,  A.H.,  “An  Investigation  of 
Transition  to  Turbulence  in  Bounded  Oscillatory  Stokes  Rows,  Part  1. 
Experiments,”  J.  Fluid  Mech.,  Vol.  225,  1991,  pp.  395-422. 

13.  Akhavan,  R.,  Kamm,  R.D.,  and  Shapiro,  A.H.,  “An  Investigation  of 
Transition  to  Turbulence  in  Bounded  Oscillatory  Stokes  Rows,  Part  2. 
Numerical  Simulations,”  J .  Fluid  Mech.,  Vol.  225,  1991,  pp.  423-444. 

14.  Choi,  K.-S.  and  Graham,  M.,  “Drag  Reduction  of  Turbulent  Pipe 
Flows  by  Circular-wall  Oscillation,”  Phys.  Fluids ,  Vol.  10(1),  1998,  pp.  7-9. 


Figure  16c.  Conditionally  sampled  near-wall  burst  signatures  at  y+  =  20: 
—  with  wall  oscillation,  —  without  wall  oscillation. 


235 


ON  THE  PHYSICS  OF  SKIN  FRICTION  REDUCTION  THROUGH  WALL  OSCILLATION 

M  R  DHANAK  AND  C  SI 
FLORIDA  ATLANTIC  UNIVERSITY 
BOCA  RATON,  FL  33431 
E-MAIL:  dhanak@oe.fau.edu 

Abstract-  The  interactions  between  streamwise  vortices  near  a  wall  and  a  modified  Stokes  layer,  induced  by  spanwise  oscillations  of  the  wall 
beneath,  is  described  using  an  exact  numerical  solution  of  the  Navier  Stokes  equations.  The  model  flow  characterizes  the  interactions  between 
quasi-streamwise  vortices  in  the  inner  layer  of  a  turbulent  boundary  layer  and  an  oscillating  wall.  In  the  absence  of  wall  oscillations,  as  shown  by 
Orlandi  and  Jimenez,  the  model  flow  involving  wall-vortex  interactions  leads  to  formation  of  low  speed  streaks  and  an  increase  in  skin  friction 
at  the  wall  surface.  The  wall  oscillation  is  shown  to  induce  annihilation  of  the  low  speed  streaks,  resulting  in  a  reduction  in  the  skin  friction,  the 
Reynolds  stress  and  the  rate  of  production  of  kinetic  energy.  These  effects  are  consistent  with  observations  in  experimental  and  DNS  studies  of 
turbulent  boundary  layers  and  channel  flows. 


L  INTRODUCTION 

There  is  significant  experimental  and  numerical  evidence  that  coherent 
structures  in  the  inner  layer  of  a  turbulent  boundary  layer  play  an  important 
role  in  the  generation  of  Reynolds  stress.  These  coherent  structures  are 
typically  in  the  form  of  long  quasi-streamwise  vortices4  which  act  to 
redistribute  the  longitudinal  velocity  field  into  alternating  high  and  low  speed 
regions  while  maintaining  the  convection  of  momentum  normal  to  the  wall 
(see  for  example,  Kim  et  al1,  Spalart2,  Jimenez  and  Moin3).  Based  on  these 
observations,  Orlandi  and  Jimenez5  have  suggested  a  cross-plane  model  for 
the  interaction  between  these  flow  structures  and  the  rigid  surface.  They 
show  that  the  model  captures  the  crucial  aspects  of  the  interactions  between 
the  coherent  structures  and  the  wall  and  predicts  fairly  well  the  formation  of 
low  speed  streaks  and  pertinent  characteristics  of  turbulent  skin  friction. 
Recent  experimental  and  direct  numerical  simulation  studies  (Laadhari  et. 
al6,  Jung  et  al.7  and  Moin  et  al.8)  also  show  that  imposition  of  an  oscillatory 
spanwise  pressure  gradient  or  spanwise  oscillation  of  the  wall  beneath  the 
boundary  layer  temporarily  inhibits  production  of  turbulence  in  the  flow, 
leading  to  transient  reductions  in  all  turbulent  quantities,  including  the 
Reynolds  stress  and  the  turbulent  kinetic  energy.  It  seems  evident  that  these 
changes  are  related  to  the  modification  of  the  coherent  flow  structures  and 
their  distribution  in  the  inner  wall  region.  In  this  paper,  we  investigate  the 
implication  of  the  wall  oscillation  on  the  interaction  between  the 
quasi-streamwise  coherent  structures  in  the  inner  layer  and  the  wall  using  the 
Orlandi-Jimenez  model.  Thus  >fre  numerically  study  the  cross-plane 
evolution  of  a  streamwise  vortex  pair  and  its  interaction  with  the  surface 
beneath,  when  the  latter  is  subjected  to  spanwise  oscillation.  Hence,  we  show 
how  the  oscillation  modifies  the  interaction,  leading  to  annihilation  of  the 
low  speed  streaks  and  a  reduction  in  the  skin  friction,  the  Reynolds  stress  and 
the  rate  of  production  of  kinetic  energy,  consistent  with  observations  in 
experimental  and  DNS  studies  of  turbulent  boundary  layers  and  channel 
flows. 

II.  FORMULATION 

We  consider  the  flow  in  a  Cartesian  co-ordinate  system  Oxyz  with  Ox 
along  the  streamwise  direction,  so  that  y—z  is  the  cross-plane  of  interest 
(figure  1).  The  vortices  in  the  inner  layer  experience  axial  stretching 
associated  with  straining  induced  by,  for  example,  other  structures;  if  the 
quasi-streamwise  vortices  arise  from  developing  hair-pin  eddies,  it  can  be 
shown  that  the  flow  induced  by  the  “head”  of  the  hairpin  can  give  rise  to  such 
straining.  We,  therefor,  consider  the  velocity  in  our  model  flow  to  be  of  the 
form, 

«  =  [<?0 (y,z,t)  +  +  qv(y,z,t)),  -  <p(y)  +  v^z.t),  wx(y,z,tj\ 

where  [x<p(y)',  -  ip(y),  0]  is  the  Hiemenz  flow9  representing  the  straining 
flow;  the  associated  straining  rate  is  here  denoted  as  a.  All  of  the  flow 
variables  are  non-dimensionalized  with  respect  to  the  wall  units.  The 
velocity  field  is  an  exact  solution  of  the  Navier-Stokes  equations  with  the  x 
component  of  vorticity,^,  satisfying, 

(§1  -  V2)ty,  =  a)x(q]  +  <j>') 

where  D/Dt  =  d/dt  +  (v  —  <p)d/dy  4-  wd/dz  and 

V2  =  d2/dy2  +  d2/dz2.  The  contribution  q0  to  the  streamwise  component 
satisfies 

({ l  -  V2)?o  =  -  <?«, (0  +  <7.)  -  C, 

where  C\  is  a  constant  to  be  determined  by  initial  conditions.  The 
contribution  qx  is  a  measure  of  the  change  in  dux/ dx  from  that  given  by  the 
Hiemenz  flow  and  satisfies, 

(§1  -  V2)tfi  =  -  9,(20  +  ?,)  -  V, 4>". 


The  cross-stream  components  of  velocity  are  obtained  by  solving  a  Poisson 
equation.  The  flow  is  considered  to  be  periodic  in  the  z-direction  with  a 
wavelength  Z.  At  the  upper  boundary  of  the  computational  domain  the  flow 
is  assumed  to  be  undisturbed  and  along  the  wall  no-slip  boundary  condition 
is  enforced.  Thus,  the  boundary  condition  at  the  wall  is  given  by 
w(x ,  0 ,z,  t)  =  [0, 0,  W0  cos(2 n(t  +  #T/7)],  where  W0  is  the  amplitude,  %  is 
the  phase  and  T  is  the  period  of  oscillation.  Fot  t  <  0,  the  flow  consists  of  a 
shear  layer  in  the  streamwise  direction  and  a  Stokes  layer  in  the  cross-plane, 
in  the  presence  of  the  straining  flow;  an  exact  solution  of  the  Navier-Stokes 
equations10  is  utilized  for  this  consideration.  At  t  =  0,  a  vortex  pair,  in  the 
form  of  unsymmetrical  vortex  sheet  sections  (see  figure  2a),  of  the  type  used 
by  Orlandi  and  Jimenez5,  is  introduced  into  the  flow.  The  ensuing  interaction 
is  studied  for  different  values  of#,  corresponding  to  the  phase  of  the 
oscillation  when  the  vortices  are  introduced  in  the  flow,  and  for  different 
values  of  the  period  T.  Time  marching  is  performed  using  a  third-order 
Runge-Kutta  scheme  in  time. 

III.  RESULTS 

We  choose  a  =  0.15  and  the  vortex  strength  T  =  ±  300  as  typical 
values4  to  illustrate  the  interaction.  The  introduction  of  the  coherent 
structures  in  the  vicinity  of  the  wall  causes  the  average  streamwise  skin 
friction  to  increase  due  to  the  convection  of  the  momentum  normal  to  the 
wall.  Figure  2(a,  b)  show  the  vorticity  contours  in  the  cross-stream  plane  at 
two  times  during  the  evolution  of  a  vortex  pair  in  the  absence  of  wall 
oscillation.  The  vortex  sheets  roll  up  into  coherent  structures  which  convect 
towards  each  other.  This  in  turn  enhances  the  self  induced  motion  of  the  pair 
away  from  tl\e  wall.  However,  the  wallward  motion  induced  by  the  straining 
flow  acts  to  attenuate  this  convection,  thereby  enhancing  the  interaction  of 
the  pair  with  the  wall.  Layers  of  vorticity  of  opposite  sign  to  that  of  the 
primary  vortices  are  generated  on  the  wall  beneath  the  vortices  and  interact 
destructively  with  the  latter.  Further,  the  oppositely  signed  coherent  vortices 
also  undergo  mutual  cancellation.  The  contours  of  the  streamwise  velocity 
contribution  qQy  corresponding  to  times  shown  in  figure  2  (a,  b)  are  depicted 
in  figures  3(a,  b)  respectively  and  illustrate  the  development  of  a  low  speed 
streak  in  the  manner  described  by  Orlandi  and  Jimenez5.  The  streak  is  most 
intense  around  t+  ~  0(7.5),  but  eventually  disappears  as  the  vorticity  in  the 
pair  undergoes  cancellation.  The  cycle  of  the  “event”,  comprising  the 
appearance  of  the  coherent  vortices  in  the  wall  region,  their  interaction  with 
the  wall,  and  subsequent  decay,  lasts  for  a  period  of  t+  =  O  (30).  However, 
on  the  basis  of  a  dimensional  argument,  Orlandi  and  Jimenez5  suggest  that 
in  turbulent  boundary  layers,  for  t+  >  0(20),  the  three-dimensional  effects 
not  accounted  for  in  the  model,  including  the  processes  which  give  rise  to  the 
coherent  vortices,  would  become  important  so  that  inferences  based  on  the 
model  for  times  beyond  this  may  not  be  reliable. 

The  effect  of  the  oscillation  was  considered  for  a  range  of  values  of  T 
and  x  f°r  a  fixe<i  value  of  WQ  —  12,  this  being  the  value  considered  in  the 
DNS  study  of  Jung  et  al7.  The  case  corresponding  to  T=  100  and  #  =  3/8 
is  illustrated  in  figures  2  and  3.  The  developing  vorticity  contours  at  /+  =  7.5 
are  shown  in  figure  2c.  During  the  depicted  phase,  the  wall  is  moving  from 
right  to  left  and  the  Stokes  layer  acts  to  sweep  the  right  vortex  beneath  the  left 
vortex,  thereby  destroying  the  approximately  symmetrical  development  of 
the  pair,  apparent  in  figure  2(b),  in  the  absence  of  oscillation.  The  orientation 
of  the  vortex  pair  is  such  that  the  straining  flow  brings  it  closer  to  the  wall, 
leading  to  an  accentuated  interaction  with  the  Stokes  layer  and  rapid 
annihilation  of  the  coherent  structures.  By =  18,  the  coherent  structures  are 
no  longer  apparent,  compared  to  the  corresponding  time  /+  -  30  in  the 
absence  of  oscillation.  The  associated  effect  on  the  low  speed  streak  is  shown 
in  figure  3c.  The  streak,  so  well  developed  at  f  -  7.5  in  the  absence  of 
oscillation,  is  barely  apparent.  The  oscillatory  motion  acts  to  severely  distort 
the  streak,  mixing  low  speed  and  high  speed  momentum,  thereby  reducing 


237 


the  region  over  which  the  Reynolds  stress  contribution  -  mV  is  positive. 
For  the  phase  corresponding  to  %  ~  0  (not  shown),  the  wall  is  moving  from 
left  to  right  when  the  vortices  are  introduced,  so  that  the  left  vortex  is  swept 
underneath  the  right  vortex.  For  other  phases,  either  of  the  vortices  may  be 
swept  beneath  the  other.  In  all  cases,  the  Reynolds  stress  contribution  is 
reduced  during  the  interaction.  The  comparison  between  the  skin  friction 
coefficient,  Cj ,  in  the  presence  of  oscillation,  averaged  over  the  different 
values  of  %  and  its  value,  c ^ ,  in  the  absence  of  oscillation,  is  shown  in  figure 
4  for  various  periods  of  wall  oscillation.  A  reduction  of  around  10%  is 
achieved  in  all  cases,  the  maximum  value  being  for  a  period  of  7+  =  75.  This 
reduction  is  consistent  with  the  results,  for  small  times,  of  the  DNS  study7  of 
turbulent  flow  in  a  channel.  For  large  times,  well  beyond  the  validity  of  the 
present  model  and  presumably  involving  many  interactions  of  the  type 
described  here,  Jung  et  al7  obtained  over  40%  reduction  in  skin  friction,  the 
maximum  reduction  corresponding  to  T+  =  100. 

For  a  fixed  value  of  a,  the  reduction  in  skin  friction  in  our  model 
increase  with  increase  in  T.  The  oscillation  also  acts  to  attenuate  the  other 
attributes  of  turbulent  flow,  such  as  the  Reynolds  stress  and  the  rate  of 
production  of  turbulent  energy,  as  shown  in  figures  5  and  6,  consistent  with 
the  results  of  the  DNS  study  of  Jung  et  al7. 

IV.  DISCUSSION 

As  shown  by  Orlandi  and  Jimenez7,  the  crucial  aspects  of  the  dominant 
feature  of  the  inner  layer  of  a  turbulent  boundary  layer,  viz.  the  formation  and 
maintenance  of  long  streamwise  streaks  with  low  streamwise-speed 
momentum  ejection  in  the  middle  and  high  streamwise-speed  down-wash 
at  each  side,  are  well  captured  by  the  cross  plane  model  described  here.  The 
model  helps  to  elucidate  the  influence  of  wall  oscillation  on  the  interactions 
in  the  wall  region.  It  illustrates  that  when  a  periodic  spanwise  cross  flow 
associated  with  the  oscillatory  motion  of  the  surface,  is  present,  the  coherent 
structures  are  deformed  in  a  way  which  promotes  their  interaction  with  the 
rigid  surface  beneath,  leading  to  their  rapid  annihilation.  The  low  speed 


streaks  are  significantly  distorted  due  to  mixing  of  momentum  associated 
with  the  low-speed  ejection  regions  and  that  associated  with  the  high-speed 
‘sweep’  regions,  resulting  in  a  reduction  in  the  rate  of  momentum  convection 
normal  to  the  wall.  This  in  turn  has  a  direct  impact  on  the  Reynolds  stress.  The 
severity  of  the  impact  of  the  oscillation  depends  on  the  phase  of  the 
oscillation  relative  to  the  time  when  the  vortices  appear  in  the  vicinity  of  the 
wall.  Besides  the  effect  on  the  Reynolds  stress,  the  wall  oscillations  also  have 
important  attenuating  effects  on  the  rate  of  production  of  kinetic  energy.  It  is 
likely  that  these  effects,  in  turn,  have  important  implications  for  the 
mechanism,  not  accounted  for  in  the  model,  which  gives  rise  to  the  coherent 
structures  and  consequently  on  the  number  density  of  the  structures  in  the 
vicinity  of  the  wall. 

ACKNOWLEDGEMENT 

This  work  was  partially  supported  by  the  Office  of  Naval  Research 
under  grant  N000 14-94-1-0453  and  by  the  National  Science  Foundation 
under  grant  BCS-92 11  847. 

REFERENCES 

1 .  J.  Kim,  R  Moin,  and  R.  Moser,  J.  Fluid Mech .,  177,  133,  1987. 

2.  P.  R.  Spalart,  J.  Fluid  Mech.,  187,  61, 1988. 

3.  J.  Jimenez,  and  P.  Moin,  J.  Fluid  Mech.,  225, 221, 1991. 

4.  S.  K.  Robinson,  Ann .  Rev.  Fluid  Mech.,  23,  601,  1991. 

5.  P.  Orlandi,  and  J.  Jimenez,  Phys.  Fluids .  6,  634—641,  1994. 

6.  F.  Laadhari,  L.  Skandaji,  and  R.  Morel.  Phys.  Fluids.  6,  3218-3220. 
(1994). 

7.  W.  Jung,  N.  Mangiavacchi,  and  R.  Akhavan,  Phys.  Fluids ,  A4,  1605, 1992. 

8.  P.  Moin,  T.  Shih,  D.  Driver,  and  N.  Mansour,  Phys .  Fluids  A2,  1846,  1 990. 

9.  H.  Schlichting,  Boundary-Layer  Theory ,  6th  ed.  McGraw-Hill,  NY,  1968. 

10.  J.  T.  Stuart,  In  Laminar  Boundary  Layers ,  Ed.  L  Rosenhead.  Dover. 
1963. 


238 


Figure  2.  Evolution  of  a  pair  of  streamwise  vortex  sheets  of  equal  but  opposite  strength,  at  (a)  t+  =  0,  and  at  t+  =  7.5  in  (b)  the  absence  of 
oscillation,  and  (c)  the  presence  of  spanwise  wall  oscillations  with  Wo  =  12,  T  =  100.  The  figures  show  vorticity  contours.  T=  300, 
a  =0.15.  A(jdx  =  0.9  in  (a)  and  0.3  in  (b)  and  (c). 


Figure  3.  Streamwise  velocity  contours  corresponding  to  the  cases  shown  in  figure  2.  The  influence  of  spanwise  wall  oscillation  on  the 
streamwise  velocity  streaks  is  apparent  in  the  figure.  3(a)  in  the  absence  of  and  3(b)  in  the  presence  of  wall  oscillation^ ^  _  q  75 


Figure  4.  Ratio  of  averaged  (with  respect  to  z, 
t  and  x)  skin  friction,  Cf  and  Cfo  as  a  function 
of  oscillation  period  T. 


Figure  5.  Comparison  of  the  Reynolds  stress  in 

the  absence  of  oscillation  ( - )  with  the 

corresponding  stress,  averaged  over  eight 
equally  spaced  phases  x,  in  the  oscillatory  case 
( — ). 


Figure  6.  Comparison  of  the  rate  of  production 
of  kinetic  energy  in  the  absence  of  oscillation 

( - )  with  the  corresponding  rate,  averaged 

over  eight  equally  spaced  phases  x,  in  the 
oscillatory  case  ( - ) . 


239 


LOCAL  OSCILLATING  BLOWING  IN  A  TURBULENT  BOUNDARY  LAYER 


Sedat  Tardu 

Laboratoire  des  Ecoulements  G6ophysiques  et  Industrie^ 
Grenoble  -  France  ;  Sedat.Tardu@hmg.inpg.fr 


Abstract-  The  effect  of  time  periodical  blowing  through  a  slot  on  the  spatio-temporal  characteristics  of  the  wall  shear  stress  and  the 
turbulence  in  the  buffer  layer  is  experimentally  investigated.  It  is  shown  that  the  local  imposed  unsteadiness  affects  considerably  the  fine 
structure  of  the  near  wall  turbulence.  The  drag  is  reduced  by  steady  blowing,  essentially  because  of  a  different  redistribution  of  the 
quadrant  events.  The  unsteady  blowing  affects  the  vorticity  generation  mechanism,  without  appreciably  interacting  with  this  redistribution. 
At  high  imposed  frequency  and  just  downstream  of  the  slit  the  near  wall  flow  is  relaminarized  during  the  acceleration  phase  while  it  is 
unstable  during  deceleration.  Spanwise  vorticity  of  the  same  sign  as  the  mean  flow  is  accumulated  and  reinforced  during  this  phase.  This 
patch  of  vorticity  rolls  up  into  a  coherent  structure  which  convects  downstream  and  increases  the  drag  in  a  predictable  way.  These  results 
may  have  important  applications  in  the  controle  of  separation. 


I .  INTRODUCTION 

Aim  of  the  research 

Intensive  research  carried  on  the  passive  means  of  managing  the  near 
wall  turbulence  with  the  main  goal  of  reducing  the  skin-friction  has  given 
somewhat  deceptive  results.  Indeed,  surface  mounted  longitudinal 
grooves,  although  being  most  successful,  cannot  achieve  skin-friction 
reduction  larger  than  10%  and  their  capacity  of  reducing  drag  is 
constrained  to  within  a  small  range  of  the  riblets  spacing  and  heights  being 
therefore  quite  sensitive  to  the  changements  of  external  flow  conditions  or 
the  Reynolds  number.  The  large  eddy  break  up  devices,  on  the  other 
hand,  do  not  result  in  a  net  reduction  of  the  skin  friction  according  to  a 
consensus  largely  established  by  now. 

The  active  and  passive  management  of  the  turbulent  wall  shear  stress  is 
ultimately  related  to  the  interaction  of  the  coherent  structures  present  in 
the  inner  layer  with  the  near  wall  flow.  The  ad-hoc  out  of  phase  active 
control  scheme  reported  by  Choi  and  al.  (1994)  may  easily  be  replaced  in 
this  context.  The  wall  shear  stress  x  is  instantaneously  enhanced  in  the 


regions  wherein  the  spanwise  vorticity  G3z>o  is  stretched  due  to  the 
stagnation  flow  induced  by  the  quasi-streamwise  vortices  -  QSV 
(Tardu,  1995,  p.  378).  A  simple  analysis  conducted  by  Orlandi  and 
Jimenez  (1994)  establishes  the  close  relationship  between  x  and  the 


«-  i  u+  f  2  v+) 

characteristics  of  the  QSW  through  T+ «*  V  Rvqs  — - — — .  In  this 

yv 


relationship,  Rvqs  and  yj  are  respectively  the  mean  Reynolds  number  and 
the  distance  to  the  wall  of  the  QS  vortical  structures.  According  to  this 
relationship,  the  drag  reduction  may  be  achieved  either  by  decreasing  the 
intensity  of  the  QSV's  or  by  pushing  them  away  from  the  wall.  The 
objective  of  this  study  is  to  explore  the  capacity  of  time  and  space 
periodical  suction  and  blowing  to  increase  yj  and  achieve  drag  reduction. 
The  reasons  of  using  such  a  scheme  are  summarized  hereafter. 

Control  strategy 

The  model  suggested  here  is  essentially  based  on  the  results  reported 
recently  by  Acton  and  Dhanak  (1993)  although  it  differs  basicaly  in  the 
methodology.  We  consider  a  distribution  of  sources  and  sinks  which  are 
uniformly  periodical  in  space  and  whose  intensities  Cn(t)  (related  to  the 
suction  and  blowing  velocities  )  are  sinusoidal  in  time  (Fig.  1).  One  has 


therefore  N  sources  and  sinks  by  wave  length  A  with  Cn(t)  =  Cn+N  (t). 
We  deal  with  the  periodicity  in  the  streamwise  direction  at  the  present 
moment  ,  but  the  same  scheme  will  be  applied  to  the  periodical  suction¬ 
blowing  in  the  spanwise  direction  too  (Fig.  2)  .  The  temporal  variation  is 

choosen  as  Cn(t)  =  (- 1  )n  Co  ^  1-  cos  |  27tfe  t  -  2%  ~  +  <X>n  jj.  In  this 
expression  fe  stands  for  the  ejection  frequency  in  the  inner  layer, 


Co  and  <J>n  are  respectively  the  amplitude  and  phase  of  the  suction  and 
blowing.  This  distribution  represents  an  injection  i  followed  by  an 


aspiration  i+1  with  a  phase  shift  of  +  Oj+i-Oi  .  An  inviscid 

N 

computation  of  the  effect  of  this  management  on  the  distance  of  a  "street" 
of  vortical  structures  shows  that  the  former  varies  in  time  with: 


n  =  N-l  1  ~ 

K  yv  =  In  a  -  —  K2  Co  t  Y  (-if  cos<Dn  +F(t/T) 

2  n  =  0  - 

where  F(t/T)  is  a  periodical  function  with  periodicity  T=l/fe.  This 
relationship  is  similar  to  that  given  by  Acton  et  Dhanak  (1993,  p.  245).  It  is 
clearly  seen  that  if  the  phases  are  manipulated  according  to 


n  =N-1 

£  {-lY  cos*I>n  <0,  the  distance  yv  of  the  vortical  structures  will 

n  =  0 

presumably  increased  once  these  structures  interact  intermittently  with  the 
pulsed  surface.  The  expected  consequence  of  this  intervention  is  a 
reduction  of  drag  according  to  the  discussion  made  in  the  first  section.  It  is 
without  saying  that  the  reaction  of  the  near  wall  turbulence  to  this 


intervention  may  not  be  predicted  by  such  a  simple  analysis  and  a  detailed 
study  is  undoubtly  necessary. 

The  present  steady  deals  with  the  effect  of  a  local  unsteady  forcing  on 
the  wall  turbulence.  The  main  aim  is  to  investigate  the  time-space 
relaxation  of  the  near  wall  flow  manipulated  by  a  time  varying  blowing 
through  a  localized  spanwise  slit.  The  control  strategy  deals  clearly  with 
first  forcing  the  near  wall  turbulence,  determining  subsequently  its 
frequency  response  and  introducing  finaly  local  suboptimal  control  with  a 
feasible  distribution  of  MEMS  depending  upon  the  reaction  of  the  near 
wall  flow. 


II.  DEFINITIONS,  EXPERIMENTAL  SET-UP  and  DATA 
REDUCTION 

An  experimental  model  has  been  developed  in  the  low-speed  wind 
tunnel  of  our  laboratory  (Fig.2a) .  The  blowing  and  suction  at  the  wall  are 
done  through  spanwise  slots  of  dimensions  0.6*100  mm  which  correspond 
to  10*1667  in  wall  units.  There  are  one  blowing  and  one  suction  slot  by 

wavelength  A  =  45  mm.  (A  =  750  )  and  the  pulsed  surface  recovers  a 


total  length  of  3 A  i.e  2250  in  wall  units  (Fig.  2,see  Tardu,  1997  for  further 
details)  .  Hereafter  (+)  denotes  values  nondimensionalized  with  the  inner 


variables,  i.e  the  shear  velocity  Ux^ 


and  the  kinematic  viscosity  v  . 


A  special  pulsating  device  has  been  designed  for  the  present  purpose. 
Quite  satisfactory  sinusoidal  waveforms  of  the  suction/blowing  wall 
normal  velocities  have  been  obtained  this  way  for  the  amplitude  of  the 


imposed  velocities  up  to  Av-y+=:0  =  A=  1.5  m/s  (  A  =6)  and  the 

imposed  frequency  10Hz  <  f  <  50  Hz  (  2.5*  1 0~3<fh<l 2.5*1 0'3  )  (see 
Fig.  2b). 

The  wall  shear  stress  measurements  have  been  performed  by  means  of 
a  Cousteix-Houdeville  wall  hot-wire  gauge  (HWG)  to  avoid  problems 
caused  by  the  conduction  into  the  substrate  .  Nice  results  have  been 
obtained  up  to  the  statistics  of  order  4  and  the  details  may  be  found  in 
Tardu  (1998).  The  length  of  the  sensing  element  is  200  p.m  which 

corresponds  to  a  spanwise  extend  of  A  \  ~  5  at  X=1  m.  from  the 

transition  point  with  U<*>  =  6  m/s  .  The  total  duration  of  each  record  is 

Ttot  **  5000  Too  where  Too  =  -2-  is  the  outer  time  scale.  This  is  enough  to 
Uoo 

ensure  the  convergence  of  the  statistics  up  to  4-th  order  moments 
including  those  of  the  time  derivative  of  the  fluctuating  signals. 

One  should  be  carefull  in  the  interpretation  of  data  in  the  presence  of 
an  organized  motion  as  is  the  case  with  unsteady  blowing  in  this  study.  In 
order  to  extract  the  deterministic  and  deduce  the  undeterministic  part  of 
the  flow  quantities  the  classical  triple  decomposition  is  used.  A  flow 

quantity  q(x,  t;  T)  is  decomposed  into  a  time  mean  q  an  oscillating  q  and 
a  fluctuating  q'  part : 

q(x,t;T)=  q(x)  +  q(x,  t/T)  +  q'(x,t) 
where  T  stands  for  the  period  of  the  oscillating  blowing.  The  ensemble  or 

the  phase  average  is  performed  in  order  to  determine  the  amplitude  Agr 

and  phase  of  the  oscillating  part  q  from  which  the  instantaneous 
fluctuating  part  q'  is  adequately  determined.  The  beginning  of  each  cycle 
was  provided  by  a  pulse  from  a  photoelectric  cell  triggered  by  the 
pulsator,  and  the  trigger  signal  was  also  recorded.  The  modulation 
characteristics  have  been  determined  through  a  least  square  Fourier 
analysis.  The  procedure  is  the  same  as  in  Tardu  et  al.  (1994)  wherein 
further  details  are  provided. 

Blowing  severity 

In  flows  with  uniformly  distributed  continuous  blowing/suction  ( 
transpired  layers  through  porous  surface),  the  parameter  which 


241 


characterizes  the  intervention  at  the  wall  is  given  by 

Bf  =  V°  ^°°  =  vo+  U~  where  Vo  stands  for  the  injection/suction  velocity  at 
Ut2 

the  wall.  This  is  expected,  since  Bf  appears  directly  in  the  momentum 
integral  equation  of  the  transpired  boundary  layer  and  plays  a  role  similar 
to  the  Clauser  pressure-gradient  parameter.  However,  the 
characterization  of  the  severity  of  local  blowing/suction  by  strips  is  not 

straightforward  and  Bf  is  not  suitable  for  describing  the  flow 
characteristics  past  the  local  intervention,  as  clearly  shown  by  Sano  and 
Hirayama  (1985)  and  Sokolov  and  Antonia  (1993)  .  Indeed,  the  local 
suction/blowing  involves  phenomena  related  to  the  relaxation  of  near  wall 

turbulence  downstream  of  the  intervention  zone.  When  Vo+  is  high,  but  the 
injection  is  done  over  large  areas,  the  flow  has  enough  time  to  relaxe  and 
reach  its  equilibrium  state  rapidly.  On  the  other  hand,  in  case  of  large 

injection  velocities  Vo+  over  short  distances,  the  near  wall  turbulence  can 
hardly  maintain  its  equilibrium  state  and  its  structure  is  expected  to  be 
strongly  affected  .  The  ratio  of  the  injection  or  suction  flow  to  the 

incoming  flow  rate,  i.e  0  =  vo  Lx  /  U  dy  is  therefore  introduced  and 

Jo 

proved  to  be  adequate  to  measure  the  blowing/suction  severity. 

We  proceeded  with  particularly  small  slot  widths  compared  with 
previous  studies  quoted  above.  For  instance,  the  experiments  reported  by 
Sano  and  Hirayama  have  been  conducted  with  two  different 
configurations  wherein  Lx  was  respectively  50  and  25  mm  corresponding 

to  «  2000  and  Lx  ~  1000  under  their  experimental  conditions.  Recall 

that  the  slit  width  is  only  L  *  =  7  here.  As  a  consequence,  the  severity 
parameter  is  low.  The  injection  velocity  in  steady  blowing  experiments 

investigated  here  is  Vo=  lm/s  and  the  severity  parameter  is  only  0  = 
0.006  .  The  shape  parameter  just  downstream  of  the  slit  at  x/5=0.1  is 
H=1.4  under  these  circumstances.  In  unsteady  blowing  experiments,  the 
injection  velocity  <vq>  changes  in  a  cyclic  manner  between  0  and  2  m/s. 
The  maximum  value  of  the  severity  parameter  in  the  oscillation  cycle  is 
therefore  0  =  0.012  .  The  shape  parameter  measured  at  the  same  station 

increased  to  H=  1.7  at  Vo  =  2  m/s  but  still  remained  below  the  critical 
value  corresponding  to  flows  prone  to  separate. 

III.  RESULTS 

One  of  the  main  aims  of  this  study  is  to  determine  whether  a  periodic 

time-varying  blowing  of  the  form  vo  =  A  (  1-005271^  )  affects  the 
near  wall  turbulence  characteristics  when  compared  with  a  steady 

_  /s 

injection  by  slot  with  the  same  time-mean  blowing  velocity  VQ~  =  vo  =  A 

resulting  in  the  same  time  mean  severity  parameter  0  =  <  ©  >  .  In  other 
words,  the  question  is  whether  the  near  wall  flow  interacts  with  the 
imposed  unsteadiness  or  not.  Therefore,  we  will  systematically  compare 
the  mean  flow  characteristics  obtained  with  unsteady  and  steady  blowing 
hereafter.  Before  discussing  the  results,  the  notation  needs  to  be  clarified. 

Here,  an  asterisk  (  *  )  refers  to  quantities  measured  in  the  manipulated 

—  * 

T  s 

boundary  layer,  while  the  subscript  S  indicates  steady  blowing.  Thus  is 

T 

the  ratio  of  the  time-mean  wall  shear  stress  in  the  presence  of  local  steady 
blowing  to  the  wall  shear  stress  of  standard  boundary  layer  (SBL),  and 
—  + 

is  the  ratio  of  the  frequency  of  the  energetic  events,  etc.  In  a  similar 

fe  -* 
manner,  the  subindex  U  corresponds  to  unsteady  blowing,  i.e  T  u  and 

T'x'  u  represent  respectively  the  wall  shear  stress  and  the  wall  shear 
stress  intensity  in  the  boundary  layer  manipulated  by  time  periodical  local 
injection. 

Main  mechanism  of  local  suction/blowing.  Equivalence  between  steady- 
unsteady  blowing 

The  management  of  the  near  wall  turbulence  by  suction/blowing  is  closely 
related  to  the  flux  of  vorticity  induced  locally  at  the  wall.  Consider  indeed 
the  phase  averaged  streamwise  equation  of  momentum  over  the  slit:: 

2 

3o<u>  i  d<po>  3o<u> 

<v0> - =  =  - - +v - — 

dy  P  dx  dy 

since  <uV>  y^  near  the  wall.  The  subindex  ”0"  in  this  equation  (  and 
hereafter  )  refers  to  quantities  computed  at  the  wall.  Noting  that  the  phase 
averaged  spanwise  vorticity  at  the  wall  is 


9o<v>  do<u>  do<u>  ,  do<v> 

<(0zo>  = - ^ - because  - - —  can  be  neglected 

dx  dy  dy  dx 

except  at  the  ends  of  the  slit  one  has: 

3o<COz> 

+  V - 

P  dx  dy 

which  expresses  the  simple  fact  that  there  is  equilibrium  between  the 
advection  of  vorticity  through  the  slit  and  flux  of  vorticity  at  the  wall.  In 
the  case  of  suction  there  is  real  physical  removal  of  spanwise  vorticity 
from  the  wall  and  the  flux  of  vorticity  is  positive  (  since 

<Vo><0  and  <G)zo>  <0  )  as  in  a  boundary  layer  with  favorable  pressure 
gradient.  The  withdrawn  vorticity  is  rapidly  replaced  at  the  wall  to  keep 
the  non  slip  condition  at  force  so  that  there  is  a  rapid  generation  of 


i  d<po> 
<v0>  <COzo>  -  x — - — 


vorticity  8<COzo>  of  the  same  sign  as  in  the  incoming  flow.  As  a 
consequence  the  flow  accelerates  by  an  amount  which  is  approximately 


S<u>  ^  5<cozo>  y  >0 
8x  Sx 

stress  by  -  ^<g>zQ—  >0. 
Sx 


resulting  in  a  local  increase  of  the  wall  shear 
Although  it  is  well  known  that  suction  is 


qualitatively  similar  to  flows  with 


<0  the  former  is  fundamentally 
dx 


different  in  turbulent  boundary  layers  because  it  involves  also  the 
removal  of  both  streamwise  and  wall  normal  vorticity  .  In  the  case  of 
blowing  there  is  no  removal  or  addition  of  vorticity  but  one  still  may  argue 
that  there  is  a  flux  of  vorticity  which  is  now  negative  as  in  adverse 
pressure  gradient  case.  The  spanwise  vorticity,  together  with  vortical 
intensive  energetic  structures  are  displaced  and  pushed  away  from  the 


wall  by  say  8<yv>  <*>  <vo>  8<tc>  where  8<tc>  is  the  effective 
convection  time  of  the  structures  as  they  are  advected  over  the  slit.  This 


induces  a  deficit  of  8<uw>  00  <COzo>8<y  v>  <0  in  the  non  slip  velocity  at 
the  wall.  This  is  subsequently  corrected  by  the  formation  of  a  thin  vortex 
sheet  in  front  of  the  wall  (and  of  its  image)  with  vorticity  of  opposite  sign 
to  that  existing  in  the  flow.  The  strength  of  this  sheet  may  be  estimated  as 


^<^0>  oo  -8<uw>  ~  -<cozo>8<yv>  which  subsequently  dilutes  through 
8x 

diffusion.  Consequently  the  flow  decelerates  near  the  wall  i.e  ^<u>  <0 

Sx 

and  the  wall  shear  stress  decreases.  This  phenomena  involves  directly 
upstream  of  the  local  blowing/suction.  The  zone  downstream  of  the  slit  is 
concerned  with  the  relaxation  of  the  turbulence  structure  modified  by  the 


discontinuous  intervention. Note  that  the  arguments  presented  here  are  not 
new  :  they  are  based  solely  on  the  spanwise  vorticity  and  does  not  include 
the  effect  on  the  quasi-streamwise  energy  producing  eddies.  The  analysis 
is  therefore  not  complete  yet  it  may  provide  a  first  schematic  model  to  go 
insight  more  complexe  phenomena. 

We  will  now  discuss  the  equivalence  between  the  unsteady  and  steady 
blowing  with  the  same  time  mean  blowing  severity  parameter  in  terms  of 
boundary  conditions  i.e  flux  of  vorticity.  First  note  that  the  pressure 


gradient  term 


d<po> 

dx 


is  retained  in  the  streamwise  momentum  equation. 


In  Falkner-Skan  type  flows  the  boundary  layer  approximation  is  often 
used  and  a  specific  distribution  of  suction/blowing  velocity  is  required  to 
obtain  similarity  solutions.  In  other  sample  computations  dealing  with 
steady  discontinuous  viscous  suction  the  pressure  gradient  is  ignored  at  a 
first  glance  (  Sherman,  1990  p.  372).  The  importance  of  this  term  needs 
detailed  full  computation  but  it  is  logical  to  neglect  it  in  an  approximate 
qualitative  analysis.  Furthermore,  in  the  case  of  unsteady  blowing  there  is 
an  additional  complexity  because  the  wall  normal  velocity  induces  an 
oscillating  pressure  gradient  without  any  flux  of  vorticity  according  to 


d<yo>  __  i  d<po> 


.  This  fact  may  question  the  boundary  layer 


dt  P  dy 

approximation  near  the  slit.  However,  the  main  mechanism  is  still  the  flux 
of  vorticity  under  the  present  working  conditions.  With  a  sinusoidal 

blowing  velocity  vo  =  A  (  l-cosco+t+ )  expressed  in  wall  units  ,  it  is  clea 

d<pft>  .  do<CC&> 

r  that  — - - A  CO  while  the  flux  of  vorticity  is - - - A  .  The 

dy+  3y+ 

maximum  imposed  frequency  in  this  study  is  C0+  =0. 1  which  shows  that 


242 


the  wall  normal  oscillating  pressure  gradient  is  an  order  of  magnitude 
smaller. 

According  to  these  remarks  the  time  mean  streamwise  momentum 
equation  reduces  to: 

_  —  I"  ~  ~  1  1  Spo  9o<o)zo> 

VoCOzO  +  L  Vo(OzoJ=  -  +  v - 

P  dx  dy 

when  the  blowing  is  unsteady.  The  time  mean  severity  parameter  is  fixed 
constant  in  this  study  between  steady  and  periodical  blowing.  That  does 
not  insure  the  same  flux  of  vorticity  for  all  that  mainly  because  of  the 

"streaming"  quantity  Vo  CGzo  in  the  brackets  of  the  preceeding  equation 
and  since  the  mean  streamwise  vorticity  can  be  different  under  steady 
and  unsteady  blowing  conditions  immediately  on  the  injection  slot.  It  turns 
out  that,  in  the  high  frequency  regime  CD+  =0.1  detailed  in  this  paper,  the 
time  mean  wall  shear  stress  is  not  affected  near  the  slit  (until  x+=40 

downstream)  and  that  the  modulation  COzo  is  approximately  in  quadrature 

with  the  injection  velocity  Vo  .  This  behaviour  may  be  explained  by  the 
fact  that  the  diffusing  vorticity  is  in  quadrature  with  the  flux  of  vorticity  in 
the  high  frequency  regime  to  the  first  order  (as  in  Stokes  flow  over  an 
oscillating  flat  plate).  This  may  be  rigourously  shown  through  a  method 
given  by  Schlichting  (1979,  p.  428)  but  the  details  will  be  omitted  here.  As 


(sweeps),  or  equivalently  the  inhibition  of  the  quadrant  2  events  with  x'<0 
(ejections)  .  We  therefore  suspect  that  the  steady  blowing  decreases  the 
drag  by  modifying  the  inner  structure  of  the  flow  through  the  distribution 
of  the  quadrant  contributions.  This  is  only  speculative  at  the  present 
moment  and  in  order  to  give  a  clear  answer  to  this  question  more  detailed 
measurements  have  to  be  performed.  The  imposed  unsteadiness 
presumably  does  not  affect  the  quadrant  distribution,  although 
measurements  of  conditional  Reynolds  stresses  may  provide  a  definitive 
answer  to  this  speculation.  It  will  be  shown  in  the  next  section  that  the 
unsteadiness  interacts  strongly  with  the  vorticity  generation  mechanism 
near  the  wall. 

The  flatness  of  the  fluctuating  wall  shear  stress  reacts  in  a  manner 

j|{  3 

similar  to  Sf  (Fig.  4b).  Ff  s  increases  significantly  near  x=0  while  the 
unsteady  blowing  does  not  affect  appreciably  the  spotty  character  of  the 
fluctuating  wall  shear  stress. 

The  skewness  Su'  and  flatness  Fu'  measured  at  y+*  =  10  and  shown 

*  * 

by  squares  in  Fig.  4  behave  in  the  same  manner  as  Sf  and  Ff  .  The 

* 

comments  are  therefore  similar  .  The  increase  of  Su‘ s  may  be 
interpreted  as  the  enhancement  of  the  convective  diffusion  by  turbulence, 


3  i  3  /  i  i 

i.e.  the  term - if  —  =--* - \  u  +uV  +uV 

3x  2  2  dx 


of  the 


a  consequence,  Vo  COzo  is  6  times  smaller  than  Vo  COzo  and  the  "streaming" 
appearing  in  the  boundary  conditions  may  be  neglected.  The  high 
frequency  case  therefore  respects  both  the  equivalence  between  time 
mean  injection  velocities  and  time  mean  vorticity  fluxes. 


Wall  shear  stress  characteristics 


if 


TT  -  and  illustrates  the 


Fig.  3  shows  the  profiles  of  the  ratios  and  _ 

T  Ur 

effect  of  steady  and  unsteady  manipulations  on  the  wall  shear  stress  and 
wall  shear  stress  intensity.  The  open  symbols  correspond  to  time-periodic 
blowing.  It  is  seen  that  both  steady  and  unsteady  local  blowing  decreases 


the  drag  appreciably  .  This  decrease  is  persistent  up  to  X+  —  500 
downstream  of  the  slot.  The  average  drag  reduction  is  approximately 
20%  .  The  imposed  unsteadiness  is  slightly  less  efficient,  but  the 


—  +  —  * 

differences  between  Xu  and  X  s  are  always  less  than  9%. 

The  first  significant  difference  between  time-periodic  and  steady  local 
injection  is  in  the  reaction  of  the  wall  shear  stress  intensity  (Fig.  3b).  The 
wall  shear  stress  intensity  is  significantly  less  reduced  by  unsteady 
blowing,  compared  with  steady  blowing.  A  similar  reaction  has  been 
observed  in  the  measurements  of  the  streamwise  turbulence  intensity 


performed  at  y+=10  and  X+  =  30  .  These  measurements  will  be 
discussed  in  the  next  section. 

The  decrease  of  the  wall  shear  stress  intensity  by  steady  blowing 
appears  surprising  at  a  first  glance,  since  one  expects  an  increase  of  the 
turbulent  intensities  in  the  presence  of  local  injection  .  However,  the 
effect  of  blowing  on  the  turbulent  intensities  is  most  significant  beyond  the 
viscous  layer  (y+  >  50  )  according  to  Sano  and  Hirayama.  These  authors 

have  shown  that  the  profiles  of  u+  s  and  ^ u--- ^  collapse  fairly  well 

UooS 


with  those  of  SBL  when  plotted  against  y+  *  =  y  —  near  the  wall  (their 
fig.  5  and  9)  .  It  is  easy  to  show,  that  under  these  circumstances 


u-uj/u_s=ik.  Since, 
Vu'u'  /u  Ut 

V  T1^ '  O 

relationship  results  in  J - - 


Jiu_  as  y+  — ^  o  the  last 

u 


The  measurements  reported 


here  are  in  good  quantitative  agreement  with  this  estimation  when  the 
blowing  is  unsteady,  but  this  correspondance  is  only  qualitative  in  the  case 
of  steady  injection.  It  has  to  be  noted  that  detailed  measurements  very 
close  to  the  wall  are  needed  in  order  to  confirm  the  analysis  above,  and 
the  closest  point  to  the  wall  in  the  data  of  Sano  and  Hirayama  is  only 


y+=s  5  . 

The  effect  of  the  unsteadiness  is  more  pronounced  with  respect  to  the 
fine  structure  of  X\  Fig.  4a  shows  that  the  skewness  of  the  wall  shear 
stress  is  increased  by  a  factor  1.8  near  the  slot  when  the  blowing  is 
steady.  In  contrast,  when  the  injection  is  unsteady  the  skewness  of  x'  is 
only  slightly  affected.  The  mechanism  of  drag  reduction  is  therefore 

certainly  different  in  both  manipulations.  The  increase  of  Sf  s  may  be 
interpreted  either  as  the  strengthening  of  the  quadrant  4  events  with  x’>0 


turbulence  energy,  q2  ,  equation.  This  term  is  an  order  of  magnitude 

3  q2 

smaller  in  the  canonical  boundary  layer  compared  with - v  —  ,  but 

dy  ^ 

it  is  certainly  important  near  the  slot  in  the  presence  of  injection.  The 

Q2 

integration  of  the  equation  —  —  between  two  planes  x/5  ~  0  at  the 
Dt  2 

injection  point,  and  at  x/5  ~  2  downstream  where  the  flow  reaches  its 
equilibrium  state,  shows  that  there  is  a  net  contribution  to  the  flux  of 


energy  of  the  order  of 


(H 


=i„'2 


3/2 


Su-  due  to  the  transfer 

r  x/s  =0  2 

from  regions  of  large  intensity  to  regions  of  smaller  intensity  as  imposed 
by  the  local  injection  at  the  wall.  The  results  presented  here  show  that  in 
the  case  of  steady  injection  there  is  an  increase  of  the  convective  flux  and 
this  is  in  agreement  with  Sano  and  Hirayama  (1983)  who  reported  that  the 
(steady)  blowing  increases  the  values  of  each  term  in  the  turbulent  energy 
equation  .  There  are  two  additional  terms  in  the  equation  governing  the 

mean  turbulent  kinetic  energy  q\j*  for  unsteady  blowing.  These  are 
respectively  in  the  advective  and  the  production  terms  and  they  result 
from  the  interactions  between  deterministic  parts  of  the  corresponding 
components  .  The  turbulent  diffusion  term  is  however  of  the  same  form  as 

in  —  q%*  /  2  .  Since  the  skewness  factors  are  only  slightly  affected  by 
Dt 

unsteady  blowing,  one  may  conclude  that  the  imposed  unsteadiness 
inhibits  considerably  the  streamwise  convective  flux  of  energy.  The 
effect  of  the  imposed  unsteadiness  is  strongly  frequency  dependent  :  at 
larger  imposed  frequencies  (ff>  0.015)  ,  the  flow  is  "relaminarized 
"during  half  of  the  oscillation  cycle  near  the  slot  and  the  flatness  and  the 
skewness  increase  during  these  periods  showing  the  presence  of  highly 
intermittent  hardly  active  sweep  type  events.  As  a  consequence  the  time 
mean  of  these  quantities  increase  also  near  the  wall.  These  points  will 
further  be  discussed  in  the  last  part  of  this  section. 


Modulation  characteristics  _ 

Fig.  5a  shows  the  phase  average  of  <u'u'>/u'u'  measured  at  y+*=10  and 
x+*=  44,  for  ^=0.0 17  .  It  is  found  that  the  streamwise  velocity  is 
modulated  but  that  sq  does  not  exceed  0.20  .  The  response  of  <u>  is 
nonlinear  and  harmonics  larger  than  one  are  of  importance  in  the  high 
imposed  frequency  regime.  _ 

The  first  streaking  feature  of  <u,u'>/u,u’  shown  in  Fig.  5a  is  the 
occurrence  of  unexpectably  large  modulations  of  the  turbulence 

intensities  which  lead  to  relative  amplitudes  as  high  as  *  0.8.  It  is 
quite  surprising  to  note  such  severe  effects  on  the  turbulence  when  one 
recalls  that  the  unsteady  <v>  forcing  is  only  local.  These  large 
modulations  point  at  the  existence  of  a  relaminarization  phase  during  the 
cyclic  oscillations. 

The  strong  modification  of  the  wall  turbulence  structure  is  better 
captured  in  Fig.  5b  which  shows  the  phase  average  of  the  skewness  of 

du’/dt  and  of  the  ejection  frequency  <fj  >  identified  by  modified  u'-level 
technique  at  ^=0.0 17  by  using  the  phase  averaged  thresholds.  Recall  that 

Sdu’/dt  is  related  to  the  vorticity  stretching  and  the  non  linearity  in  the 
inner  layer.  Fig.  5b  shows  that  both  the  vorticity  generation  and  production 


243 


mechanisms  are  altered  at  high  blowing  frequency  during  almost  the  half 
of  the  oscillation  cycle. 

The  effect  of  the  imposed  unsteadiness  on  the  vorticity  stretching 
mechanism  was  further  investigated  by  examining  the  behaviour  of 

Sdu'/dtu  at  y+=10  versus  the  imposed  frequency  (Fig.  6).  It  is  found  that 
the  steady  blowing  does  not  affect  the  skewness  of  du’/dt.  The  changes  of 

Sdu'/dt  u  indicate  therefore  a  direct  effect  of  the  imposed  unsteadiness. 
Fig.  6  shows  that  in  the  low  imposed  frequency  regime  there  is  no  effect 

of  the  oscillations  on  Sdu’/dt  u  and  Sdu'/dt  u  which  is  close  to  the  value  in 

SBL.  The  skewness  Sdu'/dt  u  decreases  steadily  once  f*  >  0.005  and  this 
constitutes  one  of  the  most  interesting  results  inferred  from  this  study.  The 
vorticity  stretching  mechanism  and  therefore  the  nonlinearity  are 
weakened  by  oscillating  blowing  by  a  factor  of  3  in  the  high  imposed 
frequency  regime  (Fig.  6).  This  effect  is  saturated  once  f*  >  0.007.  Note 
also  that  there  does  appear  to  be  a  slight  kink  in  the  data  near 

f  -f^  =0.01. 

Detailed  analysis  of  the  wall  turbulence  near  the  injection  slot  in  the 
high  frequency  regime 

It  has  been  clearly  conjectured  that  the  most  interesting  features  of 
unsteady  local  blowing  are  perceptible  in  the  high  frequency  regime. 
Detailed  analysis  in  the  region  x+50  downstream  of  the  slit  will  now  be 
given  at  the  highest  frequency  that  we  could  reach  in  this  study  i.  e 
f^O.017. 

Time  mean  flow 

Fig.  7  shows  the  time  mean  streamwise  velocity  profiles  in  the  standard 
boundary  layer  and  in  the  presence  of  steady  or  unsteady  blowing  at 
x+=31  downstream  of  the  slit.  The  velocity  u  and  the  wall  normal 
coordinate  y  are  scaled  with  the  local  inner  variables  i.e  by  ut  in  the  SBL 

and  uz  s  or  \jx  u  in  the  manipulated  boundary  layer.  The  first  streaking 
feature  of  the  results  summarized  in  Fig.  7  is  the  insensitivity  of  the  time 
mean  streamwise  velocity  profiles  to  the  imposed  unsteadiness.  It  is 

indeed  seen  that  both  u^+  and  u£i+  =  <u>+  corresponding  respectively  to 
steady  and  unsteady  blowing  collapse  fairly  well  in  the  entire  boundary 
layer.  It  is  recalled  that  the  wall  shear  stress  is  also  unaffected  at  the 

mean  by  oscillating  blowing  at  this  particular  station  and  that  =  0.67 

T 

—  * 

while  5l=0.67. 

One  distinguishes  easily  in  Fig.  7  between  the  viscous  sublayer,  the  buffer 
layer  and  the  log-layer  in  the  MBL  in  the  same  way  as  in  the  canonical 
boundary  layer.  The  viscous  sublayer  is  considerably  thickened  in  the 

presence  of  blowing  and  one  has  Us+  ~  Uu+  =  y+  at  y+  <12.  Note  also 
that  the  velocity  profiles  collapse  well  with  u+  =  2.5  lny+  +  10.5  for 
y+  >  40  pointing  at  the  existence  of  a  constant  shear  layer  with  time  mean 
equilibrium.  The  buffer  layer,  on  the  other  hand,  is  somewhat  thinned  and 

extends  from  only  y+  =  1 2  to  y+  =  40. 

The  upward  shift  observed  in  the  log  region  in  the  manipulated 
boundary  layer  is  in  agreement  with  the  direct  numerical  simulations 
conducted  by  Choi  and  all.  (1997)  who  investigated  the  effects  of  blowing 
and  suction  from  a  spanwise  slot.  This  is  a  common  feature  of  drag 
reduced  flows  and  we  will  now  show  that  it  may  be  quantitatively 
explained  by  Rotta's  theory  (1950,  see  also  Hinze,  1975;  p.  619).  Rotta 
used  the  Prandtl  mixing-length  hypothesis  and  modelled  the  shear  stress  as 


layer  encountered  in  flows  with  drag  reduction  is  a  direct  consequence  of 
the  thickening  of  the  viscous  sublayer  and  vice  versa. 

The  turbulence  intensity  u' +  =  V  u'u'  /  ux  distributions  expressed  in  local 

inner  variables  (i.e,  u's  +  =  V  u'u1  s  /  uxs  >  u’u+  =  V  u'u’u  /  uxs  )  and 
obtained  at  x+=40  are  shown  in  Fig.  u'.  The  turbulence  intensity  in  the 
manipulated  buffer  layer  exceeds  the  standard  boundary  layer  profile  by 
roughly  15%  .  There  are  noticeable  qualitative  and  quantitative 
differences  in  the  reaction  of  u'  to  steady  and  unsteady  blowing.  It  is  seen 

in  Fig.  u'  that,  in  the  presence  of  unsteady  blowing  u‘u+  reaches  its 
maximum  at  y+=10  somewhat  earlier  than  u's+.  It  keeps  its  maximum 
furthermore  in  the  whole  buffer  layer  10<y+<30  .  This  unexpected 
reaction  shows  that  the  imposed  unsteadiness  increases  mixing  in  the  inner 
layer  and  this  peculiarity  may  also  have  some  applications.  A  detailed 
analysis  of  the  fine  structure  (i.e  the  skewness  and  flatness  of  u'  and  the 
skewness  of  du’/dt)  has  revealed  that  the  turbulence  has  an  isotropic 
character  in  the  whole  buffer  layer,  indicating  that  the  imposed 
unsteadiness  acts  as  a  "whitening  filter".  The  steady  blowing,  on  the  other 

hand,  does  not  affect  the  qualitative  behaviour  of  the  Us  +  profiles  which 

presents  a  well  defined  maximum  near  y+  *  13.5  as  in  the  canonical 
boundary  layer. 

Phase  averages 
Wall  shear  stress 

Fig.  9  a  shows  the  cyclic  modulation  of  the  wall  shear  stress  at  x+=20  and 
40  downstream  of  the  slit.  The  phase  average  <t>  is  scaled  with  the  time 

mean  wall  shear  stress  Tsbl  of  the  unmanipulated  standard  boundary 
layer.  The  waveform  of  the  injection  velocity  (to  not  scale)  is  also  shown 
in  this  Fig.  It  is  clearly  seen  that  <x>  is  strongly  modulated  during  the 
oscillation  cycle  and  that  its  response  becomes  strongly  non  linear  with 
increasing  downstream  distance.  The  striking  feature  of  the  reaction  of 
<x>  takes  place  during  the  acceleration  phase  of  the  injection  velocity. 
The  wall  shear  stress  decreases  rapidly  during  this  phase  until  it  reaches 
the  laminar  limit  defined  as  the  value  that  a  laminar  Blasius  boundary 
layer  would  have  at  the  same  Reynolds  number.  The  corresponding 

phase  averages  of  the  wall  shear  stress  intensity  are  shown  in  Fig. 

t’Tsbl 

9b.  The  near  wall  turbulence  activity  is  totally  suppressed  at  x+=20  during 
half  of  the  oscillation  cycle  coinciding  once  more  with  the  acceleration 
phase  of  <Vo>.  At  x+=40  there  is  a  slight  increase  in  <x'x’>  at  t/T=  0.6. 
The  close  inspection  of  the  data  has  shown  that  this  corresponds  to  a 
transitional  spot  resulting  from  the  set-up  of  a  time  space  localized 
instability.  The  velocity  profiles  near  t/T=0.8  (i.e  in  the  middle  of  the 
deceleration  phase)  are  indeed  found  strongly  inflectional  (not  shown 
here)  indicating  that  the  flow  is  first  relaminarized  and  that  it  subsequently 
enters  into  a  retransition  phase. 

Streamwise  velocity  and  streamwise  turbulence  intensity 

The  phase  averages  of  the  streamwise  velocity  <u>  measured  at  x+=40 

are  normalized  with  the  time  mean  velocity  Uu  in  Fig.  10.  They  express 
therefore  the  relative  modulation  of  <u>.  The  modulation  of  <u>  is  large 
in  the  low  buffer  layer  y+<10  (  y+  <8)  and  decreases  very  rapidly  in  the 
low  log  layer.  The  penetration  depth  of  the  perturbation  induced  by 

oscillatory  blowing  is  about  8y+=  20  at  this  particular  x4*  position.  The 
streamwise  turbulence  intensity,  in  return  decreases  rapidly  during  the 
acceleration  phase  in  the  low  buffer  layer  (Fig.  11)  and  the  modulation 
penetrates  further  until  the  low  log  layer. 


du+  — + 
- u  v  = 

ay 


1+] 


au+ 

3yH 


du+ 
dy  + 


=1 


where,  contrarily  to  the  classical  theory,  the  mixing  length  is  taken  as 
lm  =  X  (  y+ '  $v+)  with  8V+  standing  for  the  thickness  of  the  viscous 
sublayer  in  wall  units  and  X  the  von  Karman's  universal  constant.  The 

virtual  origin  of  the  mixing  length  is  therefore  shifted  by  8V  and  the  flow 


within  y+  <  8V+  is  supposed  to  be  completely  viscous.  The  streamwise 
velocity  distribution  resulting  from  this  closure  reads  for  large  values  of 

y4"  u  +  =  A  Iny+  +  B,  with  A=—  and  B  =J-(  ln4%  -l)  +  8v+  (Hinze, 

XX 

1975;  p.  627).  It  is  seen  that  B  is  directly  related  to  the  viscous  sublayer 

thickness.  Taking  X  =  0.4  and  Sv+s  *8v+u=  12  in  the  manipulated 
boundary  layer,  leads  to  B=10.6  which  is  in  close  agreement  with  the 
results  summarized  in  Fig.  7.  Consequently,  and  according  to  the  Rotta's 
model,  one  may  easily  argue  that  the  increase  of  the  constant  B  in  the  log- 


IV.  DISCUSSION 

The  ensemble  of  ingredients  characteristic  of  relaminarization  are 
present  near  the  slot  at  x+<  40  and  during  half  of  the  cycle  namely: 

*The  wall  shear  stress  decreases  considerably  until  reaching  the  value 
that  a  laminar  boundary  layer  would  have  at  the  same  Reynolds  number. 
*Dissipation  dominates  the  near  wall  flow  which  is  stabilized. 

*The  velocity  fluctuations  in  the  inner  layer  are  not  zero  but  their 
contribution  to  the  dynamics  of  the  flow  becomes  inconsequential 
*The  frequency  of  active  Reynolds  stress  producing  events  decrease 
considerably  and  a  thin  region  near  the  wall  extending  to  approximately 
2-3  wall  units  grows  from  the  wall  being  free  of  fluctuating  streamwise 
vorticity.  The  thickness  of  this  zone  reaches  almost  5  wall  units  during 
half  of  the  oscillation  cycle. 

*  The  stretching  of  quasi-streamwise  vorticity  decreases  strongly  as 
indicated  by  even  negative  value  of  the  skewness  of  the  streamwise 
velocity  fluctuations.  This  part  of  the  oscillation  cycle  coincides  also  with 
large  increases  of  the  Taylor  time  scale. 

The  space  time  evolution  of  the  near  wall  flow  at  further  downstream 
locations  is  also  quite  interesting  altough  it  could  not  be  discussed  here  and 


244 


will  be  presented  at  the  symposium.  First  the  velocity  profiles  become 
strongly  inflectional  at  x+=40  and  the  flow  enters  into  retransition  further 
downstream  following  the  scheme  strickly  similar  to  that  reported  by 
Narasimha  and  Sreenivasan  (1973).  This  gives  place  to  the  accumulation 
and  enhencement  of  a  patch  of  spanwise  vorticity  of  the  same  sign  as  the 
mean  vorticity  during  the  decelaration  phase.  This  patch  rolls  up  into  a 
coherent  structure  near  the  wall.  The  birth  of  this  structure  (shown  by  an 
arrow  in  Fig.  9a)  and  its  subsequent  development  are  perfectly  well 
localized  both  in  time  and  space  .  This  structure  is  converted  downstream 
with  a  convection  velocity  roughly  equal  to  10  in  wall  units.  Consequently 
the  wall  shear  stress  increases  almost  in  a  Dirac  function  fashion  at  times 
and  locatios  which  are  perfectly  predictible.  The  whole  phenomena 
relaxes  further  downstream.  It  is  emhasized  here  that  the  phase  averaged 
velocity  profiles  did  show  anywhere  points  with  local  gradients  equal  to 
zero  and  therefore  the  observed  behaviour  is  not  due  to  an  unsteady 
separation  according  to  Moore-Sears  criteria. 

V.  CONCLUSION 

*The  unsteady  blowing  decreases  the  wall  shear  stress  without  affecting 
the  skewness.  In  other  words  and  presumably,  it  does  not  affect  the 
distributions  in  the  quadrants.  This  conclusion  has  to  be  checked  further 
by  detailed  <uV>  measurements. 

*  There  is  a  clear  effect  of  the  imposed  unsteadiness  on  the  the  time 
mean  flow  and  therefore  a  clear  coupling  between  the  imposed  oscillating 
blowing  and  the  near  wall  turbulence. 

*  The  modulation  of  the  shear  is  confined  in  a  layer  of  thickness 

8uns  00  l/Vf^  and  the  amplitude  of  the  shear  increases  with  imposed 
frequency.  There  is  subsequently  an  oscillating  pressure  gradient 
resulting  from  continuity.  This  imposed  nonhomogeneous  and  time 
varying  pressure  gradient  affects  locally  the  time-space  development  of 
the  coherent  structures.  On  the  other  hand,  if  it  is  argued  that  the  suction 
essentially  removes  vorticity  near  the  wall,  the  unsteady  suction  may 
allow  us  to  control  the  thickness  of  the  boundary  layer  to  manipulate.  The 
unsteady  suction  deserves  in  this  sens  a  detailed  study. 

*  The  high  sensitivity  of  <u’u’>  to  the  imposed  frequency  (Fig.  5a) 
suggests  the  possibility  of  management  of  the  near  wall  turbulence  in  an 
interesting  way.  The  unsteady  blowing  through  spanwise  slits  separated  by 
x+=50  and  through  which  the  blowing  at  one  slot  is  in  opposition  of  phase 
with  the  other,  may  result  in  important  reduction  of  the  near  wall 
turbulence  activity. 

*  Finally,  the  investigation  of  the  same  technique  by  making  use  of 
streamwise  slits  to  affect  the  quasi-streamwise  structures  may  reveal 
interesting  features. 


VI.  REFERENCES 

1.  Acton  E.,  Dhanak,  M.-R.  "  The  motion  and  stability  of  a  vortex  array 
above  a  pulsed  surface'*  J.  Fluid  Mech.  247,  pp.  231-245;  1993 

2.  Bewley  T.,  Choi  H.,  Temam  R.,  Moin  P.  "  Optimal  feedback  control  of 
turbulent  channel  flow"  Annual  Research  Briefs,  CTR;  pp.  3-14  ;  1993 

3.  Choi  H.,  Moin  P.,  Kim  J.  "Active  control  for  drag  reduction  in  wall- 
bounded  flows"  J.  Fluid  Mech.,  262,  pp.  75-110;  1994 

4.  Kim  J.,  Moin  P.,  Moser  R.,  1987  "  Turbulence  statistics  in  fully 
developed  channel  flow  at  low  Reynolds  number"  J.  Fluid  Mech.,  177,  133 

5.  Narasimha  R.,  Sreenivasan  K.R.,  1973  "Relaminarization  in  highly 
accelerated  boundary  layers"  J.  Fluid  Mech.  ,61,  pp.  417-447. 

6.  Orlandi  P.,  Jimdnez  J.,  1994  "  On  the  generation  of  turbulent  wall 
friction"  Phys.  Huids,  6,  pp.  634-641 

7.Sano  M.,  Hirayama  N.,  1985  "  Turbulent  boundary  layers  with 
injection  and  suction  through  a  slit"  Bulletin  of  JSME,  vol.28,pp. 807-8 14 

8.  Schlichting  H.,  1979  "Boundary-Layer  Theory"  Seventh  Edition 
;McGraw  Hill . 

9.  Sherman  F. ,  1990  "Viscous  Flow"  ;  McGraw  Hill 

10.  Sokolov  M.,  Antonia  R.-A.  "  Response  of  a  turbulent  boundary  layer 
to  intensive  suction  through  a  porous  strip"  Ninth  Symp.  on  Turbulent 
Shear  Flows,  Kyoto,  pp.  5-3-1  to  5-3-6,  1993. 

11.  Tardu,  S.,  Binder  G.,  Blackwelder  R.  "Turbulent  channel  flow  with 
large  amplitude  velocity  oscillations"  J.  Fluid  Mech.,  267,  pp.  109-151 

12.  Tardu,  S.,  1995  "Coherent  structures  and  riblets"  Appl.  Sc.  Research. 
,  54,  pp.  349-385 

13.  Tardu  ,S.,  1998  "Near  wall  turbulence  control  by  local  time- 
periodical  blowing"  To  appear  in  Exp.  Th.  Fluid  Science.  14  pages. 


Re  =-£-  =  30 
2tcv 


Q 


yv+  -  100 


Typical  transverse  vortical 
structures  in  the  inner  layer 


nth  source: 


Cn(t)=(-l)nC0[  l-cos( 

Figure  1  Control  strategy 

MANIPULATED 


2nfe  t-  2n-^  +  On) 


Cousteix-Houdewille 

T 

wall-wire 

k 

S  B  , 

S  B  5 

;  b 

■ 

■ 

i  r 

■1 

00 

A 

A 

f) 

U 

U 

u 

L. 

In 

J!  ■ 

, 

II 

6 

45 

igure  2  a  Are  shown  the  slots  and  their  dimensions  in  mm .  S  and  B 
refers  respectively  to  suction  and  blowing. 


<V0> 

(m/s) 


Figure  2b-  Example  of  phase  average  of  the  injection  velocity;  the 
imposed  frequency  in  wall  units  is  ff=  0.017. 


245 


—  * 

T_ 

T 


Figure  3  Ratio  of  (a)  the  time  mean  wall  shear  stress  and  (b)  the  wall 
shear  stress  intensity  (b)  in  the  manipulated  versus  standard  boundary 

layers.  Comparison  of  steady  and  unsteady  blowing;  f*  =  0.0072  and  Figure  4  -Ratio  of  (a)  the  skewness  and  (b)  flatness  of  the  instanteneous 

A+  =  5.4  for  different  x  stations  downstream  of  the  slot;  S  is  the  local  wall  shear  stress  in  the  manipulated  and  unmanipulated  boundary  layer, 
boundary  layer  thickness.  Comparison  of  steady  and  unsteady  blowing;  f  =  0.0072  and  A  =  5.4  . 

Also  shown  the  corresponding  statistics  of  u’  measured  at  y+=10.  See  (a) 
for  captions. 


246 


0,0  0,2  0,4  0,6  0,8  1 ,0 


b) 


0,0  0,2  0,4  0,6  0,8  1,0 


Figure  5  Phase  averages  at  y+=14  and  x+=  44:  a-  Turbulence 
intensity  at  ^=0.017  ;  b-  Skewness  of  time  derivative  of  u'  and 
the  ejection  frequency  determined  by  mu'-l  technique;  the  imposed 
frequency  for  (b)  is  ^=0.017 


’  0,002  0,006  0,010  0,014 


Figure  6  Skewness  of  the  streamwise  velocity  time  derivative  at 
y  +  =14  under  unsteady  blowing  vs.  the  imposed 
frequency. A  =  5.4;  U«,  =4  m/s. 


1  10  100  1000 


Figure  7  Time  mean  velocity  profiles  at  x+=40.  Comparison 
steady-unsteady  blowing.  The  imposed  frequency  is  1^=0.017  . 


Figure  8  Time  mean  streamwise  turbulence  intensity  at 
x+=40.  Comparison  steady-unsteady  blowing.  The  imposed 
frequency  is  1^=0.017  .  For  caption  see  Fig.  7 


247 


DRAG  REDUCTION  THROUGH  THE  NEAR  WALL  VORTEX  SYSTEM  MANAGEMENT 
INTERNATIONAL  SYMPOSIUM  ON  SEAWATER  DRAG  REDUCTION 


Yu.  N.  Savchenko 

Institute  of  Hydromechanics  of  Ukrainian  National  Academy  of  Sciences 
8/4,  Zhelyabov  str.,  Kyiv,  252057,  Ukraine 
Fax  (044)  446  42  29,  e-mail:  sav@ihm.kiev.ua 

The  systems  of  surface  vortices  were  observed  on  a  skin  of  quickly  swimming  dolphins,  penguins,  fishes  and  on  the  boundary  between  the 
two  streams  in  form  of  Kelvin  -  Helmgoltz  flow.  Results  of  experimental  and  theoretical  investigation  on  the  skin  friction  drag  reduction  by 
means  of  artificial  vortex  systems  generation  near  the  wall  on  the  two-dimensional  surfaces  of  bodies  of  revolution  are  presented  in  this  paper. 
The  two-dimensional  potential  model  of  the  vortex  system  near  the  solid  wall  is  considered  as  a  basic  theoretical  model.  It  was  shown  that  we 
can  choose  the  vortex  chain  parameters  so  that  the  fluid  velocity  on  the  wall  becomes  a  periodic  function  with  zero  mean  value.  The  boundary 
layer  is  not  developed  in  such  flow,  and  the  mean  value  of  the  friction  force  is  equal  to  0.  These  theoretical  investigations  help  to  choose  optimal 
parameters  of  the  vortex  system  for  drag  reduction.  The  experiments  of  the  secondary  vortex  flow  registration  in  the  hollows  of  the  traveling 
waves  along  the  surface  are  demonstrated.  It  was  shown  that  such  flow  arises  when  the  velocity  of  spreading  the  traveling  waves  is  equal  to  0.5 
of  the  free  stream  velocity.  Results  of  the  experiments  on  generation  of  the  vortex  spiral  systems  on  bodies  of  revolution  with  help  of  the  special 
rotating  turbines.  It  was  noted  that  besides  the  positive  effect  for  the  drag  reduction,  such  generators  of  the  spiral  vortices  having  turbine  shape 
can  produce  some  additional  energy. 


I.  INTRODUCTION 

In  1955  Assapian  and  Cramer  have  discovered  the  phenomenon  of 
traveling  wave  formation  on  a  skin  of  quickly  swimming  dolphins  and 
fishes  and  delivered  the  question  about  their  roles  in  reaching  the  high 
speeds  in  water  [1]. 

In  1967  Merculov  theoretically  has  shown  that  the  traveling  waves 
can  form  a  secondary  vortical  system  in  fluid  and  for  the  first  time  has 
connected  the  friction  drag  reduction  with  vortical  system  existence  near 
the  surface  [2].  This  fundamental  conclusion  has  been  confirmed 
experimentally  [3].  It  was  found  that 

(1)  the  vortex  system  formed  by  traveling  waves  is  a  main  cause  of 
reduction  of  the  surface  friction; 

(2)  the  created  vortex  system  is  relatively  steady; 

(3)  the  vortex  system  begins  to  form  when  the  phase  speed  of 
traveling  wave  C  reaches  the  half  of  the  mainstream  velocity  V ; 

(4)  at  C  /  V*  >  0.6  the  surface  drag  coefficient  ceases  to  depend 
on  Reynolds  number,  that  is  evidence  of  secondary  flow  periodicity. 

Kalugin  and  Panchuk  have  demonstrated  the  process  of  secondary 
flow  formation  by  traveling  wave  by  means  of  the  numerical  solution  of 
Navier-Stokes  equation  [4].  The  total  formation  of  vortices  has  proved 
to  cease  after  passing  by  flow  approximately  of  twenty  wave  lengths  X  . 

We  used  the  vortex  analogy  with  roller  of  radius  R  for  estimation 
of  energy  for  the  vortical  system  maintenance  in  a  traveling  wave  [5] 
(Fig.  1).  In  accordance  with  this  analogy  the  vortex  moves  relatively  to 
surface  with  velocity  0.5  and  rotates  with  angular  velocity 
o-V^/2 R  .  The  necessary  energy  along  the  length  L  and  surface 
width  unit  is  approximately  presented  in  form  of  sum  of  three  parts: 

1)  the  kinetic  energy  of  rotary  roller 
motion  E =  prc/?2  Vj  /  32X  ,  where  p  is  fluid  density; 

2)  the  kinetic  energy  belonging  to  vortex-roller  from  V „  to 
0.5  Ek  =  3p7U R2  V*  /  16X  for  fluid  deceleration; 

3)  the  viscous  dissipation  energy  Ev  ~4nvp(d2  R2  L/X  , 
where  v  is  kinetic  viscosity  coefficient. 

The  sum  has  the  form: 


£  =  Ea+Rt+Ev=^l 


1  +  — f— |  Re, 

32  U 


(1) 


In  the  case  of  large  ReL  =  Vx  LI  v  ,  a  ratio  of  the  energy  E  to  the 
turbulent  boundary  layer  energy  of  the  flat  plate  [6] 
EF  =  0.0307  LpVl  0.5  Re  ^  is  equal  to: 


(2) 


It  is  clear  that  the  possible  advantage  increases  at  increase  of  L  and  can 
reach  the  values  considerably  more  than  0\EF  . 

As  far  as  the  surface  with  traveling  waves  is  a  difficult  problem  for 
technical  realization,  it  is  appropriate  to  create  directly  a  similar  vortical 
system  by  special  generators  of  vortices  [9]. 

We  give  the  theoretical  explanation  of  concepts  of  the  friction  drag 
reduction  in  the  fluid  flow  by  means  of  a  vortex  chain  creation  near  the 
body  surface.  We  use  the  two-dimensional  potential  flow,  which  is 
parallel  to  the  flat  wall,  from  infinite  chain  of  point  vortices  as  a  basic 
theoretical  model. 

It  is  shown  that  we  can  chose  the  vortical  chain  parameters  so  that 
the  fluid  velocity  on  the  wall  becomes  a  periodic  function  with  mean 
value  0.  The  boundary  layer  is  not  developed  in  such  flow,  and  the  mean 
value  of  the  friction  force  is  equal  to  0.  The  estimations  of  real  vortex 
parameters  are  given  and  we  can  expect  advantage  in  spent  power. 

II.  THE  TWO-DIMENSIONAL  POTENTIAL  MODEL 

We  consider  the  vortex  system  near  the  solid  surface  representing 
part  of  an  infinite  chain  of  point  vortices  located  on  the  wall  parallel  to 
the  flat  wall  (Fig.  2).  We  assume  that  the  flow  is  two-dimensional  and 
potential.  The  source  of  coordinates  is  located  on  the  wall,  axis  Ox  is 
directed  to  the  free  stream,  axis  Oy  is  directed  vertically  upwards.  We 
designate  that  h  is  the  vortex  distance  from  the  wall,  /  is  the  distance 
between  the  vortices,  T  is  the  circulation  of  vortices.  If  the  rotation 
occurs  counter-clockwise,  the  circulation  is  considered  as  positive.  We 
can  easily  obtain  the  such  flow  complex  potential  by  the  reflection 
method  [7]: 


W(z)  ~  Vx  z  +  ~^~  X  In— — -7 -+ const  = 
v  '  27 xijttL  z-zk 


=  VMz  +  - 


2ni 


,  .  nlz-ih)  ,  n(z+ih) 

In  sin— - In  sin — - - - 

l  l 


(3) 


+  const) 


where  zk  =  kl  +  ih,  zk=kl-ihy  k  =  0,  ±  1 ,  ±2 . 

Differentiating  (3)  with  respect  to  z,  we  obtain  the  flow  complex 
velocity: 


n(z-ih)  n(z-ih) 

— - --cot  — - -  . 

I  l 

(4) 

In  this  case  on  wall  the  boundary  condition  of  zero  normal  velocity 
v  (  x,  0  )  =  0  is  executed.  It  is  known  [7]  that  the  point  vortices  move 
together  with  fluid.  Assuming  in  (  4  )  x  =  0,  y  =  h,  we  obtain  that  in 
equal  intervals  the  vortices  move  relatively  to  the  wall  with  velocity: 


249 


£i".  =  v,  =K.+— coth— .  (5) 

dt  1  2/  / 

Thus,  in  ratio  (3),  (4)  instead  of  z  we  should  substitute  z-V,/  for 
arbitrary  moment  t.  However,  to  consider  the  flow  instant  state  at  t  =  0 
is  enough  for  our  purposes. 

The  vortical  street  model  consisting  of  two  vortical  chains  was 
used  by  Karman  for  drag  estimation  of  bad-streamlined  bodies  in  fluid 
[7].  He  has  shown  that  the  vortical  street  with  parallel  location  of 
vortices  (3)  is  unsteady.  Therefore,  in  experiment  we  observe  the  chess 
location  of  vortices  in  the  street.  We  shall  not  here  take  into  account  the 
possible  motion  of  vortices  in  the  chain  relatively  each  other,  as  far  as: 

(1)  we  interest  the  comparatively  short  chain  section  in 
streamlined  surface  limits; 

(2)  the  vortical  chains  near  the  surfaces  are  observed  in  the 
experiment  [3]. 

Assuming  in  (4)  y  -  0,  we  obtain  the  fluid  velocity  distribution  on 
the  wall  (when  t  =  0 ): 

T  sinh  (2nhi  C) 

.  ~  j  cosh(27t/i//)-cos(2rc;t//) 


In  potential  model  of  vortical  chain  near  the  wall  (3)  the  points  of 
location  of  vortices  are  singular,  since  in  them  the  fluid  speed  is  equal  to 
+  °o  ,  and  pressure  is  equal  to  -  00  .  To  estimate  the  real  rarefaction  in  the 
centers  of  vortices  we  replace  the  point  vortices  by  vortices  of  finite 
dimensions  [7].  In  this  model  a  separate  vortex  has  a  core  with  radius  a , 
inside  of  which  the  fluid  has  constant  vorticity,  i.e,  rotates  with  constant 
angular  velocity  (0.  Outside  of  the  core  the  flow  is  considered  potential. 
We  compare  linear  velocity  value  on  the  core  boundary  and  obtain 
V- Into  a2.  If  we  write  below  the  Euler  equation  in  cylindrical 
coordinates,  then  on  the  core  surface  we  obtain: 

f  \  f  v2  ,  pr2 

p(«)  =  P.-Jp— = 

a 

And  inside  of  the  core: 

p[r)  =  p(a)  -  Jp-y-  d  r  =  - r2) . 

r 

The  pressure  minimum  is  reached  in  the  core  center: 


III.  CHOOSING  THE  VORTICAL  CHAIN  PARAMETERS 

The  fluid  speed  on  wall  (6)  is  periodic  function  in  x  with  period  /. 
We  calculate  its  mean  value  in  period: 

1 

=  yj  “».(*)  <&  =  K.+y-  (7) 

0 

We  require  that  the  mean  velocity  on  the  wall  is  equal  to  0, 

then  from  (7)  we  obtain  the  condition  connecting  the  vortical  chain 
parameters: 


r 

vj 


=  ~i . 


(8) 


In  this  case  the  speed  of  motion  of  vortices  relatively  to  the  wall  is  equal 

to: 


As  is  known  the  cavities  arise  in  cores  of  vortices  at  great  rarefaction. 
The  powerful  vortices  are  destroyed  quickly  in  water  [8].  Therefore,  to 
subordinate  the  flow  parameters  to  the  cavitation  absence  conditions  in 
vortices  is  expedient  with  account  (8): 


where  pv  is  saturated  water  vapor  pressure(  p „  =  2350 Pa  at 
temperature  20°  C  ),  ct  =  2 -  pv)f  pV2  is  cavitation  number.  The 

condition  (12)  sets  the  restriction  for  circulation  and  dimension  of 
generated  vortices.  It  slackens  with  motion  depth  increase  (i.e.  with 
increase  pM  ).  At  motion  in  air  the  cavitation  in  vortices  does  not  arise, 
the  condition  (12)  becomes  unnecessary. 


pr 

(2  %af 


1/  1/  1  1  1  2nh 

V  -  V\  1 - coth - 

2  / 


(9) 


The  function  uw  (*)  twice  changes  the  sign  and  reaches  the  values 
maximal  to  modulo  within  the  one  period  range  0  <  x  <  /: 


«„(o)=v_ 


sinh(2  tc/i  /  /) 


“co  (0.5/)  =  V 


cosh(27tfc//)-l 

^  sinh(27r/*//) 

~cosh(2?t/i//)+l 


<0, 


(10) 


>0. 


Thus,  in  arbitrary  point  of  the  wall  the  fluid  speed  may  be  presented  in 
the  form: 


/\  „  Jh\  .  (2kV.\  ,  , 

ua{t)  =  v~b  ~r  sin  — ~r~  •  b«l  (1!) 

\U  v  * 


V.  THE  ESTIMATION  OF  POWER  NECESSARY  FOR 
VORTICAL  SYSTEM  GENERATION 

The  friction  force  acts  on  one  side  of  a  plate  with  length  L  and 
single  width  in  the  uniform  flow  with  velocity  at  full  developed 
turbulent  boundary  layer  [6]: 


0.075 

(logRet-2)2  ' 


(13) 


where  R  zL=V„  L!  \  is  Reynolds  number.  The  power  necessary  to 
overcome  this  force  is  equal  to  N F  ~  F  .  Obviously,  that  the 
vortical  system  creation  to  reduce  the  friction  drag  on  the  plate  makes 
sense,  if  the  power  spent  for  creation  of  vortices  and  the  power 

necessary  to  overcome  residual  friction  force  is  less  than  N F  .  We 
evaluate  the  power  necessary  to  generate  vortices  by  two  different  ways. 

(1)  By  theorem  about  changing  the  motion  quantity.  The  single 
point  vortex  induces  the  complex  velocity  in  fluid  near  the  wall  [7]: 


Methods  of  the  boundary  layer  calculation  on  the  stationary  wall  are 
given  in  [6]  at  periodic  free  stream  in  form  of  (11).  It  is  possible  to  show 
that  in  this  case  the  friction  force  on  the  wall  is  also  periodic  function  of 
time,  and  its  mean  value  is  equal  to  0. 

IV.  THE  ESTIMATION  OF  RAREFACTION  IN  VORTICES 


1 


1 


z-ih  z  +  ih 


We  calculate  the  quantity  of  motion  per  one  second  transmitted  by  one 
fluid  vortex: 


250 


K,  =  pJ  y)dy 

—  U 


dx=4pTh_ 

3  It  ■’ 


We  obtain  the  necessary  power,  if  we  multiply  Kx  by  number  of 
generated  vortices  per  one  second  Vx  1 1  and  by  free  stream  velocity 

K. : 


N 


4pDi  Vt 
3  h  l 


V~. 


(14) 


We  can  treat  the  formula  (14)  so  that  the  drag  force  Fv  =  KXVX  / 1  acts 
on  the  mean  on  the  generator  of  vortices  (and  hence  on  the  body  ).  This 
drag  force  is  analogous  to  Karman  drag  force. 

(2)  For  vortices  of  finite  dimensions .  We  assume  that  generator 
creates  the  vortex  core  with  radius  a.  Then  it  induces  the  necessary 
velocity  field.  We  can  evaluate  the  energy  E  spent  for  vortex  generation 
as  a  sum  of  fluid  rotary  motion  kinetic  energy  in  the  core: 

E  _  nptoV  _  Pr2 

1  4  1671 

and  the  kinetic  energy  spent  for  fluid  volume  deceleration  in  the  core 
from  V„  to  Vj : 

Then  the  power  necessary  for  generation  of  vortices  Vx  / 1  for  one 
second  is  equal  to: 

Na=(El+E2 (15) 

We  have  obtained  two  various  expressions  for  required  power.  At 
that  Na  as  one  of  parameters  includes  the  vortex  core  radius  a ,  and 
Nk  does  not  depend  on  a.  We  calculate  the  value  a ,  when  both 
expressions  give  the  equal  power  value.  We  put  in  (13),  (14) 
T  =  -V^l,  Vj  =  0.5  V*, ,  then  the  equality  NK  -  Na  gives: 


a 

1 


1 

—  32 - 

3% }  l 


3 

2  ' 


(16) 


Obviously,  the  inequalities  a  <  h  and  a  <  0.5  l  should  be  fulfilled. 
The  range  0.25  <  h  / 1  <  0.75  has  practical  interest.  The  combination  of 
parameters  a  =  h-  0.25  l  corresponds  to  the  analogy  "vortices  -  rollers" 
described  in  Introduction  [5].  The  approximate  values  of  parameters  /, 
h,  a  were  observed  also  in  experiments  with  traveling  wave  [3]. 

We  shall  think  that  the  mean  residual  friction  force  is  equal  to  0  on 
the  plate.  Then  with  account  of  (8)  and  when  Vx  =  0.5  V*, ,  the  vortex 


system  generation  gives  the  advantage  in  power  in  case  of  the  condition 
being  satisfied: 


M  =  ^  =  - 
Nv 


l6KncF 


1  +  6%  2(a/l)2 


->1  or 


a  1  [S 
l  <  n  V3 


%  ncF 


--  (17) 
o 


where  n  =  L/l  is  a  number  of  vortices  along  the  plate  length. 


VI.  SPIRAL  SYSTEM  OF  TRAVELLING  VORTICES 

The  spiral  system  of  traveling  vortices  can  be  formed  by  a  rotating 
turbine  fixed  on  the  head  part  of  moving  body.  In  this  case  we  will 
obtain  the  helicoidal  system  of  vortices  running  from  turbine  blades.  It 
has  initial  circulation  T  according  to  the  trailing  edge  theory  by 
Jukovsky  (Fig.  3): 


r  =  -P/pVL. 

It  is  significant  to  note  the  influence  of  the  disposition  of  the 
angular  vortex  axis  on  the  drag  reduction  with  respect  to  a  three- 
dimensional  traveling  vortex  system.  There  are  three  main  cases: 


1.  The  axis  of  vortices  coincides  with  the  vector  of  the  external 
flow  velocity  (Gortler  vortex  system).  In  this  case  the  velocity  at  the 
vortex  boundary  cannot  coincide  with  the  vector  of  flow  at  the  wall. 
Therefore,  it  is  useless  for  the  drag  reduction. 

2.  The  vortex  axis  is  normal  to  the  external  flow  vector.  In  this 
case  a  full  coincidence  of  vortex  velocities  with  the  flow  and  wall  is 
possible  according  to  the  2D  traveling  vortex  flow  model. 

3.  Intermediate  angular  disposition  of  the  vortex  line.  In  this  case 
the  velocity  coincidence  is  possible  only  with  a  component  of  the 
external  flow  vector.  This  vortex  system  can  be  produced  by  turbine 
having  the  power: 

N  =  TptpVjS, , 

where  St  is  working  area  [m2  ],  r|  =  0.59  is  the  maximum  efficiency 
of  the  turbine.  The  spiral  vortex  system  on  the  body  is  shown  in  Fig.  4. 

m  EXPERIMENTAL  INVESTIGATIONS 

Bionics  conception  for  direct  vortex  system  creation  is  based  on  a 
structure  of  sawfish  and  swordfish  bodies. 

Other  examples  exist  in  hydromechanics  where  a  similar  vortex 
system  really  appears  -  as  Kalvin-Helmholts  vortices  (Fig.  5)  on  the 
joint  boundary  of  two  opposite  flows  [10]. 

In  the  experiments  a  few  types  of  devices  were  used  as  vortex 
system  generators:  an  oscillating  disk  or  a  cone,  and  a  turbine  (Fig.  6) 
The  vortex  generator  is  fixed  on  the  conical  head  of  the  circular  cylinder 
part  of  the  model.  The  photos  of  the  vortex  street  are  taken  by  a  moving 
camera.  Visualization  of  vortical  structures  used  a  semisubmerged 
model  of  revolution,  aluminum  particle  additions  in  a  water  flow. 
Experiments  indicated  the  possibility  of  producing  a  vortex  system  up 
to  50  vortex  diameters  along  the  length.  When  we  tested  a  model  with 
turbine  on  the  conical  head,  the  drag  was  measured  on  the  cylindrical 
part  and  on  the  conical  head  part  separately.  The  spiral  vortex  generator 
(turbine)  is  fixed  on  the  conical  head,  and  has  possibility  to  do  useful 
work  (electric  power).  In  this  case,  the  total  effect  consists  of  the  power, 
Nd  ,  which  includes  the  drag  reduction  ,  AX  ,  and  the  useful  turbine 
power,  Nt 


N  =  Nd  +  Nt  =A XV^+N,  . 


The  maximum  of  drag  reduction  attained  on  the  cylindrical  part 
was  18  %.  The  total  maximal  effect  of  the  drag  reduction  by  vortex 
system  and  combined  turbine  power  was  33  %  (Fig.  7).  The  turbine 
power  was  estimated  at  assumption  that  the  efficiency  was  maximal  ( 

'H/max  -  0-59,  Nlm.iX  =  0.28pVjS,  ,  where  St  is  working  section  of  the 


turbine). 

These  experiments  was  carried  out  with  hydrofoil  boat  in 
undisturbed  flow  conditions. 

Another  method  of  drag  measurement  is  based  on  free 
immersion  of  body  in  water.  For  stable  immersion  regime  the  model 

OV2 

weight  M  in  water  is  equal  to  the  drag  force  F  =  %  ■  — - S 


M  =  F 


dt 


0 


Scheme  of  the  experiment  is  shown  in  Fig  8.  Wire  supported 
model  was  used  in  these  experiments  (Fig.  9). 

The  drag  coefficient  may  be  calculated  according  to  the  formula 


0  7 

where:  V  is  velocity  of  stable  motion  ( V  =  m/s);  S  is  area  of 

h 

wetted  surface;  M  =  F  is  model  weight  in  water. 


251 


The  maximal  direct  effect  of  drag  reduction  obtained  by  using 
special  turbine  was  about  13%.  This  result  was  obtained  from 
comparison  of  the  model  tests  with  turbine  and  without  turbine. 

It  is  necessary  to  note  the  total  drag  reduction  result  in  this  case 
will  be  more  high  because  of  useful  turbine  work  has  not  considered. 

It  is  anticipated  that  total  advantage  of  drag  reduction  with  the 
optimization  will  reach  25  -  30%.  The  observation  and  photo¬ 
registration  of  the  vortex  systems  on  body  of  model  was  made  through 
caissons  windows.  Visualization  of  spiral  vortex  systems  was  made  due 
to  air  bubbles  presence  in  the  vortex  cores  on  initial  part  of  underwater 
trajectory  near  free  surface  (Fig.  4). 

vm.  CONCLUSIONS 

*  The  analysis  of  two-dimensional  potential  model  of  vortical 
chain  parallel  flat  wall  has  shown,  that  such  vortex  system  can  create 
the  periodic  flow  with  mean  speed  equal  to  0  on  wall.  It  is  assumed,  that 
the  size  of  vortices  is  much  more  than  boundary  layer  thickness  on  wall. 
Therefore,  this  flow  is  external  on  relation  to  boundary  layer.  In  real 
fluid  in  such  boundary  layer  the  flow  also  will  be  periodic,  and  we  can 
expect  the  abrupt  reduction  of  mean  value  of  friction  drag  on  wall.  Thus, 
he  advantage  will  be  reached  in  such  case,  if  the  power  spent  for 
creation  of  vortices  will  less  of  power  for  overcoming  the  friction  drag, 
at  uniform  flow  around  a  plate. 

*  The  simple  estimations  of  power  Na  necessary  to  create 
vortical  system  and  rarefaction  in  vortices  p permit  the  parameters  of 
generator  of  vortices  giving  the  power  advantage  to  choose. 

*  The  obtained  results  for  two-dimensional  modeling  flow  was 
possible  to  be  applied  for  calculation  of  real  feasible  flows.  In  this  case 
the  turbine  taking  away  the  energy  from  mainstream  and  returning  it  to 
moving  body  can  be  as  a  generator  of  vortices. 

*  The  experimental  results  have  shown  the  real  possibility  for  the 
friction  drag  reduction  on  a  body  of  revolution  about  13%  without 
additional  useful  power  on  a  turbine.  The  experiments  on  secondary 
flow  visualization  have  proved  that  the  drag  reduction  effect  occurs  due 
to  the  spiral  vortex  system  generation. 

IX.  REFERENCES 

1.  Hydrobionics  in  shipbuilding.  L.:  TsNII  TEI,  1970.-272  p.  (In 
Russian) 

2.  Merkulov  V.I.  “The  flow  of  viscous  fluid  along  the  traveling  wave”, 
News  of  SD  AS  USSR  in  series  ofTechn.  Sciences ,  1967,  2th  ed.,  #8, 
pp.  3-9.  (In  Russian) 

3.  Savchenko  Yu.N.  and  Merculov  V.I.  “The  experimental  studies  of 
the  flow  along  the  traveling  wave”.  Bionics ,  1970,  4th  ed.,  pp.  1 16-120. 
(In  Russian) 

4.  Kalugin  V.I.  and  Panchuk  V.I.  “The  flow  of  viscous  incompressible 
fluid  along  the  traveling  wave”,  Bionics ,  1970,  N4,  pp.  104-110.  (In 
Russian) 

5.  Savchenko  Yu.N.  “Hydrodynamic  effects  of  traveling  wave”, 
Bionics,  1979,  13th  ed.,  pp.  19-24.  (In  Russian) 

6.  Schlichting  H.  “Boundary  Layer  Theory”,  6th  ed.  -  New  York: 
McGraw-Hill  Book  Co.,  1968. 

7.  Kochin  N.Ye.,  Kibel  I.A.,  Poze  N.V.  “The  theoretical 

hydromechanics”,  l,2parts,M.,  GRPhML,  1963.(In  Russian) 

8.  Knapp  R.T.,  Daily  I.W.  Hammitt  F.G.  “Cavitation”.  McGraw-Hill 
Book  Co.,  1970. 

9.  Savchenko  Yu.N.,  Korennaya  L.I.,  Savchenko  V.T.  Skin  friction  drag 
with  special  vortex  systems  in  boundary  layers.  Proceeding  of 
Conference.  (,Evromech  372 ”,  Kiev,  1994. 

10.  Milton  Van  Dyke  “An  Album  of  Fluid  Motion”,  The  Parabolic 
Press,  Stanford ,  California,  1982. 


252 


'  Figure  2.  Scheme  of  vortex  chain 


Figure  3.  Scheme  of  spiral  system  of  vortices 


Figure  5.  Kalvin-Helmgolts  vortex  system 


Figure  6.  Vortex  generators 


Figure  7.  Drag  of  models  in  experiment 


254 


Figure  9.  Scheme  of  model  with  turbine  type  of  vortex  generator 


255 


BOUNDARY  LAYER  CONTROL  AT  WAVE-LIKE  SWIMMING 


Lyudmyla  Koryenna 

National  Academy  of  Sciences  of  Ukraine  -  Institute  of  Hydromechanics 
8/4,  Zhelyabov  str.,  Kyev,  252057,  Ukraine 
Fax  (044)  446  42  29,  e-mail:  sav@ihm.kiev.ua 

Boundary  layer  formation  on  the  wave-like  deformable  body  are  here  considered.  Concepts  similar  to  Prandtl’s  about  boundary  layer 
control  by  means  of  the  moving  surface  of  the  body  has  existed  in  nature  at  wave-like  swimming.  This  is  fish  and  dolphins  motion  with 
running  waves.  The  delay  of  transition  from  the  laminar  to  turbulent  boundary  layer  takes  place  at  greater  critical  Reynolds  numbers.  And 
the  •  reduction  of  the  surface  friction  takes  place  at  Reynolds  numbers  which  are  less  than  critical  ones.  The  correlation  between 
parameters  of  the  wave  is  a  main  thing  here  for  engineering.  The  wave-like  deformable  body  can  be  used  not  only  as  the  mechanism  for 
creation  of  a  thrust  force  but  also  as  the  mechanism  influencing  on  the  boundary  layer  in  control  systems  for  decrease  of  the  resistance  forces. 


I.  INTRODUCTION 

In  the  present  research  there  are  used  two  big  experimental  works: 
the  measurements  of  the  thrust  force  of  the  wave-like  deformable  plate 
in  three-dimensional  flow  on  specially  constructed  equipment,  Figure 

I.  carried  out  by  author  and  the  data  for  water  animal  kinematics 
taken  from  earlier  reports  of  the  Institute  of  Hydromechanics.  Actually 
the  wave  plate  is  a  mechanical  model  of  wave  propulsion  having 
prescribed  kinematic  parameters.  The  range  of  these  parameters  is 
wider  in  comparison  with  the  range  for  water  animals  (fish  and 
dolphins).  The  surface  friction  on  the  working  elements  of  the  wave 
propulsion  is  internal  losses  in  the  propulsion.  There  is  an  example  of 
struggle  for  reduction  of  the  surface  friction  in  nature,  by  the  correlation 
between  the  wave  parameters  with  regard  to  Reynolds  numbers. 

II.  KINEMATICS 

The  coordinate  system  oxyz  connected  with  the  body  moves 
uniformly  and  with  the  velocity  V  relative  to  the  stationary 
fluid,  Figure  2.  The  running  wave 

y  =  A  ( x)sin  (cor  +  pjt  +  (p0)  ( 1 ) 

propagates  along  the  body  in  the  direction  from  the  leading  edge  to  the 
trailing  edge  with  the  constant  relative  velocity  C  =  Xf  .  Here,  A(x )  is 
the  amplitude  function,  (0  =  2nf  is  the  circular  frequency,  p  =  2k  /  X 
is  the  wave  number,  X  is  the  wavelength,  /  is  the  frequency,  (p0  is 
the  phase  angle. 

The  wave  was  generated  the  following  way.  Seven  links  were  fixed 
to  the  plate,  Figure  1 .  They  produced  phase-shifted  sine  oscillations  so 
that  the  running  wave  was  created. 

It  is  possible  to  imagine  the  running  wave  as  follows.  We  take  a 
rigid  "infinite"  sinusoid  enclosed  in  a  piece  of  a  flexible  sleeve.  This 
sleeve  plays  the  role  of  the  wave-like  deformable  body.  When  the 
sinusoid  is  moved  inside  the  sleeve,  all  elements  of  the  sleeve  are 
subjected  to  transverse  oscillations.  The  sleeve  represents  a 
transversely  deformable  body  according  to  the  wave  propagation.  The 
velocity  of  the  sinusoid  inside  the  sleeve  is  the  wave  velocity,  C.  The 
body  begins  its  motion  opposite  to  the  direction  of  the  running  wave 
with  velocity  V",  and  always  V  <  C  in  the  propulsion  regime. 

We  see  this  is  a  body  having  the  form  of  a  sinusoid  in  the  flow.  In 
each  following  moment  of  time  the  very  same  element  of  the  sinusoid 
takes  the  new  element  of  the  plate.  Thus  the  surface  (or  boundary)  of 
this  sinusoid  is  moving  along  the  sinusoid. 

Each  element  of  the  wave-like  deformable  body  “n”  in  Figure  2 
moves  along  the  sinusoid  and  on  the  other  hand  it  makes  a  transverse 
oscillatory  motion.  There  is  a  velocity  of  moving  surface  WL  ;  an 

external  flow  velocity,  W *  ;  a  tangential  component  of  the  external  flow 
velocity,  W*  .  The  values  of  the  instantaneous  flow  velocity  and  the 
instantaneous  velocity  of  the  moving  surface  of  each  element  change 
continuously. 

III.  SOME  EXPERIMENTAL  RESULTS 

The  thrust  force  of  the  plate  was  measured  experimentally  for 
successively  modified  parameters  V,  f  A(x),  L/X  (L  is  the 
streamwise  length  of  the  plate).  The  velocities  V  and  C  were  held 
constant  for  each  experiment. 


The  Reynolds  numbers  RL  =  VL  /  v,  where  v  is  the  kinematic 
viscosity  of  fluid,  and  the  Strouhal  number  SL  = fL/V  were  changed 
respectively  in  limits  from  1.25  to  4.6xl05and  from  0.6  to  6.  The 
ratio  of  velocities  C  /  V  ~  Sx  was  limited  from  0.64  to  21. 

It  is  necessary  to  draw  attention  to  the  regimes  of  plate 
deformations  on  which  the  thrust  of  the  plate  is  equal  zero.  These 
regimes  are  analogous  to  those  of  fish  motion  as  the  thrust  force  created 
by  the  fish  body  is  equal  on  value  and  is  directed  oppositely  to  the 
resistance  force  of  the  fish  body.  For  the  plate  on  these  regimes 
Strouhal  numbers  calculated  with  the  wavelength  Sx  =  /A/V  = 
C/V  were  within  the  limits  1 . 1 8  to  1 .44.  For  fish  and  dolphins  Strouhal 
numbers  Sx  =  f  7JV  ~  C/V  range  from  1.05  to  1.59  in  experiments 

done  earlier  by  other  authors  in  the  water  tunnel  of  the  Institute  of 
Hydromechanics.  Thus  the  range  of  Strouhal  numbers  for  our  plate  is 
within  the  range  of  Strouhal  numbers  for  water  animals.  This  fact 
shows  the  reliability  of  data  obtained  in  experiments  with  the  plate 
and  in  experiments  with  fish  and  dolphins.  But  it  must  be  discussed 
further  in  the  following  way. 

For  complete  identity  of  the  conditions  for  formation  of  the 
hydrodynamic  forces  on  the  wave-like  deformable  plate  and  at  active 
motion  of  water  animals  there  are  missing  mucus  of  fish  and  compliant 
skin  of  dolphins  in  experiments  with  plate.  That  is  why  the  Strouhal 
number  scale  for  plate  is  inside  the  one  for  fish  and  dolphins,  Figure  3. 
It  should  be  noted  that  scale  for  plate  is  exactly  in  the  center  of  the  one 
for  fish  and  dolphins,  i.e.  our  experimental  results  agrees  with  the 
kinematic  data  of  the  water  animals  very  well.  We  have  full  simulation 
on  the  hydrodynamic  forces  due  to  kinematics  and  effect  of  the  moving 
surface. 

IV.  FRICTION  FORCES 

Effects  of  moving  surface  (by  L.Prandtl  and  H.Cherny): 
An  idea  of  L.Prandtl  was  to  reduce  the  velocities  in  the  boundary  layer 
by  means  of  moving  surface  of  the  body  in  the  flow  direction.  It  is 
possible  to  remove  completely  the  boundary  layer  if  the  surface  of  the 
body  has  the  velocity  that  is  equal  to  the  external  flow  velocity. 

The  theoretical  and  experimental  researches  of  moving  surfaces 
were  undertaken  more  than  once  including  the  question  of  boundary 
layer  control.  The  parameter  of  the  moving  surface  p  was  introduced 
into  the  theoretical  research  [1  ]  for  the  plate  in  the  form  of  the 
half-plane  as  the  ratio  of  the  velocity  of  the  moving  surface  to  the 
mainstream  velocity.  The  following  conclusions  were  derived  which 
reveal  the  effects  of  moving  surfaces. 

When  the  velocity  of  the  moving  surface  equals  the  value  and 
direction  of  the  mainstream  velocity,  p  =  1 ,  the  hydrodynamic  forces  do 
not  act  on  the  plate.  The  flow  around  the  plate  is  potential. 

When  the  velocity  of  the  moving  surface  is  more  than  the 
mainstream  velocity,  p  >  1 ,  the  plate  has  no  resistance  force,  it  has 
thrust  force. 

When  the  velocity  of  the  moving  surface  and  the  mainstream 
velocity  are  directed  opposite  to  each  other,  p  <  0 ,  the  plate  has  a 
resistance  force  less  than  on  stationary  surface  at  p  -  0. 

The  effects  of  the  moving  surfaces  in  applications  in 
engineering  could  be  very  useful.  But  complexity  of  design  and 
increase  of  cost  block  the  way  to  the  technical  applications  of  the 


257 


effects  of  the  moving  surfaces.  At  the  same  time  nature  makes  wide 
use  of  the  effects  of  moving  surfaces  as  will  be  shown  below. 

Parameter  of  the  moving  surface  of  the  running  wave:  Let  us 
enter  the  parameter  p,  similar  by  structure  to  the  parameter  for  the 
half-plane.  This  is  the  ratio  of  the  velocity  of  the  moving  surface  WL  to 

tangential  component  of  the  external  flow  velocity  W*  on  the  plate 
element  “n”,  Figure  2.  Naturally  this  parameter  has  another  value  for 
each  element  of  the  wave-like  deformable  plate  and  in  each  following 
moment  of  time  on  the  individual  plate  element. 


For  the  regime  of  propulsion  under  consideration  the  surface 
moving  in  flow  direction  takes  place  necessarily  in  the  extreme  points 
of  our  sinusoid,  y  =  ymax ,  as  the  velocities  WL  =  -C  and 


Physical  processes  of  boundary  layer  control  with  running 
wave:  The  knowledge  of  the  physical  processes  taking  place  in  the 

boundary  layer  of  the  wave-like  deformable  body  is  necessary  for 
successful  use  of  the  effects  of  the  running  wave  and  the  moving  surface 
in  engineering.  The  method  of  geometrical  summation  of  the  velocity 
profiles  in  the  boundary  layer  of  the  wave-like  deformable  body  is  here 
offered  for  the  case  of  the  moving  surface  in  the  flow  direction  and  for 
the  case  of  a  moving  surface  oppositely  to  the  flow  direction,  Figure  5. 
This  is  the  first  step  to  uncovering  the  physical  processes  and  for 
qualitative  comparisons.  The  two  regimes  below,  which  were  close  to 
the  regimes  of  the  live  moving  water  animals  and  to  the  regimes  in  both 
[  2  ]  and  the  author’s  experiments,  were  chosen  for  accuracy  and 
clearness. 

Regime  A:  p  =  4.33;  V=  0.5  m/s;  C  =  0.65  m/s;  C/V  =1.3 


W*  -  U*  =  -(C-V)  are  directed  to  one  side,  Figure  2.  Bearing  in 
mind  that  Sx  =  fXJV  =  C/V  we  have 


C-V 


(3) 


The  parameter  p  at  the  extreme  points  of  the  sinusoid 


depends  only  on  Strouhal  number.  The  regimes  L/X  =  1  and  the 
thrust  T  =  0  for  experiments  with  the  plate  are  the  closest  to  the  regimes 
of  the  water  animal's  motion.  The  range  of  parameter  pw  ,  3.28- 


6.55,  for  the  plate  in  this  regimes  is  within  the  range  of  parameter 
p  ,  2.7-21,  in  experiments  with  live  water  animals. 


Going  over  to  the  general  case,  not  the  extreme  points  of  the 
sinusoid,  we  must  take  into  account  the  velocity  of  oscillatory  motion  of 
the  considered  plate  element  Vy  =  dy  /  dt ,  Figure  2b.  The  angle  a 


formed  by  the  neutral  axis  of  the  running  wave  and  the  considered 
element  of  the  plate,  a  =  tan~]  dy  /  dx  ,  indicates  the  position  of  the 
considered  plate  element. 

In  general  case 

C + V  dy  /  dx 

p  = - y— -  (4) 

C-V -Vydy/dx 


We  see,  from  (4),  the  surface  moving  in  the  flow  direction  is  realized  if 


C-V  >  Vydy  / dx  (5) 

And  the  surface  moving  oppositely  to  the  flow  direction  take  place  if 
C-V  <  Vydy  / dx  (6) 

The  kinematic  data  of  the  water  animals  were  used  for 
calculations.  The  following  results  were  obtained. 

The  ratio  (5)  is  fulfilled  on  all  points  of  the  dolphin  body.  The 
scheme  of  the  moving  surface  in  the  flow  direction  is  fully  realized 
here. 

The  ratio  (6)  is  fulfilled  for  fish  on  a  significant  part  of  their  body. 
Consequently  p  <  0  and  the  scheme  of  the  moving  surface  oppositely 
to  the  direction  of  the  flow  takes  place  here. 

It  is- necessary  to  note,  that  p  for  the  different  fish  species  has 
close  values,  in  the  range  from  -2.54  to  -2.68  for  the  caudal  flipper 
at  y  =  0  .  It  is  considerably  different  from  p  =  389  for  the  dolphin,  see 
the  table.  Figure  4. 

So,  the  scheme  of  the  moving  surface  in  the  flow  direction,  p  >  0  , 
is  realized  for  the  entire  length  of  the  dolphin  body  moving  at  R  >  Rcr , 
and  the  scheme  of  the  moving  surface  oppositely  to  the  flow  direction, 
p  <  0 ,  is  realized  on  a  significant  part  of  the  fish  body  moving 
at  R  <  Rcr . 

From  structure  of  (3)  follows  that  when  V  =  0  and  y  -  ym(lx ,  then 
=  1.  Hence,  friction  forces  at  extreme  points  of  the  sinusoid  are 

absent,  and  in  other  points  of  the  sinusoid  are  less  than  they  were  at 
regimes  when  V  is  not  equal  to  0.  Therefore,  in  order  to  reduce  the 
influence  of  the  friction  forces  (internal  losses  in  propulsion),  the 
regimes  V  =  0  must  use  in  the  analysis  of  experimental  results. 


Regime  B:  p  =  -2.33;  V=  0.5  m/s;  C  =  0.35  m/s;  C/V  =0.7 

All  velocity  profiles  are  constructed  in  the  same  scale.  Figure  5. 
The  theoretical  Blasius  profile  for  the  laminar  boundary  layer  was 
used  for  construction  of  the  velocity  profiles  a  for  W*  and  b  for  WL . 
It  was  taken  into  consideration  that  the  velocities  W*  and  WL 
complete  the  total  cycle  of  changes  for  the  distance  that  equals  1/2 
wavelength.  The  velocity  profile  c  is  obtained  by  geometrical 
summation  of  the  profiles  a  and  b.  The  resulting  profile  c  is 
constructed  in  coordinate  system  connected  with  the  element  of  the 
"sinusoid".  It  is  necessary  to  take  up  the  coordinate  system  connected 
with  the  moving  surface  (with  the  plate).  There  were  given  velocities 
equal  in  magnitude  WL  and  directed  oppositely  to  WL  for  the  plate 
element  and  for  the  environmental  fluid,  profile  d.  The  velocity  of 
the  external  flow  in  the  resulting  profile  e  is  equal  in  magnitude  of  the 
velocity  V  and  in  the  opposite  direction. 

The  theoretical  Blasius  profile  for  the  laminar  boundary  layer  on  the 
flat  plate  is  the  dot-and-dash  curve  in  the  profile  e. 

Comparing  the  calculated  velocity  profiles  for  wave-like 
deformable  plate  at  p>  0  and  p<  0  we  will  note  the  following 
important  properties  of  these  profiles. 

Regime  A:  The  resulting  profile  e  at  p  >  0  is  similar  in  form  to  the 
experimental  velocity  profile  in  the  boundary  layer  of  the  wave-like 
deformable  plate  [2].  This  velocity  profile  is  more  convex  in 
comparison  with  the  one  on  the  flat  plate  and  is  similar  to  the  profiles 
of  the  stable  type.  Transition  from  laminar  to  turbulent  boundary 
layer  is  delayed  in  this  case  [3]. 

The  scheme  of  the  moving  surface  in  the  flow  direction  is  realized 
on  the  entire  body  length  of  the  dolphin  moving  at  Reynolds  numbers 
which  are  larger  than  critical  ones.  Hence  the  velocity  profile  in  the 
boundary  layer  of  the  dolphin  body  should  be  the  profile  of  the  stable 
type,  and  transition  in  the  boundary  layer  is  delayed. 

Really,  there  are  interesting  results  in  [4],  The  amplitude  of  the 
pressure  pulsation  in  the  boundary  layer  depends  on  the  type  of  the 
dolphin  motion  at  R  >  Rcr .  The  level  of  the  pressure  pulsation  in  the 
boundary  layer  corresponds  to  the  developed  turbulent  flow  for  passive 
motion  (inertial).  But  for  active  motion  the  level  of  the  pressure 
pulsation  is  considerably  less  (1.5  -  2  times)  and  corresponds  to 
insufficiently  advanced  turbulent  flow. 

Regime  B:  In  case  of  p  <  0  (the  scheme  of  the  moving  surface 
oppositely  to  the  flow  direction)  the  value  of  the  velocity  gradient 
(du  /  dyx )  at  yx  =  0  is  less  in  comparison  to  the  velocity  gradient 
(du/  dyx )  at  y,  =  0  on  the  flat  plate.  As  the  local  viscous  shear  on  the 
body  surface  is  directly  proportional  (du/  dyx )  at  yx  -  0  ,  then  the 
surface  friction  should  be  slightly  smaller  than  on  the  flat  plate.  This 
agrees  with  the  conclusions  in  [1). 

The  scheme  of  the  moving  surface  against  the  flow  direction 
is  realized  for  a  significant  part  of  the  fish  body  moving  at  Reynolds 
numbers  which  are  lower  than  critical.  Hence  the  local  viscous  shear 
for  fish  should  be  smaller  than  on  the  flat  plate. 


258 


V.  CONCLUSION 

The  nature  suggests  the  detailed  perfect  boundary  layer  control 
method.  The  surface  friction  at  wave-lake  swimming  is  decided  by 
Reynolds  number  and  correlation  of  the  running  wave  kinematic 
parameters  corresponding  to  Reynolds  number.  There  is  a  principal 
result: 

if  R>Rcr,  then  C-V  >Vydy/dx  , 
if  R<Rcr,  then  C-V  <Vydy/dx 

which  should  come  in  useful  for  designers  of  boundary  layer  control 
systems.  It  is  important  to  remember  that  in  addition  to  effects  of  the 
moving  surface  the  devices  like  that  can  simultaneously  create  the 
thrust  force  which  is  useful  force. 

VI.  REFERENCES 

1.  H.H.  Cherny  "Boundary  Layer  on  a  Plate  with  Moving  Surface", 
Reports  Akademii  Nauk  SSSR ,  213,  4,  pp  802-803. 

2.  S.  Taneda,  Y.  Tomonari  "An  Experiment  on  the  Flow  around  a 
Waving  Plate",  J. Physical  Society  of  Japan,  36,  5,  May  1974,  pp 
1683-1689. 

3.  H.  Schlihting  "  Theory  of  Boundary  Layer  ",  Moscow ,  Russia,  Nauka , 
1974,  pp  197-205. 

4.  Ye.V.  Romanenko  “Foundations  of  Statistical  Biohydrodynamics“, 
Moscow,  Russia,  Nauka ,  1976. 


259 


Water 

animal 

varieties 

(Latin) 

V 

[m/s] 

VS52 

n 

r 

(Hz) 

B| 

(r'iL 

C-K 

1 

Tursiops 

truneadus 

2.60 

2.34 

6-10‘ 

3.12 

0.78 

1.64 

0.77 

0.99 

389 

Belone 

0.48 

1.05 

4.5  •  10’ 

1.21 

0.16 

0.22 

0.03 

5.58 

r.04 

6.53 

-2.55 

Pomatomus 

saltatrix 

0.42 

1.72 

6.5-10’ 

1.95 

0.23 

0.37 

0.05 

5.27 

1.61 

7.00 

-2.58 

Sarda  sarda 

0.16 

1.12 

1.6*  10' 

1.25 

0.13 

0.13 

0.02 

9.58 

0.94 

7.53 

-2.68 

Cristi  vomer 
namaycutfi 

0.21 

1.33 

9.74 

1.21 

8.10 

-2.54 

Figure  4.  Parameter  of  the  moving  surface  p  for  the  caudal  flipper  of  the  dolphin 
(first  line  of  the  Table)  and  of  four  fish  species  ( other  lines  of  the  Table). 


1/ 


C 


u*  =  -(C  -  V) 


Regime  A:  p  =  4.33 

V  —  0.5 m/s;  C  =  0.65m/s;  C/  V  =  1 .3 


i 


'^1 


Profile  of  the 
stable  type  ! 


Blasius 


u 


Regime  B:  p  =  -2.33 

V  =  0.5m/s;  C  =  0.35m/s;  C/V  =  0.7 


Figure  5.  Velocity  profiles  in  a  boundary  layer  of  the  wave-like  deformable  body. 


261 


SUBSTITUTION  OF  ROLLING  FOR  SLIPPING  AS  AN  EFFECTIVE 
MECHANISM  OF  DECREASING  HYDRODYNAMIC  DRAG 


Vladimir  I.  Merkulov 

Institute  of  Theoretical  and  Applied  Mechanic 
SB  of  the  Russian  Academy  of  Sciences,  Novosibirsk,  630090,  Russia 
merkulov@itam.nsc.ru 

Abstract-  As  is  shown  by  theoretical  and  experimental  researches,  the  general  mechanism  of  crucial  reduction  of  hydrody¬ 
namic  drag  consists  in  substituting  rolling  friction  for  slipping  fricti  on  (l).This  mechanism  is  realized  at  a  boundary  layer 
reconstruction  with  formation  of  periodic  transverse  vortices  that  are  r  oiling  wit  hout  slipping  over  the  body  surface.  A  sm¬ 
all  velocity  gradient  characterizing  such  a  motion  conditions  low  energy  dissipation.  A  travelling  wave  on  elastic  body  surfa- 
ceworks  as  a  mechanism  of  formation  of  a  periodic  vortex  structure  for  s  ome  water  animals, such  as  dolphins.  At  appropriate  e- 
lastic  parameters  of  the  surface,  the  wave  is  excited  in  a  regime  of  hyd  roelastic  flutter.  The  surface  roughness,  as  it  takes 
place  with  sharks,  expands  the  range  of  velocities  at  which  travelling  w  aves  are  excited,  though  it  decreases  their  energy  e- 
fficiency.  Another  vortex  formation  mechanism  abundant  in  nature  employs  the  specifics  of  the  flow  along  a  slender  rough  body. 
Analytical  calculations  validated  by  direct  experiments  showed  that  hel  ical  vortices  with  a  high  amplitude  growth  increment 
are  generated  on  a  slender  rough  body.  Arriving  at  the  fish  body,  well-d  eveloped  helical  vortices  reconstruct  the  boundary  la¬ 
yer  in  such  a  way  that  the  normal  flow  with  slipping  of  fluid  layers  wit  ha  high  velocity  gradient  is  replaced  by  a  motion  with 
rolling  of  vortices  with  a  small  velocity  gradient  and,  as  a  consequence  ,  with  low  hydrodynamic  drag. 


I.  INTRODUCTION 

The  rostrum  of  a  sword-fish  is  a  slender  body  covered  by 
small-scale  roughness.  Nearly  parallel  flow  is  formed  at  a  small 
distance  from  the  leading  edge,  which  changes  weakly  down¬ 
stream  due  to  both  viscosity  and  slight  thickening  of  the  ros¬ 
trum.  One  can  try  to  approximate  this  flow  by  fluid  motion 
along  an  infinite  thin  rough  needle. 

The  needle  surface  roughness  generates  continuously  small 
disturbances  in  the  flow.  The  stability  of  initial  laminar  flow 
guarantees  the  absence  of  other  disturbances  except  for  those 
diffusing  from  the  cylinder  surface.  For  one-scale  roughness, 
we  will  have  one-scale  turbulence  with  a  known  mixing  path 
length. 

The  presence  of  turbulent  oscillations  causes  the  appear¬ 
ance  of  turbulent  viscosity  that  exceeds  multiply  the  molecular 
viscosity  in  the  gradient  flow  region.  The  flow  which  is  of  in¬ 
terest  to  us  can  be  described  by  the  Reynolds  equations  with 
a  certain  turbulent  viscosity  which  can  be  determined  using 
the  Prandtl  technique  in  terms  of  known,  in  the  present  case 
constant  mixing  path  length.  The  solution  obtained  can  be 
analyzed  for  stability.  Inviscid  solutions  depend  on  turbulent 
viscosity  only  via  the  averaged  velocity  profile. 


II. MATHEMATICAL  FORMULATION  OF 
THE  PROBLEM. 

The  equation  of  the  average  momentum  in  the  boundary 
layer  model  in  the  cylindrical  coordinate  system  r,  2  is  written 
as 


Assuming  the  needle  diameter  to  be  equal  to  zero,  we  obtain 
the  following  boundary  conditions  for  unknown  functions  U 
and  V. 

U  =  V  =  0  for  r  —  0,  z  >  0 

U  =  1,  V  0  for  r  — >  00 

One  can  conclude  from  the  form  of  equation  (1)  that  it 
is  independent  of  velocity  scale  but  depends  on  the  roughness 
scale.  Assuming  the  coordinates  r,  z  be  normalized  to  a  certain 
size  L,  the  quantity  l  will  be  a  measure  of  relative  roughness. 


III.  SOLUTION  OF  THE  PROBLEM 

From  the  analysis  of  dimensionality  of  equation  (l),  it  fol¬ 
lows  the  existence  of  a  self-similar  solution  of  the  form  U  = 
U(ri)  where  r)  =  r/(l2z )U3.  Let  us  represent  the  function 
U(r))  in  terms  of  the  second  derivative  of  some  other  unknown 
function  4>(rj) 

■U  =  <f>''(  v) 

and  determine  the  second  component  of  velocity  from  the  con¬ 
tinuity  equation  (2). 

For  this  purpose,  let  us  pass  to  new  variables  ..£  =  (;  rj  — 

r/(/2z)U3 . 

Then  we  will  need  the  relations  dr\jdr  =  77/r  =  l/(^2^)1^3 

dr)/dz  —  —r]/3z 

d£/dr  =  0;  d£,/dz  =  1. 

Let  us  substitute  in  equation  (2)  the  relation  for  the  func¬ 
tion  U. 


d(Ur)  _ 
dr 

whence  we  can  obtain 


dU 


dz 


P(V 


dU 

dz 


_ rdU  1  d  _ . 

+  V^  =  —rTr(rpUV) 


Here,  U  and  V  are  components  of  the  averaged  velocity 
profile,  u,  v  are  components  of  the  fluctuating  velocity. 

According  to  the  Prandtl  model  [1],  the  Reynolds  stress 
can  be  expressed  in  terms  of  the  averaged  velocity  gradient 
(dU /dr)  and  mixing  path  l  as  follows: 

uv=  -l2  (dU/dr)2. 


°{VrW^  =  t^r. 

dr)  3£ 

v  =  f  4>'"n2dv  =  (f2g)1/°  [v2<t>"  -  2n<t>'  +  24,}.  (3) 

Now  we  will  turn  to  the  momentum  equation  (l). 

After  substituting  the  above  formulas  for  U  and  V,  the 
left-hand  side  is  converted  to  the  following  form 


Thus,  the  averaged  momentum  equation  is  reduced  to  the 
equation 


u™  +  v™ 

dz  dr 


l 2  d 


■  (dU\ 
dr  ^  dr  ^ 


The  continuity  equation  has  a  usual  form. 


(i) 


d(Ur)  d(Vr ) 

dz  dr 


(2) 


•  — (-2770'  +  2  <f>) 


Let  us  now  transform  the  right-hand  side  of  this  equation. 

\  =  d4>"'t'o(<f>'"  +  2v<t>"") 


r  V  dr  1 


263 


Finally,  we  obtain  an  equation  for  4>{r)) 

*"'(2.,*,,"  +  *"'  +  §>tf'-§*)  =  o  (4) 

with  the  boundary  conditions 
4>u  =  0  for  q  =  0 
lim(4>/q  —  4>')  =  0  npn  r?  — >  0 
lim((f),fr)  —  20'  +  20/7?)  =  0  npn  q  — ►  oo 

IV.  ANALYSIS  OF  EQUATION  (4). 

For  small  values  of  argument  q  in  equation  (4),  the  main 
terms  are  the  highest  derivatives  that  describe  viscous  forces 

2q<t>""  +  <f>(”  =  0, 

which  has  the  following  solution 

<t>"  =  yfi. 

For  large  values  of  q  the  main  terms  are  the  convective  terms 

t"  =  y/n 

which  vanish  at  0  =  q2 . 


V.  ANALYSIS  OF  STABILITY  OF 
THE  SOLUTION. 

Let  us  designate  by  the  letters  u,v,w,p  the  small  pertur¬ 
bations  of  components  of  velocity  vector  and  pressure,  which 
will  be  sought  in  the  form 

u,  v,u>,p  =  Reel[Fr,  iGr ,  Hr,  pPr]  exp (in<f>  +  ios(x  -  ct)). 

Here,  a  is  the  wave  number  and  c  is  the  phase  velocity.  For 
unknown  functions  F(r),  G(r),H(r)  after  eliminating  P(r),  we 
obtain  the  following  system  of  ordinary  differential  equations 

n(U  -  c)G  +  —[(U  -  c)rH]  =  0 


a(U  -  c)(nF  -  arH)  +  nU'G  =  0 
d 

arF  +  r — G  +  G  +  nH  =  0 
dr 

,  that  must  be  solved  with  uniform  boundary  conditions  F,  G,H,P—± 
0  at  r  0  and  r  — Y  oo. 

The  second  equation  of  this  system  is  an  algebraic  one  and 
makes  it  possible  to  exclude  the  function  F. 

As  a  result,  one  can  obtain  a  system  of  two  equations  of 
the  first  order  for  two  unknowns  H,  G. 

n(U  -  c)G  +  ^-[(U  -  c)rH]  =  0  (5) 


n(U  -c)(r —  +  G)-nrU'G+(n2  +c,2r2)(U -c)H  =  0  (6) 
dr 

Excluding  H  from  this  system,  we  obtain  one  second-order 
equation  with  one  unknown. 


(U-c) 


d 


drln 2  +  a2r2  dr 


(rG)]- 


(7) 


(U  —  c)G  -  G  —  ( 


rU' 


drx  n2  +  a2r2 


)  =  0 


The  system  of  equations  (5)-(6)  or  equation  (7)  equivalent  to 
it  with  uniform  boundary  conditions  can  have  a  solution  only 
for  certain  values  of  c  and  a  that  are  called  eigenvalues. 

Stability  of  various  axisymmetric  flows  is  studied  in  detail 
in  a  well-known  paper  of  Batchelor  and  Gill  [4].  In  particu¬ 
lar,  they  showed  that  the  flow  can  lose  stability  with  respect 
to  inviscid  form  of  perturbations  if  the  following  condition  is 
satisfied  at  some  internal  point: 


rU' 


-( 

dr  n 2  -f  a2r 2 


)  =  o. 


Here,  as  usually,  n  is  the  number  of  the  azimuthal  mode,  and 
a  is  the  wave  number  of  the  longitudinal  travelling  wave. 


This  condition  is  a  generalization  of  the  known  condition 
on  an  inflection  point  in  the  profile  of  a  parallel- plane  flow  to 
an  axisymmetric  flow. 

It  is  easy  to  see  that  this  condition  is  not  valid  for  the 
Poiseuille  flow  with  a  logarithmic  profile  and  for  any  profile  if 
we  confine  ourselves  to  axisymmetric  disturbances  (n  =  0). 

At  the  same  time,  for  a  profile  on  a  rough  cylinder  obtained 
by  us,  this  condition  is  always  valid  at  point  r &  =  njs/ 3  a. 

Batchelor  and  Gill  showed  that  most  unstable  are  distur¬ 
bances  with  the  number  n  =  1. 

Concerning  the  conditions  of  physical  realization,  we  are 
interested  in  the  case  when  the  product  ac  =  u>  is  a  real  num¬ 
ber,  hence,  or  is  a  complex  number  conjugated  with  c.  In  this 
case,  the  real  part  of  the  wave  number  cxr  determines  the  wave 
length  A  in  accordance  with  the  relation  ar  =  2n/X}  and  the 
imaginary  part  cxi  determines  the  downstream  change  of  dis¬ 
turbance  amplitude  according  to  the  law  exp(— ol{Z. 

The  reference  length  in  the  problem  under  consideration 
can  be  only  the  wave  length,  which  will  be  accepted  as  a  unit 
of  measurement.  With  such  normalization,  ar  =  2ir,  and 


rfc  =  Reei-L-  =  ar .  =  _ i _ 

\/3a  a2  +  oi\  27iV3[l  +  {oti/oir)2] 

Since  ai  <  ar,  then  the  dimensionless  distance  to  the  critical 
layer  will  be  determined  by  a  small  number  0.092. 

Let  us  rewrite  equation  (7)  in  the  following  way: 


drln 2  -f  c*2r2  dr 


(rG)]  -  rG  - 


(8) 


r2  G  d  rU* 

U  —  c  dr  n2  +  a2  r2 

Let  us  represent  an  approximate  solution  to  this  equation, 
which  satisfies  uniform  boundary  conditions,  in  the  following 
form: 

rG  =  0  for  r  <  r^ 
rG  =  rKi(ra)  for  r  >  r* 

Here  Ki  is  the  Hankel  function  of  the  Ith  order. 

The  condition  of  continuity  of  this  function  at  point  r  =  r* 


K[  (rka)  =  0  (9) 

can  be  provided  by  choosing  an  arbitrary  value  of  the  wave 
number  a. 

Using  direct  substitution,  one  can  verify  that  the  chosen 
function  satisfies  equation  (8)  for  velocity  profile 

U  =  y/ratr  <  rk 

JJ  =  constatr  >  rk 

and  is  an  approximate  solution  for.  all  profiles  similar  to  this 
one. 

The  first  root  of  equation  (9)  has  the  following  complex 
value:  0.90  -  t'0.58.  The  negative  imaginary  part  ensures  a 
rapid  growth  of  disturbance  amplitude. 


VI.  CONCLUSION. 

The  conducted  qualitative  analysis  of  solution  properties 
and  the  estimate  of  some  of  its  parameters  allows  one  to  pre¬ 
pare  an  experimental  verification  of  the  hypothesis  according 
to  which  a  thin  rough  rostrum  of  a  sword-fish  performs  a  func¬ 
tion  of  vortex  generator. 

Firstly,  we  found  out  that  dimensionless  parameters  of  the 
flow  along  a  rough  cylinder  are  independent  of  velocity  scale. 
This  makes  it  possible  to  carry  out  experiments  with  an  arbi¬ 
trary  velocity  convenient  for  the  experimentor. 

Secondly,  we  found  out  that  the  velocity  profile  formed 
by  the  rough  cylinder  is  stable  with  respect  to  axisymmetric 
disturbances.  At  the  same  time,  helical  disturbances  of  the 
travelling  wave  shape 

f(r)exp[ia(z  —  ct)  +  ind] 

are  unstable  with  a  continuous  spectrum  of  frequencies. 
This  means  that  forced  generation  of  such  disturbances  with 


264 


a  small  initial  amplitude  ensures  an  onset  of  increasing  distur¬ 
bances  which,  having  achieved  a  certain  amplitude,  as  we  sup¬ 
pose,  form  a  steady  periodic  flow.  The  most  unstable  form  is  a 
helical  vortex  filament  corresponding  to  the  value  n  =  ±1.  Su¬ 
perposition  of  two  such  forms  provides  an  intersecting  vortex 
geometry  that  will  then  evolve  into  inclined  circular  vortices 
embracing  the  cylinder.  Such  waves  can  be  generated  by  trans¬ 
verse  oscillations  of  the  cylinder  in  one  plane,  two  disturbance 
waves  being  excited  during  one  period  of  oscillations. 


VII.  REFERENCES 

1.  Merkulov  V.I.  Fluid  Flow  Control,  Nauka,  Novosibirsk, 
1981,  180  p. 

2.  Schlichting  H.  Grenzschicht-Theorie,  Verlag  G. Braun, 
Karlsruhe,  1951. 

3.  Betchov  R.,  Criminale  W.O.,  Jr.  Stability  of  Parallel 
Flows,  Academic  Press,  New  York,  London,  1967. 

4.  Batchelor  F.K.,  Gill  A.E.  Analysis  of  the  axisymmetric 
jets,  J. Fluid  Mech.,  14,  pp. 529-551,  1962. 


Turbulent  Drag  Reduction 
Methods:  Polymer 


THE  OF  COMBINATION  POLYMER,  COMPLIANT  WALL  AND  MICROBUBBLE 

DRAG  REDUCTION  SCHEMES 


Boris.N.  Semenov 

Institute  of  Thermophysics,  Siberian  Branch  of  Russian  Academy  of  Sciences, 
Prospekt  Ac.  Lavrentyev,  1,  Novosibirsk,  630090,  Russia  irena@hydro.nsc.ru 


Abstract  -The  promising  study  of  turbulence  management  by  joint  use  of  compliant  coatings  with  other  drag  reduction  means  is  proposed.  Its  outlooks  are 
conditioned  by  different  considered  factors  and  confirmed  by  the  first  experimental  and  theoretical  results. 


I.  INTRODUCTION 

The  combined  use  of  different  means  is  one  of  the  main  principles  of 
nature  development.  The  study  of  hydrodynamic  problems  of  bionics 
(Aleyev  [1],  Bushnell  &  Moore  [2])  also  convinces  us  of  correctness  of 
this  statement.  Bionics  is  the  way  from  observations  and  astonishment  at 
making  the  first  estimations  (the  conclusion  about  the  paradox  existence) 
to  the  explanation  for  the  phenomenon. 

The  characteristic  “nature”  example  of  the  study  of  bodies  with  low 
drag  is  the  investigation  of  dolphins,  the  search  of  reasons  of  well  known 
paradox  of  Gray  [3].  These  investigations  showed  that  in  consequence  of 
long  evolution  dolphins  possess  different  variants  of  adaptation  to  the 
different,  rapidly  changing  conditions  of  their  inhabitation  in  sea 
(Woodcock  [4],  Focke  [5],  Semenov  [6],  Alekseeva  &  Semenov  [7],  Wu  & 
Chwang  [8]).  Here  the  excellent  variants  of  economical  swimming  of 
dolphins  were  discovered  and  described.  For  example,  Woodcock  [4] 
described  the  ’’motionless”  swimming  of  dolphins  near  the  ship  nosing. 
Focke  [5]  investigated  this  fact.  He  showed  by  calculations  that  dolphins 
(using  pressure  distribution  near  the  ship  nosing)  can  swim  with  any  ship 
velocity  and  without  essential  energy  losses  (as  “external  passengers  of 
ship-travellers  without  tickets”).  The  other  example:  Wu  and  Chwang  [8] 
show  by  theoretical  calculations  that  dolphins  can  obtain  an  energy  for 
their  swimming  from  a  wavy  stream.  So  they  can  swim  in  sea  waves  with 
minimum  energy  losses  (quoted  work  permit  to  explain  the  physical 
essence  of  surf  boards  too).  Above-mentioned  results  requested  to 
introduce  new,  additional  conditions  for  a  selection  of  dolphin  speed 
observations  (used  for  analysis  of  Gray’s  paradox).  But  note:  they  can’t 
explain  Gray’s  paradox  for  observations  of  high  speed  swimming  of 
dolphins  under  conditions  of  the  absolute  calm,  far  from  ships.  And  here 
the  other  conclusion  is  important.  As  the  result  of  long  evolution  dolphins 
enjoyed  different  variants  of  an  adaption  to  very  different  and  often 
changed  residing  conditions  in  sea.  So  our  problem  is  a  search  and  a  study 
of  many  “secrets”of  dolphins.  Here  the  analysis  of  the  dolphin  body  shape 
(Young  [9],  Hertel  [10])  was  the  important  step  to  explain  the  observed 
low  drag.  The  other  important  step  was  made  by  Kramer  [11-13],  who 
simulated  the  dolphin  skin  compliance  in  delaying  the  transition  to 
turbulence.  Now  Semenov  [14]  has  given  the  additional  explanation  for 
low  drag  (of  dolphin  Tursiops  Tursio  Ponticus)  taking  into  account  also 
the  possibilities  of  joint  use  of  compliant  dolphin  skin,  water-soluble 
secretions  decreasing  drag  and  gas  microbubbles  observed  in  experiments. 

Technical  progress  is  connected  with  this  main  principle  of  nature 
development  (the  combined  use  of  different  means)  too.  There  are  a  lot  of 
possible  variants  of  the  combined  use  of  different  (and  numerous)  methods 
of  drag  reduction  for  different  hydrodynamic  conditions.  Two  passive 
means  (compliant  coatings  and  riblets)  and  two  active  means  (polymeric 
additives  and  gas  microbubbles)  are  considered  here  in  order  to  estimate 
outlooks  for  their  joint  action  investigations. 

II.  SOME  NOTES  ON  INVESTIGATION  OUTLOOKS 

These  notes  can  be  interesting  to  both  researches  of  near-wall 
turbulence  and  representatives  of  industry  using  scientific  successes.  So 
first  of  all  it  is  important  to  note  that  all  considered  methods  of  turbulence 
management  (compliant  coatings,  riblets,  air  microbubbles,  PEO  additives) 
satisfy  the  requirements  of  the  ecology. 

The  motivations  of  fine  outlook  on  joint  use  of  the  considered 
methods  of  drag  reduction  can  be  divided  into  four  groups: 

Initial  approach. 

The  initial  approach  to  joint  use  of  different  drag  reducing  means 
took  into  account  only  the  simplified  dependence  of  possible  drag 
reduction  efficiency  *F  for  their  joint  action  on  their  individual 
efficiencies  \P. : 


T  =  1-(1-¥1)(I-'P2)...(1-T'„)  (1) 

This  expression  is  correct  if  all  considered  drag  reducing  means  act 
independently  and  don’t  change  the  action  conditions  for  the  others.* 

In  this  case  the  possible  drag  reduction  efficiency  for  joint  action  of 
different  drag  reducing  means  must  be  less  then  the  sum  of  their  individual 
drag  reducing  possibilities 

vP<£xl'  for  >0  (2) 

/=0 

The  prognosticated  negative  deviation  from  the  sum  of  individual 


n 

efficiencies  dev  *F  =  *F  —  ^  depends  on  their  values  and 

/= 0 

number  n  of  means  used  jointly  for  turbulence  management. 

These  dependences  can  be  analysed  at  ease  for  the  variant  of  equal 

individual  efficiencies:  x¥l  =  *F2  =  ...  =  x¥n .  So  the  deviation  from 
the  sum  of  individual  efficiencies  is  calculated  as 


dev'¥  =  \-y£'¥i- \\-Z%  n 
1=0  V  /= o  /  , 

This  deviation  increases  for  increasing  n. 

And  for  n»  1  it  has  the  limit: 

n  (  n  ^ 

lim  (dev  VF)  =  1-£'I'  -  exp  ]T  y. 

;=0  X i=0  ' 


(3) 


(4) 


Figure  1.  The  deviation  of  drag  reduction  for  joint  use  of  different 
drag  reducing  means  from  the  sum  of  their  individual  efficiency 
values:  prognosis  according  to  (3)  and  (4). 

Results  of  this  prognosis  are  shown  in  Fifure  1.  The  prognosticated 
negative  deviations  are  small  when  the  sum  of  individual  efficiencies  is 
less  then  20%.  But  they  are  very  considerable  for  80%  sum:  for  example, 
devx¥  =  —  0.16  for  two  combined  drag  reducing  means  and 

dev *F  =  -  0.25  for  n»  1. 


*Here  and  further  drag  reduction  efficiency  is  considered  concerning 
turbulent  friction  coefficient  c/o  for  smooth  hard  surface: 

-<•,/«/»■ 


269 


This  approach  was  used  for  our  initial  estimations.  Viscoelastic 
coatings,  riblets,  gas  bubbles  and  polymer  additives  are  four  well  known 
means  for  the  action  on  near-wall  turbulence.  Their  actions  for  the 
decrease  of  the  turbulence  production  are  very  different. 

Compliant  surface  reacts  on  the  long-wave  disturbances.  According 
to  the  estimation  of  the  interference  theory  of  Semenov  [15]  and 
experimental  data  of  Kulik  et  al.[16]  the  real  viscoelastic  coating  is 
deformed  by  the  pressure  wave  with  length  more  than  one  thousand 

viscous  scales.  Viscous  scale  is  vj Ud  ,  where  friction  velocity  is 

vd  =  (tw  Ipf  ,  p  and  V  are  density  and  viscosity  of  flow, 

T  w  is  friction  stress  on  a  wall  (Hinze  [17]).  The  small  additives  in  a  flow 
put  out  the  microeddy  turbulence  for  the  turbulence  linear  scales  less  than 
one  hundred  viscous  scales  (Greshilov  et  al.[18]).  Riblets  manage 
microeddy  structures  too  (Choi  [19]).  The  flowing  screen  of  gas  bubbles 
can  destroy  the  long-wave  powerful  fluctuations  going  to  the  wall  from  the 
turbulent  core  and  background  flow  (Bogdevich  et  al.[20]). 

It  is  known  (Hinze  [17],  Cantwell  [21])  that  in  the  main  both 
microeddies  of  viscous  sublayer  and  long  waves  of  turbulent  core  generate 
a  new  turbulence.  So  the  joint  use  of  considered  methods  of  drag  reduction 
gives  possibility  to  wait  for  new  qualities  of  turbulence  production 
decrease.  Therefore  the  combined  use  of  these  four  methods  permits  to 
obtain  the  best  results  in  turbulent  drag  reduction  as  compared  with  above 
described  prognosis. 

Association  of  useful  qualities. 

A  study  of  joint  use  of  different  methods  of  drag  reduction  is 
promising  because  of  a  number  of  other  reasons  too.  It  is  attractive  already 
as  the  base  for  a  possible  association  of  other  (in  addition  to  drag  reduction 
possibility)  useful  properties  which  are  inherent  in  separate  methods. 

For  example,  drag  reducing  compliant  coatings  can  have  the  high 
anti-corrosion  properties.  One-layer  coatings  created  in  Institute  of 
Thermophysics  of  Russian  Academy  of  Sciences  (Kulik  et  al.[22])  have 
the  excellent  immunity  to  a  damage  by  acids  and  alkalis. 

An  other  example:  the  tests  carried  out  by  Russian  and  Bulgarian 
scientists  (Malyuga  et  al.[23])  show  that  the  creation  of  an  air-bubble  layer 
in  near-wall  region  is  a  sufficiently  effective  method  for  reducing  the 
amplitudes  of  the  propelled  -  induced  pressures  and  the  plate  vibrations  for 
ships. 

And  thirdly,  for  joint  use  of  compliant  coatings,  air  microbubbles  and 
polymeric  additives  it  is  possible  to  suppress  the  turbulent  wall-pressure 
fluctuations  in  the  very  wide  frequency  band,  that  is  impossible  for  any 
method  used  separately.  So  it  is  possible  to  believe  that  these  combinations 
will  lead  to  the  strong  decrease  of  the  hydrodynamic  noise  in  the  very  wide 
frequency  band  too. 

Here  it  is  important  into  take  to  account  the  economic  factor. 

The  turbulence  management  by  compliant  coatings  and  riblets  is 
particularly  useful  due  to  their  passive  nature.  As  a  result  additional  energy 
is  not  required  for  the  turbulence  control.  The  injection  of  gas 
microbubbles  and  polymer  additives  is  connected  with  the  consumption  of 
some  energy  and  materials.  Although  drag  reduction  by  the  high-molecular 
polymer  additive  use  is  realized  for  its  very  small  concentration  in  a  flow, 
the  expenses  for  its  use  may  be  higher  than  the  economy  (for  example)  of 
expenses  for  fuel.  Therefore  Berman  [24]  suggested  to  estimate  the 
specific  efficiency  /c  ,  determining  the  expediency  of  drag 

reduction.  He  had  shown  that  for  a  flow  in  pipe  ^ pjcp  was  decreased 

as  the  concentration  C p  was  increased  (for  a  flow  with  constant 

concentration  of  polymer  additives)  and  was  significantly  less  at  the 
friction  minimization  than  specific  efficiency  at  moderate  values  of  drag 
reduction  Wp  .  It  is  connected  with  nonlinear  form  of  dependence  of 

on  C p  and  asymptotic  achievement  of  maximum  value  of  drag 

reduction.  Semenov  [25,  26]  has  carried  out  analogous  analysis  for  a  flow 
with  variable  concentration  of  polymer  additives  in  a  flow  (for  turbulent 
boundary  layer  on  a  plate)  and  showed  that  from  the  point  of  view  of  profit 
it  is  worth  while  not  to  tend  to  the  drag  minimization  but  to  restrict  drag 


reduction  nearly  twice  (*p  <  50%).  So  the  combined  investigations  must 

be  carried  out  for  variants  of  small  consumptions  of  PEO  too.  And  only  the 
joint  use  of  the  considered  methods  can  permit  to  achieve  maximum  and 
profitable  efficiency  of  drag  reduction. 

The  similar  situation  is  realized  for  drag  reduction  using  gas-bubbles. 
However  in  this  case  it  is  possible  even  to  achieve  drag  reduction  “free  of 
charge”  by  the  use  of  engine  exhaust. 

“Mutual  aid”  of  different  drag  reducing  means. 

And  after  all  here  it  is  necessary  to  enumerate  to  some  other  factors 
of  an  interaction  between  jointly  used  methods  of  turbulence  management. 
They  are  subject  to  a  study  as  proposed  factors  of  "a  mutual  aid" 
promoting  to  an  appearance  of  new  qualities. 

The  flowing  screen  of  gas  bubbles  destroyes  the  powerful 
fluctuations  going  to  a  wall  from  the  turbulent  core  and  background  flow. 
So  the  bubble  screen  defends  polymer  additives  acting  with  high  efficiency 
just  in  near-wall  region.  It  decreases  their  ousting  from  this  region. 

The  drag  reducing  polymers  (polyethylene  oxide,  polyacril  amide 
etc.)  are  the  surface-active  substances  which  decrease  the  surface  tension 
and  so  the  separation  diameter  of  a  bubble  at  its  generation  on  the  porous 
injecting  insert.  Besides  polymer  additives  in  flow  prevent  the  bubble 
coalescence  and  also  impede  bubble  rising.  Note  that  it  is  very  important 
for  drag  reduction  to  have  microbubbles  with  diameter  less  than  0.2  mm. 
The  decrease  of  microbubble  diameter  leads  to  an  improvement  of 
screening  properties  of  bubble  layer,  to  a  displacement  of  the  peak 
concentration  of  gas  bubbles  in  water  flow  to  a  wall  and  to  a  decrease  of 
the  bubble  buoyancy  velocity.  Hence,  one  can  expect  that  the  flow  of  high- 
polymer  solutions  aerated  by  gas  bubbles  will  result  in  mutual  increase  of 
the  effects  of  drag  reduction  on  a  streamlined  surface  (Malyuga  et  al.[27, 
28]). 

Waves  and  eddies  are  responsible  for  the  near-wall  turbulence 
production  near  smooth  surface.  The  wave  action  role  is  decreased  as  a 
result  of  the  surface  roughness  increase.  Compliant  coatings  respond  to  the 
pressure  fluctuation  waves.  So  the  viscoelastic  boundary  action  losses  a 
physical  sense  as  a  result  of  high  roughness  of  surface  (Semenov  & 
Semenova  [29,  30]).  The  increase  of  the  viscous  sublayer  thickness  by 
polymer  additives  increases  the  permissible  roughness  of  compliant 
surface  that  simplifies  and  cheapens  the  coatings  preparation  technology. 

Semenov  &  Semenova  [29,  30,  31]  have  carried  out  the  first 
calculations  for  joint  action  of  compliant  boundary  and  polymer  additives 
in  the  turbulent  boundary  layer  in  order  to  explain  the  obtained 
experimental  results  (Semenov  et  al.[32,  33],  Kulik  et  al.[34,  35]).  One  of 
possible  factors  of  an  interaction  between  two  considered  methods  of 
turbulence  management  is  the  action  of  compliant  boundary  on  mass 
transfer  in  near-wall  region.  Carried  out  calculations  showed  that  the  mass 
transfer  decrease  (increase)  by  the  use  of  viscoelastic  coating  decreases 
(increases)  the  polymer  consumption  a  little.  The  other  factor  is  the 
influence  of  polymer  additives  in  a  flow  on  the  interference  action  of 
viscoelastic  boundary  on  near-wall  turbulence.  The  calculations  show  that 
injected  polymer  additives  extend  the  phase-frequency  region  of  positive 
action  of  compliant  boundary,  i.e.  they  extend  possibilities  of  drag  (and 
noise)  reduction  by  compliant  coatings.  These  two  problems  are  described 
in  Section  IV  in  details. 

Semenov  &  Semenova  [29,  30]  considered  the  action  of  drag 
reducing  riblets  for  joint  use  with  compliant  coating  and  concluded  that  its 
extend  the  phase-frequency  region  of  positive  action  of  compliant 
boundary  too. 

The  viscoelastic  coating  for  drag  reduction  is  the  mechanical 
vibrational  system  with  amplitude-phase-frequency  characteristic  chosen 
for  action  on  near-wall  turbulence  spectrum  band  responsible  for  the  main 
production  of  new  turbulence.  And,  of  course,  this  choice  must  take  into 
account  the  existence  of  the  natural  turbulence  background  conditions. 
However,  both  for  different  usual  experimental  hydrodynamic  installations 
and  for  practical  objects  (ships,  pipe-lines)  the  existence  of  additional 
strong  pressure  fluctuations  in  flow  is  quite  possible.  These  additional 
pressure  fluctuations  can  swing  the  compliant  coating  in  the  frequency 
region  of  its  negative  action  very  essentially.  So  the  total  production  of 
new  turbulence  (for  all  frequency  region)  can  be  even  increased.  The 
important  factor  of  an  action  of  gas  bubble  layer  is  the  defence  of  near¬ 
wall  region  of  the  turbulent  boundary  layer.  So  the  injection  of  gas  bubbles 
into  near-wall  flow  will  ensure  stable  drag  reduction  action  of  viscoelastic 
coating  for  different  exploitation  conditions. 


270 


Further  the  following  indexes  are  used  for  meaning:  compliant  surface 
-  C,  polymer  additives  -  P ,  air-microbubbles  -  A ,  riblets  -  r  and  joint  use  - 
their  combinations. 

III.  EXPERIMENTAL  INVESTIGATIONS 

Quantity  of  experimental  investigations  is  the  little  still.  Only  some 
variants  of  joint  use  of  different  drag  reducing  means  were  considered. 

Already  the  first  experiments  (carried  out  at  the  Institute  of 
Thermophysics  RAS)  for  joint  use  of  compliant  coatings  and  polymer 
additives  (Semenov  et  al.[32,  33])  showed  fine  outlooks  of  this  study.  There 
was  obtained  that  the  total  effectiveness  of  turbulent  drag  reduction  is  equal 
to  the  algebraic  sum  of  the  individual  small  effectivenesses  of  these  methods 
of  turbulence  management.  These  successes  initiated  new  investigations. 

Experimental  conditions. 

The  experiments  were  carried  out  in  the  saline  lake  Issyk-Kool  where 
2Am  -  long,  0. 175/w  -  diameter  streamline  body  of  revolution  was  towed  by 
the  tow  boat  with  speed  [/  =  6  -  1 5 mis. 


1  11  2  11  JJ 


J _ L-L 


f-  f 


Figure  2.  Scheme  of  the  model  with  the  dimensionless  hydrodynamic 
pressure  distribution.  1  -  nosing,  2  -  floating  cylindrical  element,  3  -  stem 
part,  4  -  thrust  tube,  5  -  knife  strut,  6  -  ringed  slot,  7  -  porous  insert, 
8  -  floating-drag  balance,  9  -  piezoresistive  pressure  transducer,  10  -  three- 
component  balance,  1 1  -  ringed  slit. 

This  model  (see  Fig.  2)  was  described  in  details  formerly  by  Kulik  et 
al.[16,  36].  It  was  equiped  (in  the  middle  of  its  length)  with  0.66 m  -  long 
“floating”  surface  element  for  measuring  of  the  skin-friction  drag.  There 
were  tested  different  variants  of  these  cylindrical  elements.  OneTrad-a^olid 
smooth  surface  and  the  others  were  mounted  with  compliant  coatings. 
Careful  measurement  of  friction  coefficient  for  the  case  of  hard  polished 

surface  in  water  flow  cf  was  used  for  comparison  as  a  standard. 

Jo 


Figure  3.  The  dimensionless  spectra  of  wall-pressure  fluctuations  measured 
behind  floating  element  with  hard  surface.  JJQ=  9  m/s. 

The  model  nosing  had  a  ring  slot  for  polymeric  solution  injection.  The 
model  was  equiped  with  the  35-mm  long  insert  made  from  porous  metal  for 
air  injection.  Sizes  of  injected  microbubbles  are  varied  from  0.07  mm  to  0.2 
mm. 


All  experiments  were  carried  out  for  low  background  turbulence 
conditions.  The  spectrum  analysis  of  measured  wall-pressure  fluctuations 
(see  the  example  in  Figure  3)  in  frequency  band  from  10  Hz  to  10  kHz 
revealed  strong  peaked  deviation  from  smooth  distribution  in  frequency  only 
for  low  frequencies  (below  20  Hz),  that  is  inessential  for  these 
investigations. 

All  experimental  conditions  were  described  in  details  by  Semenov  et 
al.  [37]. 

Joint  action  of  compliant  coatings  and  polymer  additives. 

New  results  of  these  investigations  were  described  by  Kulik  et  al.[34, 
35],  Semenov  et  al.[37].  There  was  varied  the  mass  consumption  q  of 
polyethylene  oxide  (PEO  of  different  molecular  mass  M).  The  corresponding 
dimensionless  parameter  is  qs  -q  j^ppnD  6  U0)>  where  D  is  diameter 

of  the  measured  “floating”  element,  pp  -  density  of  PEO,  8  -  thickness 
of  turbulent  boundary  layer  calculated  for  water  flow  (with  temperature  7) 
without  polymer  additives  for  the  middle  abscissa  of  the  “floating”  element 
(with  solid  smooth  surface).  According  to  Kutateladze  &  Leontyev  [38]  the 
thicknesses  of  diffusion  and  dynamic  turbulent  layers  near  this  “floating” 
element  are  approximately  equal.  So  q5  is  like  to  the  near-wall 

concentration  of  PEO  for  the  middle  abscissa  of  the  “floating”  element. 

The  first  experimental  results  of  Semenov  et  al.[32,  33]  showed  that 

¥ rCP(qs)  ls  shifts  concerning  s0  351 

xPCp(<3f(y)  «  'i'c  +  ^ P  (#<?)»  i  e-  ^  summarizing  property  was 

discovered  for  the  joint  of  compliant  coating  and  polymer  additives  that 
confirmed  our  initial  prognosis  for  small  individual  effectivenesses. 
However  contrary  to  initial  estimations  it  was  noted  that  for  the  case  of 
increase  of  separate  effects  the  magnitude  of  combined  drag  reduction 
exceeded  their  sum.  So  further  it  is  considered  the  deviation  of  the  drag 
reduction  efficiency  for  joint  action  from  the  sum  of  the  drag  reduction 
efficiencies  for  separate  actions  in  order  to  investigate  this  summarizing 
property. 


Figure  4.  Deviation  of  friction  reduction  for  joint  use  of  compliant  coating 
and  polymer  additives  from  the  sum  of  their  individual  efficiencies  as  a 
function  of  efficiency  of  joint  action. 

For  U0  =9  m/s: 

^  coating  N6  (  from  compound  Nl,  H~ 2  mm  ),  T  =  16... 17  °C 
y/c  =  —1 1.5%,  Af(PEO)  =3.5  min.,  2.1  •  10"6  <  qs  <  1.2  •  1(T5 ; 

coating  A,  T  -  8.5... 10.5  °C,  ^c=+2.6%>  Af(PEO)=4.5  min., 
6.0- 10~8  <  qs  <  5*  10"7  i 

®  coating  N10  (from  compound  N2,  H  -  7  mm),  T=  17°C,  y/c  =  +6%  > 
Af(PEO)  =  3.5  min,  1.6 -10“6  <qs  <M0"5; 

^  coating  N  10,  T  =10.5  °C,  ^c  =  +12%,  MPEO)=3.5  min., 

3.5  •  1 0”6  <  qs  <  5.5  ■  10“6 ; 

For  U0=  7  m/s:  T=  6.5...8.5  °C,  M(PEO)  =  4.7  min, 

M coating N 10,  y/c  =  +5%  ,  4-10"7  <qs  <  3.5- 10"6 ; 

^  coating  N7  (from  compound  N2,  H  ~  2.5  mm\  ^c  =  +9%, 

4*  10“7  <qs  <  3.5 « 10"6  • 


271 


In  Figure  4  are  shown  data  (from  Semenov  et  al.[37])  for  the  joint  use 
of  different  compliant  coatings  (both  decreasing  and  increasing  the  turbulent 
friction)  and  polymer  additives  (for  the  great  variation  of  polymer 
consumption  and,  accordingly  ).  These  results  witness  the  existence  of 
three  zones: 

1)  zone  of  the  exact  sum  of  individual  efficiencies 

2)  zone  of  positive  deviation  (VFC?(^^)>  4^  +  4* ^ 

3)  zone  of  negative  deviation  CP  (q  g')  <  4*  c  +  4/ P  (<?  *  )  )• 

Here  the  zone  of  the  exact  sum  is  observed  for  all  tested  variants  till 
<  20%  •  Zones  of  positive  and  negative  deviations  follow  the  zone 
of  the  exact  sum  when  polymer  consumption  increases.  But  here  we  see 
considerable  differences  for  different  tested  variants. 


p 


Figure  5.  The  comparison  of  drag  reduction  deviations  calculated  according 
to  (5)  (lines)  with  measured  deviations  (signs) 

A 

Wc 


=-115%.  >ine  1; 

+12%.  line  2; 

=  +6%  ,  line  3; 

■t1  y/c  =  +2.6% ,  line  4; 

c  =  +9%  .line  5; 

®  i//c  =+5%.  line  6 

Experimental  results  from  Figure  4  are  shown  in  Figures  again  for 
their  comparison  with  initial  prognosis.  Here  these  results  are  considered  in 
dependence  on  drag  reduction  of  hard  surface  by  polymer  additives  i.e.  on 
individual  efficiency  of  polymer  additives  *¥p . 

According  to  (1):  ^cp  =  1  -  (l  -  4'c)(l  -  4^) .  The  prognosticated 
deviation  must  be 

dev  'V  m  yc/,  -  (^c  +  %,)  =  (5) 

So  in  this  case  the  deviation  must  be  negative  for  “positive  coating” 
( 4/c  >  0 )  and  positive  for  “negative  coating”(  4/c  <  0  )■ 

The  deviations  prognosticated  according  to  (5)  (shown  in  Figure  5  by 
lines)  are  contrary  to  experimental  data  for  the  second  and  third  zones.  Thus 
these  results  show  the  presence  of  an  interaction  of  compliant  coating  and 
polymeric  additives.  So  above  mentioned  zones  can  be  termed  as: 

2)  zone  of  positive  interaction  of  two  considered  methods  of  drag  reduction 

(With  'VCP{qs)>  vc  +¥, (*,)); 

3)  zone  of  negative  interaction  of  two  considered  methods  of  drag  reduction 

(w  i*’M*,)<,rc  +  'F,(9,))- 

Joint  action  of  air-microbubbles  and  polymer  additives. 

Malyuga  et  al.  [27,  28]  carried  out  the  first  experiments  on  drag 
reduction  using  the  injection  of  PEO  (WSR-301)  -  solutions  aerated  by  air 
bubbles.  They  measured  the  friction  in  3  points  of  the  hard  flat  plate  from 


distance  0.25m  (Nl),  0.99m  (N2)  and  2.23m  (N3)  behind  the  slot  for  JJ  0  * 
5  -  10 m/s.  They  determined  that  an  aeration  of  injected  PEO  solutions  can 
lead  to  an  increase  of  their  efficiency  of  drag  reduction.  The  maximum 
additional  increase  of  their  efficiency  was  measured:  36%  in  point  N2  and 
16%  in  point  N3.  But  in  point  N2  were  measured  both  an  increase  and  a 
decrease  of  drag  reduction  efficiency.  And  here  the  results  were  worse  for  an 
increase  of  PEO  consumption.  It  is  important  to  note,  that  used  highly  large 
consumptions  of  injected  air  and  polymer  were  in  this  experiment.  The 
corresponding  dimensionless  parameters  were 

1.3  •  1CT3  <  CA  =  Q/(U0  ■  S)  <  1.7  •  10“3 ; 

1.05  -1(T6  <qs  <7.8-10~6. 

Here  S'  is  the  surface  of  studied  plate  part,  Q  is  the  volumetric  consumption 
of  injected  air. 


% 


Figure  6.  Deviation  of  friction  reduction  on  hard  surface  for  joint  use  of 
polymer  additives  and  air  microbubbles  from  the  sum  of  their  individual 
efficiencies  as  a  function  of  efficiency  of  joint  action. 

+  u  0=  9  m/s,  M(PEO)=4.5  min.,  1.0  •  107  <qs  <4.6-l(T7, 

2.3  10-4  <CA  <3.2  10'4; 

•  u  0=  7  m/s,  WSR-301,  1.0  •  10'6  <  qs  <  2.7  •  10'\ 

1.36-1 0'3  <CA<>  1.73-1  O’3. 

Some  above  mentioned  results  and  new  data  (Semenov  et  al.[37]) 
obtained  in  experiments  (described  in  Section  “Experimental  conditions”) 
for  very  small  consumptions  of  air  and  polymer  are  shown  in  Figure  6.  Here 
we  can  see  the  same  three  zones:  the  zone  of  exact  sum,  zones  of  positive 
and  negative  interaction. 

Note,  that  the  negative  interaction  zone  corresponds  to  very  high 
consumptions  of  PEO  and  air. 

Joint  action  of  compliant  coating  and  air-microbubbles. 

The  first  experiment  is  described  by  Semenov  et  al.  [37].  One 
compliant  coating  was  tested  for  very  small  consumption  of  injected  air: 
2.M0"4  <tCA  <  3.7*  10-4  ♦  U  0  =  9  m/s,  T=  8.5... 10.5  °C.  Drag  reduction 
of  hard  surface  by  air-microbubbles  tp  was  varied  from  7%  to  14%.  There 
was  obtained  that  the  total  efficiency  of  turbulent  drag  reduction  is  equal  to 
the  sum  of  individual  efficiencies:  mcA  =  4^  +  4^  • 

Joint  action  of  riblets  and  surface  compliance. 

According  to  theoretical  estimations  of  Semenov  &  Semenova  [29] 
this  combination  must  be  the  fine  variant  of  passive  (without  energy 
expenditure)  methods  of  turbulent  drag  reduction. 

But  experimental  data  are  still  absent. 

Joint  action  of  riblets  and  polymer  additives. 

The  first  experimental  results  were  described  by  Reidy  &  Anderson 
[39]  and  Choi  et  al.  [40].  They  have  found  that  the  individual  effectivenesses 
of  two  methods  of  drag  reduction  are  sumed  up  for  their  joint  use.  Note:  they 
considered  very  small  consumptions  of  polymers. 

Koury  &  Virk  [41]  and  Virk  &  Koury  [42]  investigated  this  problem  in 

detail:  for  two  polyethyleneoxides  (M~  5.3*  106 and  M  =  7.9*106)  and 
one  polyacrylamide  ( M  =  7.4*  106),  in  two  hydraulically  smooth  pipes  of 
7.82mm  and  10.2mm  i.d.  and  in  four 


272 


riblets  pipes  formed  by  respectively  lining  each  of  the  smooth  pipes  with 
0.11  mm  and  0.15 mm  V  -  groove  riblets  of  equal  height  and  spacing. 
Within  the  polymeric  regime,  at  moderate  drag  reductions  of  order  50%, 
drag  reduction  in  the  riblet  walled  pipe  significantly  exceeded  that  in  the 
smooth  pipe,  by  as  much  as  15%.  But  the  greatest  drag  reduction  by  riblets 
in  water  was  measured  -  10%.  So  the  positive  deviation  from  the  exact 
sum  of  individual  effectivenesses  is  observed  here.  At  conditions  of 
asymptotic  maximum  drag  reduction,  of  order  80%,  friction  factors  in  the 

present  riblet-walled  pipe  were  identical  to  smooth  for  h+ <  10,  but 
departed  off  the  smooth  asymptote  in  the  direction  of  lesser  drag  reduction 

for  h+  >  10.  And  here  the  negative  interaction  is  observed. 

Joint  action  of  riblets  and  air-microbubbles. 

The  opinion  about  the  promising  study  of  this  combination  is  based 
on  an  expectation  that  riblets  and  air-microbubbles  manage  with  very 
differed  structures  of  turbulence.  But  both  experimental  and  theoretical 
investigations  were  not  carried  out  still. 

Joint  action  of  compliant  coating,  air-microbubbles  and  polymeric 
additives. 

The  first  experiment  is  described  by  Semenov  et  al.  [37].  Russian 
scientists  measured  the  friction  of  floating  cylindrical  element  (see 
“Experimental  conditions”  here).  They  carried  out  tests  for  very  small 
consumptions  of  air  and  PEO.  They  used  the  one-layer  compliant  coating 
tested  also  by  Choi  et  al.  [43]  after  this  experiment.  Results  are  shown  in 
Figure  7.  Here  the  positive  deviation  increases  monotonously  with 
increasing  consumptions  of  air  and  PEO.  It  showes  the  presence  of  an 
interaction  of  compliant  coating,  air-microbubbles  and  polymer  additives 
in  whole  region  of  this  investigation. 

Note:  the  effectiveness  of  drag  reduction  for  joint  use  of  compliant 
coating,  air-microbubbles  and  PEO-additives  exceeded  the  sum  of 
individual  effectivenesses  by  as  much  as  1 1%  (for  =35%). 


% 


Figure  7.  Deviation  of  friction  reduction  for  joint  use  of  compliant  coating 
A,  air  microbubbles  and  polymer  additives  from  the  sum  of  their  individual 
efficiencies  as  a  function  of  efficiency  of  joint  action.  T  ~  8. 5. ..10. 5  °C, 
f/0=  9  m/s,  M( PEO)=4.5  min,  15- 1CT7  <  qs  <  4.5  •  10'7 , 
2.0 -KT4  <  CA  <3.7-1  O’4. 

IV.  THEORETICAL  ANALYSIS  OF  INTERACTION  BETWEEN 
COMPLIANT  BOUNDARY  AND  POLYMER  ADDITIVES 

The  discovered  peculiarities  of  drag  reduction  using  a  complex  of 
different  methods  of  turbulence  management  require  theoretical 
explanations. 

Compliant  coatings  and  polymer  additives  manage  with  very  differed 
structures  of  near-wall  turbulence.  So  both  methods  of  drag  reduction  are 
independent  according  to  this  point  of  view. 

But  other  factor  of  an  interaction  between  compliant  boundary  and 
polymer  additives  is  a  possible  reason  of  observed  contradictions  between 
experimental  data  and  initial  prognosis:  a  change  of  action  conditions  of 
one  method  by  other  method  of  drag  reduction. 

The  considered  influence  of  the  viscoelastic  boundary  on  the  turbulent 
diffusion  of  polymer  additives. 

One  possible  factor  of  an  interaction  between  two  considered 
methods  of  turbulence  management  is  the  action  of  compliant  boundary  on 


mass  transfer  in  near-wall  region.  Here  the  integral  approach  was  used. 
The  calculation  analysis  was  carried  out  on  the  base  of  approximate  model 
[26]  for  a  flat  plate  analogous  to  the  construction  scheme  tested  in  quoted 
experiments  [32-35]  described  here  in  Section  “Experimental  conditions”. 

It  is  supposed  that  the  slot  injection  of  PEO-solutions  at  x ,  satisfies 
the  conditions  of  pulseless  injection  of  polymeric  additives  into  near-wall 
flow  [25].  Here  the  constant  efficiency  of  drag  variation  using  compliant 
coating  *FC  (independent  on  polymer  additives  in  flow)  is  considered  from 
X\~  0.35 L  to  jc 2  =  0.65 L .  L  is  the  body  length.  For  this  part  of  the 
body  it  was  calculated: 

\{'Vc  +  'VT-Vc'VI)cfodx  \cf,dx  (6) 

/  JCi 

The  local  friction  reduction  by  PEO  additives  is  determined  according  to 
the  formula  grounded  in  [26]: 

Tr  =  0.5  larct^'i  cw  Moss)  (7) 

The  near-wall  concentration  of  PEO  may  be  determined  according  to 
the  experimental  data  of  Fabula  &  Bums  [44]  as: 

Cw  —  'IqL/Sw  (8) 

The  thickness  of  turbulent  boundary  layer  Sy  is  determined  as 

(9) 

X , 

where  R  q}  =  U0  Xi/  V ,  V  is  the  kinematic  coefficient  of  water 
viscosity,  4^  =  0  for  x  <  X\  and  x  >  X2-  Here  the  existence  of  laminar 
boundary  layer  from  X  =  0  to  jc/  is  proposed.  In  the  point  of  transition 
from  laminar  form  a  flow  to  a  turbulent  one  (at  jc  =  x,)  the  condition  of 
continuity  of  momentum  thickness  is  written.  On  its  base  the  initial 
thickness  of  turbulent  boundary  layer  at  x  =  Xi  is  determined.  Here  the 
power  form  of  the  velocity  profile  with  index  1/1 1  was  taken. 

So  the  friction  coefficient  (without  polymer  injection)  is  calculated 
according  to  the  Falkner’s  formula  [45]: 

c/o =  0.0256(xt/0/v)X  (10) 

The  system  of  equations  (7),  (8),  (9)  is  solved  for  given  molecular  M, 
dimensionless  coefficient  of  PEO  consumption  q=q/pjJ0S, 
Reynolds  number  R q  =  (J0L/v-  After  its  solution  the  drag  variation 

'Vcp  (for  *  0)  and  drag  reduction  'Fp  (for  4^c  =  0)  are  calculated 
according  to  (6).  On  the  base  of  these  calculations  the  deviation  of  drag 
reduction  for  joint  use  of  compliant  surface  and  polymer  additives  from  the 
sum  of  efficiencies  for  separate  actions  is  determined. 

% 


Figure  8.  The  estimation  of  the  mass  transfer  change  influence  by  the 
viscoelastic  boundary  on  drag  reduction  deviation  (points).  Lines 
correspond  to  the  initial  prognosis  according  to  (5). 

The  carried  out  calculations  show  that  the  mass  transfer  decrease 
(increase)  by  use  of  viscoelastic  coating  decreases 


273 


(increases)  the  polymer  consumption  a  little.  So  it  is  unlikely  that  is  the 
main  factor  of  the  interaction  between  these  two  methods  of  turbulence 
management.  However  this  approach  can  and  must  be  taken  into  account 
for  future  investigations  and  accurate  analysis. 

One  example  is  shown  in  Fig. 8.  We  see  that  in  both  considered  cases 
(vpc  =  20%  and  %  =  -20%)  the  calculated  deviations  (points)  differ  from 
the  initial  prognosis  (lines)  inessentially. 

The  interference  action  of  viscoelastic  boundary  on  near-wall 
turbulence  in  flow  with  polymer  additives. 

Here  the  other  factor  of  interaction  between  two  methods  of  drag 
reduction  (the  influence  of  polymer  additives  in  a  flow  on  the  interference 
action  of  viscoelastic  boundary  on  near-wall  turbulence)  is  considered. 

Formerly  the  interference  form  of  compliant  boundary  action  was 
analysed  by  Semenov  [46,15]  for  turbulent  near-wall  flow  of  Newtonian 
fluids.  He  used  the  near-wall  turbulence  model  of  Sternberg  [47].  The  main 
modelling  parameter  (written  by  Semenov  for  solution  of  problem  [46])  is 
the  complex  dimensionless  compliance  of  boundary.  He  determined  the 
region  of  this  parameter  values  for  drag  reduction  [48-50].  This  theoretical 
model  was  used  for  modelling  and  choice  of  one-layer  compliant  drag 
reducing  coatings.  These  coatings  provided  up  to  20%  drag  reduction  in 
experiments  [16,  36].  They  were  used  in  above  -  written  experimental 
combined  investigations  of  different  methods  of  turbulence  management 
too. 

Here  the  interference  approach  is  used  for  a  compliant  boundary  of  a 
water  flow  with  PEO  additives.  In  this  case  is  suitable  the  former  solution 

[46]  of  the  problem  on  an  interaction  between  a  viscoelastic  boundary  and 
the  viscous  sublayer  of  a  turbulent  boundary  layer.  Here  we  take  into 
account  that  PEO  additives  in  a  flow  don’t  change  the  long-wave  structures, 
the  ratio  of  wave-numbers  for  transverse  ( jCz )  and  main  ( )  directions. 

Drag  reduction  by  polymer  additives,  a  change  of  velocity  profile 
£/(}>)  >  viscosity  and  wave-velocity  are  taken  into  account  in  calculations.  It 
is  important  to  note  that  the  increase  of  the  viscous  sublayer  thickness  by 
polymer  additives  increases  the  region  of  permissible  use  of  the  linear 
theory  near  a  wall. 

The  complex  compliance  of  the  boundary  (the  modelling  parameter) 
is  characterised  by  amplitude  and  phase  of  the  boundary  displacement 
relative  to  the  turbulent  pressure  fluctuation.  This  parameter  must  be 
determined  for  the  frequency  band  of  the  main  production  of  turbulence.  In 
connection  with  increase  of  thickness  of  viscous  sublayer,  permissible 
amplitudes  of  oscillations  of  viscoelastic  boundary  increase. 

The  obtained  solution  [46]  shows  the  restriction  of  the  phase  region 
0  | ' a for  positive  action  of  viscoelastic  boundary  (for  drag  reduction). 
This  positive  action  is  connected  with  decrease  of  near-wall  turbulence 
production.  For  fixed  frequency  CO  {CO  —  27tf ,  where  f  is  cyclic 
frequency)  the  production  change  of  the  turbulence  energy  should  be 

-  J \{uv){dU I dy)  -  (uv)c(dU/dy)c\  dy>0  O') 

0 

Index  V  corresponds  to  compliant  boundary.  The  interference  action  of 
compliant  boundary  for  fixed  frequency  CO  is  neutral  if  this  integral  is 
equal  to  zero.  According  to  the  near-wall  turbulence  model  of  Sternberg 

[47]  the  calculated  viscous  sublayer  thickness  /  is  connected  with  the 

fluctuation  frequency  as  /  ~  * 

For  the  neutral  action  variant,  the  mean  velocity  profile  u(y)  is 
written  according  to  the  experimental  data  for  a  hard  wall. 

The  improved  interference  theory  (presented  by  Semenov  & 
Semenova  [29]  at  this  Symposium)  was  used  for  the  first  calculations  of 
joint  action  of  compliant  boundary  and  polymer  additives. 

Neutral  phase-frequency  lines  (calculated  according  to  the  condition 
(1 1))  restrict  (from  below)  a  region  of  0  for  positive  action  of  compliant 
boundary  (*RC  >  0).  One  example  for  Re0  =  6.2  *106  is  shown  in  Figure 
9  (for  two  variants  of  the  abscissa).  The  phase  shift  0  of  the  compliant 
boundary  displacement  relative  to  acting  fluctuating  pressure  is  on  the 
ordinate.  The  dimensionless  frequency  is  on  the  abscissa.  In  the  upper 
Figure  it  is  made  dimensionless  by  the  use  of  real  flow  viscosity  V  near  a 

wall  and  real  friction  velocity  V d  .In  the  lower  Figure  it  is  made 


dimensionless  by  the  use  of  kinematic  viscosity  of  water  vw  and  friction 

velocity  without  drag  reduction  odv/  in  order  to  compare  the  different 
influences  of  drag  reducing  polymer  additives  for  identical  conditions  of  a 
water  flow. 


Figure  9.  Dependence  of  PFRPA  of  smooth  compliant  surface  on  drag 
reduction  using  polymer  additives:  (1)  4^  =  0,  (2)  xi/p  =  5%, 

(3)  %=  10%,  (4)  20%,  (5)  “  30%,  (6)4^  =  40%,  (7)4^  = 

50%,  (8)  =  60%;  Re0=  6.2xl06 ;  kjkx  -1.0. 

We  see  that  injected  polymer  additives  extend  the  phase-frequency 
region  of  positive  action  (PFRPA)  of  compliant  boundary.  This  extension 
of  PFRPA  is  maximum  at  vyp  «  40% . 

The  injection  of  drag  reducing  polymeric  additives  into  a  flow  leads 
to  a  displacement  of  PFRPA  to  the  left  that  can  lead  even  to  the  change  of 
the  action  sign  of  compliant  boundary  (from  “+”  to  and  on  the 
contrary). 

We  see,  that  from  yp  *  30%  the  right  branch  of  the  neutral  line  is 

displaced  distinctly  to  the  left.  So  minimum  velocity  of  possible  drag 

reduction  using  compliant  coating  must  increase  with  increasing  individual 
efficiency  of  drag  reducing  polymeric  additives.  For  example,  it  must 
increase  to  two  times  at  xyp  «  50%  ■ 

It  leads  to  explanation  of  reasons  of  drag  reduction  peculiarities 
discovered  in  experiments  [32-35,  37]  on  joint  use  of  compliant  coating 
and  polymer  additives. 

The  used  theoretical  approach  doesn't  permit  still  to  carry  out  a 
quantitative  comparison.  It  is  a  problem  for  future  investigations. 

ACKNOWLEDGEMENTS 

The  work  was  supported  by  the  INTAS  Research  Grant  N  94—3737. 


274 


REFERENCES 

1.  Y.G.  Aleyev  “Nekton”,  1977,  Dr. W. Junk  b.v.  Publ.,  the  Hague. 

2.  D.M.  Bushnell  &  K.J  Moore  “Drag  Reduction  in  Nature”,  Annu .  Rev. 
Fluid  Meek,  1991, 23,  65-79. 

3.  J.  Gray  “Studies  in  Animal  Locomotion.  The  Propulsive  Powers  of  the 
Dolphin”,  J.  Exp .  Biol. ,  1936, 13,  192-199. 

4.  A.H.  Woodcock  “The  Swimming  of  Dolphins”,  Nature ,  1948,  161, 
602. 

5.  H.  Focke  “Ueber  die  Ursachen  der  Hohen  Schwimmgeschwin-digkeiten 
der  Delphine”,  Z.  Flugwiss .,  1965, 13,  N2,  54-61. 

6.  B.N  Semenov  “On  the  Existence  of  the  Hydrodynamic  Phenomenon  of 
Dolphins  (Tursiops  Tursio  Ponticusf,  Bionika,  1969,  Naukova  Dumka, 
Kiev,  N3,  54-61. 

7.  T.E.  Alekseeva  &  B.N.  Semenov  “On  the  Determination  of  the 
Hydrodynamic  Drag  of  Dolphins”,  Zh.  Prikl.  Mech.  Tekhn.  Fiz .,  1971, 
N2,  160-164. 

8.  T.Y.  Wu,  &  A.T.  Chwang  “Extraction  of  Flow  Energy  by  Fish  and 
Birds  in  a  Wavy  Stream”,  Swimming  and  Flying  in  Nature ,  1975, 
Plenum  Press-New- York,  687-702. 

9.  A.D.  Young  “The  Calculation  of  the  Total  and  Skin  Friction  Drags  of 
Bodies  of  Revolution  at  0°  Incidence”,  1939,  ARC  RM 1947, 

10.  H.  Hertel  “Structur-Form-Bewegung”,  1963,  Krauskopf  Verlag- 
Mainz. 

11.  M.O.  Kramer  “The  Dolphin’s  Secret”,  New  scientist,  1960,  7,  1118- 

1120. 

12.  M.O.  Kramer  “Boundary  Layer  Stabilization  by  Distributed  Damping”, 
J.Amer.  Soc.  Nav.  Eng.,  1960,  72,  Nl,  25-33. 

13.  M.O.  Kramer  “Boundary  Layer  Stabilization  by  Distributed  Damping”, 
Nav.  Eng  J.,  1962,  74,  N2, 341-348. 

14.  B.N.  Semenov  “The  Study  of  Dolphins  as  Low-Drag  Bodies  (e.g. 
Tursiops  Tursio  Ponticus)”,  Proc.  4th  Int.  Congress  Soc.  Techn. 
Biology  and  Bionics ,  1998,  Munich. 

15.  B.N.  Semenov  “On  Conditions  of  Modelling  and  Choice  of 
Viscoelastic  Coatings  for  Drag  Reduction”,  Recent  Developments  in 
Turbulence  Management,  1991,  Kluwer,  241-262. 

16.  V.M.  Kulik,  I.S.  Poguda  &  B.N.  Semenov  “Experimental  Investigation 
of  One-Layer  Viscoelastic  Coating  Action  on  Turbulent  Friction  and 
Wall  Pressure  Pulsations”,  Recent  Developments  in  Turbulence 
Management ,  1991, Kluwer,  236-289. 

17.  J.O.  Hinze  “Turbulence”,  1959,  Me  Graw-Hill. 

18.  E.M.  Greshilov,  A.M.  Evtushenko,  L.M.  Lyamshev  &  N.L.  Shirokova 
“Some  Peculiarities  of  an  Action  of  Polymeric  on  Near-Wall 
Turbulence”,  J.  Eng.  Physics ,  1973,  25,  999-1004. 

19.  K.-S.  Choi  “Turbulent  Drag  Reduction  Strategies”,  Emerging 
Techniques  in  Drag  Reduction ,  1996,  MEP,  London  and  Bury  St. 
Edmunds,  77-98. 

20.  V.G.  Bogdevich,  N.V.  Malykh,  A.G.  Malyuga  &  I.A.  Ogorodnikov 
“Acoustic  Properties  of  Wall  Bubble  Layer  in  Water  of  Great  Void 
Fraction”,  Hydrodynamics  and  Acoustics  of  Near-Wall  and  Free  Flows , 
1981,  IT  AN  SSSR,  Novosibirsk,  77-107. 

21.  B.J.  Cantwell  “Organized  Motion  in  Turbulent  Flow”,  Annu.  Rev.  Fluid 
Mech.,  1981,  13, 457-515. 

22.  V.M.  Kulik,  I.S.  Poguda  &  B.N.  Semenov  “The  Action  of  Viscoelastic 
Coatings  on  the  Friction  Reduction  for  Flows  of  Water  and  Polymeric 
Solutions”,  Proc.  12th  Short  Course  for  Pipe-Line  Problems,  1989, 
Upha,  42-43. 

23.  A.G.  Malyuga,  V.I.  Mikuta,  &  G.  Gerchev  “The  Influence  of  Near-Wall 
Bubble  Layer  on  Screw  Propeller-Induced  Effects  on  the  Wall”,  Proc. 
17th  Session  ofBSHC ,  1988,  Varna,  2, 42/1-42/12. 

24.  N.S.  Berman  “Drag  Reduction  by  Polymers”,  Annu.  Rev.  Fluid  Mech., 
1978, 10,  47-64. 

25.  B.N.  Semenov  “The  Polymeric  Solution  Injection  into  Flow  for  Drag 
Reduction”,  Siberian  Phys.  Techn.  J.,  1991,  N4,  99-108. 

26.  B.N.  Semenov  “Tho  Pulseless  Injection  of  Polymeric  Additives  into 
Near-Wall  Flow  and  Perspectives  of  Drag  Reduction”,  Recent 
Developments  in  Turbulence  Management,  1991,  Kluwer,  293-308. 

27.  A.G.  Malyuga,  V.I.  Mikuta  &  O.I.  Stoyanovsky  “Turbulent  Drag 
Reduction  at  Flow  of  Polymer  Solutions  Aerated  by  Air  Bubbles”, 
Near-Wall  and  Free  Turbulent  Flows,  1988,  IT  AN  SSSR,  Novosibirsk, 
121-130. 


28.  A.Malyuga,  V.Mikuta,  A.Nenashev,  S.Kravchenko  &  O.Stoyanovsky 
“Local  Drag  Reduction  at  Flow  of  Polymer  Solutions  Aerated  by  Air 
Bubbles”,  Proc.  6th  Nat.  Congress ,  1989,  Varna,  74/1-74/6. 

29.  B.N.  Semenov  &  A.V.  Semenova  “Recent  Developments  in 
Interference  Analysis  of  Compliant  Boundary  Action  on  Near-Wall 
Turbulence”,  Proc.  Int.  Symposium  on  Sea  Water  Drag  Reduction , 
1998,  Newport. 

30.  B.N.  Semenov  &  A.V.  Semenova  “The  Interference  Action  of 
Compliant  Boundary  on  Near-Wall  Turbulence”,  Zh.  Prikl.  Mekh.  Tekh. 
Fiz.  (to  be  publish). 

31.  B.N.  Semenov  &  A.V.  Semenova  “Joint  Influence  of  Compliant 
Boundary  and  Polymer  Additives  on  Near-Wall  Turbulent  Flow”, 
Thermophysics  and  Aeromechanics  (to  be  publish). 

32.  B.N.  Semenov,  V.M.  Kulik,  V.A.  Lopyrev,  B.P.  Mironov,  I.S.  Poguda 
&  T.I.  Yushmanova  “The  Combined  Effect  of  Small  Quantities  of 
Polymeric  Additives  and  Pliability  of  the  Wall  on  Friction  in  Turbulent 
Flow”,  Fluid  Mech.  Soviet  Research,  1985, 14,  Nl,  143-149. 

33.  B.N.Semenov,  V.M.Kulik,  V.A.Lopyrev,  B.P.Mironov,  I.S.Poguda  & 
T.I.  Yushmanova  “Towards  the  Influence  of  Flow  Polymer  Additives 
and  Surface  Compliance  on  Wall-Turbulence”,  Proc.  5th  Nat.  Congress 
Theor.  Appl.  Mech.,  1985,  Vama-Sofia2,  371-376. 

34.  V.M.  Kulik,  I.S.  Poguda,  B.N.  Semenov  &  T.I.  Yushmanova  “The 
Influence  of  Flow  Velocity  for  Combined  Effect  of  Compliant  Surface 
and  Polymer  Additives  on  Turbulent  Friction”,  Izvestiya  SO  AN  SSSR, 
Ser. Techn.  Nauk,  1987,  Nl 5,  42-46. 

35.  V.M.  Kulik,  I.S.  Poguda,  B.N.  Semenov  &  T.I.  Yushmanova  “Effect  of 
Flow  Velocity  on  the  Synergistic  Decrease  of  Turbulent  Friction  by  a 
Compliant  Wall  and  a  Polymeric  Additive”,  Soviet  J.  Appl.  Phys.,  1988, 
2,  N  1,49-54. 

36.  V.M.  Kulik,  I.S.  Poguda  &  B.N.  Semenov  “Experimental  Study  of  the 
Effect  of  One-Layer  Viscoelastic  Coatings  on  the  Turbulent  Friction 
and  Pressure  Pulsations  at  the  Wall”,  J.  Eng.  Phys.,  1984,  47,  N2,  189- 
196. 

37.  B.N.  Semenov,  A.I.  Amirov,  V.M.  Kulik,  A.G.  Malyuga  &  I.S.  Poguda 
“The  Experiment  on  Turbulent  Drag  Reduction  by  Joint  Use  of 
Compliant  Coating,  Gas  Microbubbles  and  Polymer  Additives”, 
Thermophysics  and  Aeromechanics  (to  be  publish). 

38.  S.S.  Kutateladze  &  A.I.  Leontyev  “Heat  and  Mass  Transfer  and  Friction 
in  Turbulent  Boundary  Layers”,  1972,  Moscow,  Energiya. 

39.  L.W.  Reidy  &  G.W.  Anderson  “Drag  Reduction  for  External  and 
Internal  Boundary  Layer  Using  Riblets  and  Polymers”,  AIAA  Paper, 
1988,  N138. 

40.  K.-S.  Choi,  G.E.  Gadd,  H.H.  Pearcey,  A.M.  Savill  &  S.  Svensson 
“Tests  of  Drag-Reducing  Polymer  Coated  on  a  Riblet  Surface”,  Appl. 
Sci.  Res.,  1989,  46,  209-216. 

41.  E.  Koury  &  P.S.  Virk  “Drag  Reduction  by  Polymer  Solutions  in  Riblet- 
Lined  Pipes”,  Abstracts  8th  European  Drag  Reduction  Working 
Meeting,  1993,  Lausanne. 

42.  P.S.  Virk  &  E.  Koury  “Maximum  Drag  Reduction  by  Polymer 
Solutions  in  Riblet-Lined  Pipes”,  Abstracts  9th  European  Drag 
Reduction  Meeting,  1995,  Ravello-Napoly. 

43.  K.-S.  Choi,  X.Yang,  B.R.  Clayton,  T.  Glover,  M.  Atlar,  B.N.  Semenov 
&  V.M.  Kulik  “Turbulent  Drag  Reduction  Using  Compliant  Surfaces”, 
Proceedings  of  Royal  Society,  A,  1997,  453, 2229-2240. 

44.  A.G.  Fabula  &  T.G.  Bums  “Dilution  in  a  Turbulent  Boundary  Layer 
with  Polymeric  Friction  Reduction”,  1970,  Pasadena-Califomia:  Nava! 
Undersea  Res.  &  Development  Center,  TP171. 

45.  Ya.  I.  Voitkunsky,  R.Ya.  Pershitz  &  I. A.  Titov  “Handbook  on  Theory 
of  a  Ship”,  1960,  Sudpromgiz,  Leningrad. 

46.  B.N.  Semenov  “Interaction  of  an  Elastic  Boundary  with  the  Viscous 
Sublayer  of  a  Turbulent  Boundary  Layer”,  Zh.  Prikl.  Mekh.  Tekh.  Fiz., 
1971,  N3,  58-62. 

47.  J.  Sternberg  “A  Theory  for  Viscous  Sublayer  of  a  Turbulent  Flow”,  J. 
Fluid  Mech.,  1962, 13,  N2,  241-271. 

48.  B.N.  Semenov  “Analysis  of  Deformation  Characteristics  of  Viscoelastic 
Coatings”,  Hydrodynamics  and  Acoustics  of  Near-Wall  and  Free 
Flows,  1981,  Nauka,  Novosibirsk,  57-76. 

49.  B.N.  Semenov  “On  the  Properties  of  Viscoelastic  Boundary  for 
Turbulent  Friction  Reduction”,  Sib.Fiz.Tech.  Zn.,  1993,  Nl,  63-73. 

50.  B.N.  Semenov  “Analysis  of  Four  Types  of  Viscoelastic  Coating  for 
Turbulent  Drag  Reduction”,  Emerging  Techniques  in  Drag  Reduction, 
1996,  MEP,  London  and  Bury  St.  Edmunds,  187-206. 


275 


SIMILARITIES  AND  DIFFERENCES  IN  DRAG  REDUCTION  BEHAVIOR  OF 
HIGH  POLYMER  AND  SURFACTANT  SOLUTIONS 


Jacques  L.  Zakin 

Department  of  Chemical  Engineering 
The  Ohio  State  University 
Columbus,  OH  43210 
zakin.l@osu.edu 


Jiri  Myska  Zhiqing  Lin 

Institute  of  Hydrodynamiccs  Department  of  Chmical  Engineering 

Czech  Academy  of  Sciences  The  Ohio  State  University 
Prague,  Czech  Republic  Columbus,  OH  43210 

lin.379@osu.edu 


Abstract  -  The  two  most  widely  studied  types  of  drag  reducing  additives  are  high  polymers  and  surfactants.  Their  turbulent  flow  behaviors  have  many 
similarities  but  significant  differences  exist  in  their  maximum  drag  reducing  asymptotes,  the  limiting  slopes  of  their  mean  velocity  profiles  for 
maximum  drag  reducing  solutions  as  well  as  the  magnitudes  of  peak  values  of  v’/u*  and  the  peak  locations.  Stress  deficits  due  to  small  values  of 
Reynolds  stresses  have  been  observed  for  both  types  of  additives  but  zero  Reynolds  stress  profiles  have  been  reported  only  for  surfactant  solutions. 
These  differences  indicate  that  the  mechanisms  of  drag  reduction  for  the  two  types  of  additives  are  different.  The  fact  that  mechanical  degradation  of 
surfactant  systems  is  reversible  while  for  high  polymers  it  is  irreversible  make  the  former  more  versatile  for  applications. 


I.  INTRODUCTION 

Drag  reduction  in  turbulent  flow  was  first  recognized  by  Mysels,  et  al 
some  fifty  years  ago  [1,2,3].  They  found  the  pressure  drop  in  pipe  flow  for 
gasoline  thickened  by  aluminum  disoaps  was  less  than  that  of  gasoline  at 
the  same  flow  rate.  Soon  after,  Toms  [4,5]  reported  similar  results  with 
dilute  solutions  of  high  molecular  weight  polymethylmethacrylate  in 
monochlorobenzene.  Because  of  wartime  security  considerations,  Mysels 
results  were  published  after  Toms*.  In  the  past  five  decades  turbulent  drag 
reduction  has  been  an  active  research  field  with  over  4900  references  [6], 
most  of  them  dealing  with  high  polymer  drag  reduction. 

High  polymers  are  very  effective  in  reducing  friction  losses  and  have 
proven  valuable  in  increasing  flow  rates  in  crude  oil  and  other  hydrocarbon 
pipelines  most  spectacularly  in  the  48-inch,  800-mile  long  Alyeska 
Pipeline  from  the  North  Slope  in  Alaska  to  Valdez.  With  currently 
available  polymers,  concentrations  of  1  ppm  in  crude  oil  can  give 
significant  drag  reduction  [7]. 

Polymer  additives  are,  however,  susceptible  to  mechanical  degradation 
and  chemical  bonds  are  broken  irreversibly  and  the  highest  molecular 
weight,  most  effective  molecules  are  the  ones  most  sensitive  to  scission. 
Thus  polymers  lose  their  effectiveness  when  passing  through  a  pump  and 
additional  polymer  must  be  injected  downstream  of  a  pumping  station  to 
reduce  friction  losses  in  the  next  pipeline  section.  Polymers  are  therefore 
only  useful  in  once-through  applications.  Fortunately  polymer  injection  at 
only  a  few  “bottleneck”  sections  of  the  Alyeska  Pipeline  was  needed  to 
increase  throughput  when  North  Slope  production  exceeded  pipeline 
capacity  [7]. 

Surfactant  additives  in  water  generally  require  higher  concentrations 
than  high  polymers  but  their  microstructures  do  reform  quickly  after 
mechanical  degradation  in  pumps  or  in  other  regions  of  high  shear. 
Surfactants  have  low  molecular  weights,  of  the  order  of  hundreds,  but  can 
form  long  worm-like  micelles  which  are  believed  to  form  3-D  network 
structures.  While  these  structures  are  easily  broken,  they  reform  rapidly  so 
that  the  surfactant  solutions  regain  their  effectiveness  rapidly.  Thus 
surfactants  can  be  used  in  recirculation  systems  such  as  district  heating  or 
district  cooling  systems  and  research  activity  on  surfactant  drag  reduction 
has  grown  appreciably  in  the  past  ten  to  fifteen  years. 

Catonic,  nonionic,  anionic  and  zwitterionic  surfactants  have  all  been 
shown  to  be  effective  drag  reducing  additives.  Often  a  counterion  is 
required  to  obtain  good  drag  reduction. 

This  paper  will  discuss  similarities  and  differences  in  drag  reduction 
behavior  between  high  polymer  and  surfactant  systems.  Significant 
differences  in  their  behaviors  indicate  that  the  nature  of  their  interactions 
with  the  turbulent  flow  field  may  be  different.  Since  most  studies  have 
been  done  with  cationic  surfactants,  this  type  of  additive  will  be  compared 
with  high  polymer  additives. 


IL  COMPARISONS  OF  HIGH  POLYMER  AND  SURFACTANT 
DRAG  REDUCERS  AND  OF  THEIR  TURBULENT  BEHAVIORS 
A  Microstructure 

The  microstructures  of  polymers  and  surfactant  drag  reducing 
additives  are  quite  different.  Uncharged,  flexible  polymers  form  random 
coils  in  solution  which  may  uncoil  and  elongate  under  shear  or 
elongational  forces.  Polymers  which  contain  charged  groups  are  elongated 
even  at  rest.  It  is  generally  believed  that  surfactants  that  are  effective  drag 
reducers  have  worm-like  or  thread-like  micelle  structures.  These  systems 
may  form  three-dimensional  networks  which  fully  pervade  the  solution  at 
rest  or  they  may  require  shear  to  form  networks. 

B.  Onset  of  Drag  Reduction 

Figure  1,  in  which  friction  factor  is  plotted  against  generalized 
Reynolds  number,  illustrates  the  types  of  onset  behavior  observed  in  high 
polymer  systems  [8].  The  solution  is  a  200  ppm  polyethylene  oxide 
(400,00*0  molecular  weight)  in  benzene.  Onset  for  polymer  drag  reduction 
occurs  when  a  critical  shear  rate  is  reached.  This  shear  rate  decreases  with 
molecular  weight,  concentration,  goodness  of  the  solvent  and,  for  coiled 
polymers,  the  flexibility  of  the  polymer  solution  chain  [9].  If  the  critical 
shear  rate  occurs  in  the  laminar  flow  region,  no  sharp  onset  is  observed  but 
only  a  gradual  departure  from  the  laminar  line  as  Reynolds  number 
increases  (see  Fig  1,  0.833mm  ID  tube).  Liaw  et  al  [9]  called  this 
“concentrated”  polymer  solution  drag  reducing  behavior.  For  the  larger 
tubes,  onset  is  observed  as  departures  from  the  Von  Karman  turbulent 
friction  factor  curve  at  higher  Reynolds  numbers  when  a  critical  shear  rate 
is  exceeded.  Decrease  of  polymer  concentration  in  a  single  tube  yields 
similar  changes  in  onset  behavior,  ie  increase  in  the  critical  Reynolds 
number.  “Concentrated”  and  “dilute”  drag  reducing  behavior  correspond  to 
Type  B  and  Type  A  behavior  noted  by  Virk  [10]. 


277 


Almost  all  surfactant  drag  reduction  friction  factor  data  reported  show 
gradual  departure  from  the  laminar  friction  factor  line.  There  are  a  small 
number  of  reports  of  onset  in  the  turbulent  region.  For  example  Gyr  and 
Bewersdorff  [1 1]  show  an  example  of  a  dilute  surfactant  solution  (2mM  of 
tetradecyl  trimethyl  ammonium  bromide  and  sodium  salicylate  with  2mM 
sodium  bromide  added)  giving  onset  in  the  turbulent  regime. 


The  limiting  asymptote  equation  for  surfactant  and  aluminum  disoap 
solutions  is  [18]: 

f  =  0.32  Nr€  '°‘55  (3) 

This  equation  predicts  friction  factors  more  than  40%  lower  than  Eq.  2  in 
some  regions. 


C.  Mechanical  Degradation 

As  noted  earlier,  the  high  molecular  weight  polymers  which  are  the 
most  effective  drag  reducers,  are  also  the  most  susceptible  to  chain  scission 
in  shear  fields  [12].  Extensional  flows  are  even  more  effective  than  shear 
flows  in  causing  degradation.  Many  investigators  have  reported  on  shear 
degradation  of  high  polymers  and  some  on  the  effects  of  predominantly 
extensional  flows.  Once  a  primary  chemical  bond  has  been  broken,  there  is 
almost  ho  chance  that  it  will  reform  so  polymer  degradation  is  irreversible. 
Thus  polymers  can  only  be  effective  in  once-through  operations. 

Surfactant  micellar  structures,  on  the  other  hand,  rapidly  self-assemble 
after  mechanical  degradation.  The  easily  broken  up  microstructures 
reassemble  in  times  of  the  order  of  seconds.  Thus  these  additives  have  been 
successfully  field  tested  in  district  heating  and  district  cooling  recirculation 
systems  providing  energy  savings  of  30  percent  or  more[13-16]. 

D.  Maximum  Drag  Reduction  Asymptotes 

Virk  demonstrated  that  for  high  polymers,  a  maximum  drag  reduction 
asymptote  exists  [17].  However,  a  number  of  experimenters,  using 
surfactant  and  aluminum  disoap  drag  reducing  additives,  have  reported 
friction  factor  data  lying  significantly  below  Virk’s  limiting  drag  reducing 
asymptote.  Zakin  et  al  [18]  examined  these  data  as  well  as  their  own  and 
proposed  a  new  limiting  asymptote  for  surfactant  and  aluminum  disoap 
systems.  The  two  asymptotes  are  shown  in  Figure  2.  Virk’s  equation  for 
the  high  polymer  asymptote  is  [17]: 

1/  vy  =  19.01og,oCNRe77)-32-4  (!) 

or 

f  =  O^Nr*-0 38  (for  Nr*  *  4,000  to  40,000)  (2) 

where  f  =  friction  factor  and  Nr*  =  Reynolds  number. 


Figure  2.  Friction  factor  vs  Reynolds  number 


E.  Mean  Velocity  Profile 

For  high  polymer  drag  reducing  systems,  Virk  proposed  an  elastic 
sublayer  model  with  a  limiting  mean  velocity  profile  equation: 

u+  =  26.9  logi0y+-17  (4) 

This  limiting  velocity  profile  is  consistent  with  the  maximum  drag 
reduction  asymptote  for  high  polymers  (Eq.  1). 

Recently,  Zakin  et  al  [18]  offered  another  limiting  profile  equation 
reflecting  the  steeper  slope  they  observed  in  the  intermediate  region  for 
surfactant  solutions  approaching  the  maximum  drag  reducing  asymptote 
for  surfactants  (Eq.  3)  and  also  for  aluminum  disoaps  in  hydrocarbons: 

u+  -  53.9  logi0y+-65  (5) 

where  u+  =  u/u*,  u  =  local  mean  velocity,  u*  =  friction  velocity,  y+  = 
yu*/v,  y  «  distance  from  the  wall  and  v  =  kinematic  viscosity.  This 
limiting  slope  for  surfactant  and  aluminium  disoap  solutions  is  twice  that 
for  high  polymers.  The  lower  limiting  drag  reducing  friction  factor 
asympotote  for  surfactants,  Eq.  3,  is  a  consequence  of  this  steeper  slope. 

A  schematic  illustrating  the  two  limiting  equations  is  shown  in  Figure 
3.  Eq.  5  indicates  a  mixing  length  constant  half  of  that  of  Eq.  4. 


F.  Turbulence  Measurements 
1 .  Axial  Intensity  Measurements 

A  number  of  investigators  have  measured  axial  turbulence  intensities 
of  drag  reducing  fluids  in  channels  and  in  pipes.  Unfortunately,  direct 
comparisons  of  the  two  types  of  additives  in  the  same  test  systems  are  not 
available  but  some  comparisons  can  be  made. 

Root  mean  square  axial  turbulence  intensities  at  the  center  of  the 
channel  or  the  pipe  for  drag  reducing  polymer  and  surfactant  solutions  are 
about  equal  to  or  lower  than  for  Newtonian  solvents  at  the  same  Reynolds 


278 


number  [19].  Peak  values  of  u’/u*  near  the  wall  of  about  2  to  4  were 
observed  for  most  drag  reducing  systems  compared  with  2.5  to  3.0  for  the 
solvents.  However,  a  peak  value  of  8  was  reported  by  Rudd  [20]  for  a 
polymer  solution  in  a  channel  and  by  BewersdorfF  and  Ohlendorf  [21]  for  a 
surfactant  solution  in  a  pipe  at  very  high  Reynolds  number.  Peak  values 
increase  with  Reynolds  numbers,  as  clearly  shown  in  the  data  for  a  drag 
reducing  surfactant  solution  of  Schmidt  [22],  T.J.  Hanratty’s  student.  In 
contrast,  his  peak  water  intensities  decreased  slightly  with  Reynolds 
number. 

In  the  data  shown  by  Gampert  and  Rensch  [19]  and  others,  the  u’/u* 
peak  occurred  at  higher  y+  values  for  drag  reducing  systems  than  the  y+  « 
10-15  location  typical  of  solvent  data.  Peak  location  is  relatively 
insensitive  to  Reynolds  number  for  solvents  and  for  drag  reducing  systems. 

2.  Transverse  or  Radial  intensity  Measurements 

Radial  intensities  in  the  core  region  are  lower  for  drag  reducing 
solutions  than  for  Newtonian  solvents,  both  in  absolute  intensities,  v’,  and 
in  normalized  intensities,  v’/u*  [22-24].  While  maximum  intensities  occur 
at  y+  «  100  for  Newtonian  solvents,  for  drag  reducing  polymer  solutions 
Gampert  and  Rensch  [19]  show  a  shift  of  the  maximum  intensity  of  v’/u* 
to  somewhat  higher  values  of  y+  with  modest  decrease  in  peak  intensities. 
Schmidt  [22],  on  the  other  hand,  shows  peak  intensities  reduced  by  65%  to 
90%  compared  to  water  for  a  surfactant  drag  reducing  system.  Peak  values 
for  this  system  were  shifted  to  lower  y+  values  than  those  for  water. 

3.  Reynolds  Stresses 

Wei  and  Willmarth  [25]  found  ‘large’  negative  Reynolds  stresses  in 
the  near  wall  region  of  their  channel  into  which  concentrated  PEO 
solutions  were  injected  and  small  Reynolds  stresses  across  the  profile. 
Earlier,  Durst  et  al  [26]  had  also  observed  negative  Reynolds  stresses  close 
to  the  wall.  Schummer  and  Thielen  [27],  Willmarth  et  al  [28]  and 
BewersdorfF  [29]  had  earlier  noted  stress  deficit  profiles  based  on  their 
measurements  of  Reynolds  stresses  and  mean  velocity  profiles.  A  stress 
deficit  can  also  be  seen  near  the  wall  in  the  earlier  data  of  Patterson  et  al 
[30]  for  a  high  molecular  weight  polyisobutylene  in  mineral  oil  drag 
reducing  solution. 

Schmidt’s  [22]  Reynolds  stress  measurements  in  a  cationic  surfactant 
drag  reducing  solution  (Ethoquad  T/13-50  —  Sodium  Salicylate)  in  a 
channel  showed  nearly  zero  Reynolds  stress  profiles  at  Reynolds  numbers 
of  19,060,  29,750  and  49,130.  This  result,  like  those  mentioned  above, 
requires  postulation  of  an  additional  (viscoelastic)  stress  term  of  significant 
magnitude.  Kawaguchi  et  al  [31,  32]  obtained  similar  zero  Reynolds 
stress  profile  results  with  a  different  cationic  surfactant  solution  in  a 
channel.  The  zero  values  are  probably  caused  by  a  combination  of  low  v’ 
values  of  these  surfactant  solutions  and  phase  differences  between  the  u’ 
and  the  v’  intensities.  Conditioned  sampling  of  Reynolds  stress  data  for 
these  surfactant  systems  is  needed  to  determine  the  magnitudes  of  the  four 
possible  combinations  of  u’  and  v’  values.  This  would  clarify  how  and 
why  they  sum  to  zero  Reynolds  stress  and  also  the  behaviors  of  turbulent 
sweeps  and  ejections  in  these  systems. 


III.  CONCLUSIONS 

While  there  are  similarities  in  the  drag  reducing  behavior  of  high 
polymer  and  surfactant  systems,  there  are  significant  differences,  most 
notably  the  limiting  asymptotes  for  maximum  drag  reduction  and  the 
ultimate  slopes  of  the  mean  velocity  profiles.  Other  differences  are  the 
larger  reductions  in  peak  v’/u*  values  for  surfactant  drag  reducing 
solutions  and  a  shift  in  the  location  of  the  peak  value  to  lower  y+  compared 
to  Newtonian  solvents  while  the  polymer  solution  peaks  shifted  to  higher 

y. 

Both  types  of  additives  have  demonstrated  a  stress  deficit,  but  near 
zero  Reynold  stress  profiles  have  been  observed  in  surfactant  solutions,  but 
not  in  polymer  solutions.  These  differences  indicate  that  there  is  some 
difference  in  the  mechanism(s)  for  drag  reduction  for  the  two  types  of 
additives  most  probably  because  of  differences  in  the  interactions  between 
turbulent  eddies  and  elongated  polymer  molecules  and  their  interactions 
with  surfactant  networks. 


Finally,  the  ability  of  surfactant  solutions  to  recover  after  mechanical 
degradation  while  high  polymers  are  irreversibly  degraded,  allows  the 
former  to  be  used  in  a  wider  variety  of  applications  including  recirculation 
systems. 

Acknowledgments 

This  research  was  supported  in  part  under  Grant  12.074E,  Program  in 
Science  and  Technology  Cooperation,  Office  of  Science  Advisor,  U.S. 
Agency  for  International  Development.  Financial  support  by  the  Czech 
Agency  of  the  Czech  Republic,  Praha,  is  also  gratefully  acknowledged. 

IV.  REFERENCES 

1.  K.J.  Mysels,  US  Patent  2,492,173  (1949). 

2.  G.A  Agoston,  W.H.  Harte,  H.C.  Hottel,  W.A  Hottel,  W.A  Klemrn, 
K.J.  Mysels,  H.H.  Pomeroy  and  J.M.  Thompson,  Ind.  Eng.  Chem., 
46,  1017-1019(1954). 

3.  K.J.  Mysels,  Chem.  Eng.  Prog.  Symp.  Series,  67,  45-49  (1971). 

4.  B.A  Toms,  “Some  Observations  on  the  Flow  of  Linear  Polymer 
Solutions  Through  Straight  Tubes  at  Large  Reynolds  Numbers,”  in 
Proc.  1st  Int’l  Rheological  Congress ,  II,  Part  2,  North  Holland 
Publishing  Co.,  Netherlands,  1949. 

5.  B.A  Toms,  Phys.  Fluids,  20,  53-55  (1977). 

6.  R.H.  Nadolink  and  W.W.  Haigh,  Appl.  Mech.  Rev.,  48,  351-460 
(1995). 

7.  J.F.  Motier,  L.-C.  Chou  and  N.  Kommareddi,  “Commercial  Drag 
Reduction,  Past,  Present  and  Future,”  in  Turbulence  Modification 
and  Drag  Reductions ,  ASME  Pub,  FED  -  vol,  237(2),  229-234 
(1996). 

8.  G.C.  Liaw,  PhD  Dissertation,  Univ  of  Missouri-Rolla,  1968. 

9.  G.C.  Liaw,  J.L.  Zakin  and  G.K.  Patterson,  AIChE  J.,  17,  391-397 
(1971). 

10.  P.S.  Virk,  Nature,  253,  109  (1975). 

11.  A  Gyr  and  H.-W.  BewersdorfF,  Drag  Reduction  of  Turbulent  Flows 
by  Additives ,  Kluwer  Academic  Publishers,  Dordrecht,  The 
Netherlands,  1995,  page  161. 

12.  G.K.  Patterson,  H.C.  Hershey,  C.D.  Green  and  J.L.  Zakin,  Trans.  Soc. 
Rheol.,  10,489-500(1966). 

13.  F.  Hammer,  “Demonstration  of  Smooth  Water  in  the  District  Heating 
System  of  Heming,  Denmark,”  in  Proc .  Int’l  Symp.  on  Fluids  for 
District  Heating,  Copenhagen,  pp.  139-150  (1991). 

14.  H.H.  Kleuker,  W.  Althaus,  A  Steiffand  P.M.  Weinspack,  “Results  of 
the  Eco-Demonstration-Project  in  Volklingen  (Germany),”  in  Proc. 
Int’l  Symp.  on  Fluids  for  District  Heating,  Copenhagen,  pp.  123-137 
(1991). 

15.  J.  Pollert,  J.L.  Zakin,  J.  Myska  and  P.  Kratochivel,  “Use  of  Friction 
Reducing  Additives  in  District  Heating  Systems  at  Kladno- 
Krocehlavy,  Czech  Republic,”  in  Proc.  85th  Int'l  District  Heating 
and  Cooling  Assoc.,  Seattle,  pp.  141-1 56  (1994). 

16.  K.  Gasljevic  and  E.F.  Matthys,  “Field  Test  of  a  Drag  Reducing 
Surfactant  Additive  in  a  Hydraulic  Cooling  System,”  in  Turbulence 
Modification  and  Drag  Reduction,  ASME  Pub,  FED-vol  237(2), 
249-260  (1996). 

17.  P.S.  Virk,  AIChE  J.,  21,  625  (1975). 

18.  J.L.  Zakin,  J.  Myska  and  Z.  Chara,  AIChE  J.,  42,  3544-3546  (1996). 


279 


19.  Gampert  and  A.  Rensch,  “Polymer  Concentration  and  Near  Wall 
Turbulence  Structure  of  Chemical  Flow  of  Polymer  Solutions,”  in 
Turbulence  Modification  and  Drag  Reduction,  ASME  Pub,  FED-vol 
237(21.  129-136(1996). 

20.  M.J.  Rudd,  J.  Fluid  Mech.,  5L  673-685  (1972). 

21.  H.-W.,  Bewersdorff  and  D.  Ohlendorf,  Colloid  Poly.  Sci.,  266,  941- 
953(1988). 

22.  G.M.  Schmidt,  “Surfactant  Induced  Drag  Reduction  in  a  Channel  Flow 
Facility,”  B.S.  Thesis,  Univ.  of  Illinois,  Urbana-Champaign,  1997, 
Prof.  T.J.  Hanratty,  Advisor. 

23.  B.  Gampert  and  C.K.  Yang,  “The  Influence  of  Polymer  Additives  on 
the  Coherent  Structure  of  Turbulent  Channel  Flow,”  in  Structure  of 
Turbulence  and  Drag  Reduction ,  A.  Gyr.  Editor,  Springer-Verlag, 
Berlin,  1990. 

24.  J.  Myska,  Z.  Chara  and  J.L.  Zakin,  J.  Hydrol.  Hydromech,  45,  151- 
172(1997). 

25.  T.  Wei  and  W.W.  Wiilworth,  J.  Fluid  Mech.,  245,  619-641  (1992). 


26.  F.  Durst,  T.  Keck  and  R.  Kleine,  “Turbulence  Quantities  and  Reynolds 
Stress  in  Pipe  Flows  of  Polymer  Solution,”  in  Proc.  1st  Int’l  Confi  on 
Laser  Anemometry  Advances  and  Applications,  BHRA,  1985. 

27.  P.  Schummer  and  W.  Thielen,  Chem  Eng  Comm.,  4,  593-606  (1980). 

28.  W.W.  Willmarth,  T.  Wei  and  C.O.  Lee,  Phys.  Fluids,  30*  933  (1987). 

29.  H.-W.  Bewersdorff,  Rheol.  Acta,  23,  527  (1984). 

30.  G.K.  Patterson,  J.  Chosnek  and  J.L.  Zakin,  Phys.  Fluids,  20,  S89  -  S99 
(1977) 

31.  Y.  Kawaguchi,  Y.  Tawaraya,  A.  Yobe,  K.  Hishida  and  M.  Maeda,” 
Turbulent  Transport  Mechanism  in  a  Drag  Reducing  Flow  with 
Surfactant  Additive  Investigated  by  Two  Component  LDV,”  in  Proc. 
8th  Int’l  Symp.  on  Application  of  Laser  Techniques  to  Fluid 
Mechanics ,  Lisbon,  July  8-11, 1996 

32.  Y.  Kawaguchi,  Y.  Tawaraya,  A  Yabe,  K.  Hishida  and  M.  Maeda, 
“Active  Control  of  Turbulent  Drag  Reduction  in  Surfactant  Solutions 
by  Wall  Heating,”  in  Turbulence  Modification  and  Drag  Reduction, 
ASME  Pub,  FED-vol.237(2L  47-52  (1996). 


280 


DRAG-REDUCING  ADDITIVES  FOR  RECIRCULATING  HYDRONIC  SYSTEMS  :  FULL-SCALE 
SYSTEM  ENGINEERING  ANALYSIS  AND  FIELD  TEST 

K.  Gasljevic,  K.  Hoyer,  and  E.F.  Matthys 
Department  of  Mechanical  and  Environmental  Engineering 
University  of  California,  Santa  Barbara 
Santa  Barbara,  CA  93106,  USA 

Abstract  -  In  addition  to  several  laboratory  studies,  we  have  conducted  engineering  system  analyses  and  a  full-scale  field  test  to  investigate  the 
suitability  of  surfactant  drag-reducing  additives  for  recirculating  fluid  transport  and  hydronic  thermal  distribution  systems.  The  objective  of  using 
such  additives  can  be  energy  conservation,  a  decrease  in  pipe  and  pump  size,  an  increase  in  flow  rate  or  heat  transfer,  an  increase  in  system  length, 
or  even  a  combination  thereof.  Many  such  systems  involve  numerous  pipe  loops,  fittings,  valves,  pumps,  filters,  and  heat  exchangers;  which  may 
all  affect  the  fluid  or  be  affected  by  it  in  various  ways.  Accordingly,  we  chose  a  relatively  complex  cooling  system  in  a  building  as  a 
representative  system  in  which  to  conduct  a  large-scale  engineering  field  test  of  the  additive  technology.  This  system  was  extensively  analyzed 
and  instrumented.  It  was  then  found  during  the  field  test  that  it  is  indeed  possible  to  achieve  significant  reductions  in  pumping  power  while 
keeping  the  system  fully-operational,  controllable,  and  able  to  deliver  nominal  performance,  yet  without  requiring  special  maintenance  or  new 
hardware.  For  this  to  be  possible,  however,  we  found  that  it  was  necessary  to  overcome  critical  reductions  in  the  heat  exchangers  performance. 
We  were  indeed  able  to  do  so,  and  the  field  test  was  judged  to  be  very  successful,  clearly  proving  the  technical  viability  of  the  drag-reducing 
additive  technology  for  this  type  of  system,  and  providing  also  a  wealth  of  new  information  essential  to  the  implementation  of  this  technology  in 
industrial,  commercial,  or  militaiy  applications. 


1.  INTRODUCTION 

In  our  work  we  have  focused  on  the  application  of  drag-reducing 
additives  in  recirculating  internal  flow  applications  such  as  those  involving 
heating  or  cooling  of  space  and  equipment,  for  example.  In  such 
applications,  the  objective  of  the  technology  may  be  a  decrease  in  energy 
consumption,  a  decrease  in  pipe  and  pump  size,  an  increase  in  flow  rate 
and  heat  transfer,  an  increase  in  system  length,  or  a  combination  thereof. 
For  recirculating  applications,  surfactant  additives  are  much  better-suited 
than  polymeric  ones,  although  much  less  studied  until  recently.  We 
conducted  therefore  a  wide  variety  of  laboratory  tests  ranging  from  very 
fundamental  issues  of  turbulence  /  fluid  interactions  to  more  applied  issues 
such  as  pump  or  heat  exchanger  performance  studies  for  these  fluids. 
Drag-reducing  additives  have  long  been  studied  with  the  hope  to 
implement  them  in  practical  engineering  situations.  Often,  however,  the 
practical  implementation  of  the  technology  has  proven  much  more 
complicated  than  anticipated  and  in  some  cases  fraught  with  apparently 
insurmountable  difficulties,  often  resulting  from  complex  interactions 
between  components  at  the  system-wide  level.  This  has  been  the  case  in 
particular  for  applications  aiming  at  energy  savings  in  recirculating 
systems.  We  believed  therefore  that  a  large-scale  field  test  in  an 
operational  system  would  be  essential  for  both  viability  assessment  and 
technology  optimization. 

In  order  to  conduct  a  large-scale  test  that  would  cover  all  the  main 
technological  issues  that  are  common  to  recirculating  systems,  we  chose  as 
representative  system  a  relatively  complex  hydronic  space  cooling  system 
in  a  building,  with  our  main  objective  being  a  reduction  in  energy  usage 
for  the  system.  This  particular  objective  is,  of  course,  in  itself  of  great 
interest  for  many  applications,  but  all  the  finding  of  the  test  are  also  readily 
translatable  in  terms  of  hardware  size  reduction,  or  an  increase  in  flow  rate, 
heat  transfer,  or  system  length,  as  desired.  Similarly,  our  findings  can  also 
be  readily  extended  to  other  types  of  internal  recirculating  systems  such  as 
equipment  cooling  or  heating,  power  generation,  chemical  processes,  etc. 
For  conciseness,  we  will  focus  in  the  remainder  of  this  article  on  energy 
savings  in  hydronic  systems,  but  the  reader  is  urged  to  keep  the  broader 
applicability  of  the  results  in  mind. 

Although  polymers  are  very  effective  drag-reducing  additives,  it  has 
been  generally  recognized  by  now  that  polymeric  drag-reducing  additives 
are  not  well-suited  for  recirculating  flow  applications  because  of  their 
susceptibility  to  permanent  mechanical  degradation,  but  that  surfactant 
additives  -on  the  contrary-  are  very  promising  fluids  for  those  applications, 
because  they  do  not  suffer  from  permanent  mechanical  degradation.  These 
surfactants  are  the  additives  we  have  been  studying  for  hydronic  heating 
and  cooling  systems  applications.  Such  systems  in  large  buildings  or 
groups  of  buildings  appear  to  be  promising  potential  energy  conservation 
applications  for  surfactant  drag-reducing  additives.  About  15%  or  20%  of 
the  chiller  full-load  power  consumption  in  a  large  cooling  system  may  be 


spent  to  drive  the  circulating  pumps.  Savings  of,  say,  50%  of  this  energy, 
(which  our  preliminary  analyses  suggest  is  possible),  would  indeed  be 
substantial.  In  some  cases,  like  flow  in  long  straight  pipes,  the 
implementation  of  drag-reducing  additives  is  straightforward.  Cooling  and 
heating  systems  are  complex,  however,  and  typically  include  many  fittings, 
valves,  heat  exchangers,  pumps,  etc.  The  flow  conditions  within  these 
systems  may  also  change  significantly  depending  on  load.  An  appropriate 
drag-reducing  additive  should  then  provide  satisfactory  drag-reduction 
efficiency  over  the  full  range  of  changing  system  conditions,  while  not 
impairing  system  performance.  In  addition  to  system  control  and 
performance,  one  must  also  consider  corrosion,  fouling,  and  general 
maintenance  issues.  This  type  of  application  is  therefore  significantly 
more  complex  than  large  primary  distribution  loops  which  involve  mostly 
long  straight  pipes. 

In  a  previous  feasibility  study  [1]  we  have  analyzed  the  general 
characteristics  of  hydronic  cooling  and  heating  systems  on  the  one  hand, 
additive  properties  on  the  other,  and  interactions  between  the  two.  A 
number  of  potential  problems  and  proposed  solutions  were  identified. 
Various  interaction  issues  between  drag-reducing  surfactant  additives  and 
typical  components  of  hydronic  systems  were  also  tested  in  our  laboratory  : 
pumps  [2],  heat  exchangers  [3],  flow  development  and  entry  effects  [4], 
fittings,  etc. 

Some  field  tests  on  drag-reducing  additives  in  hydronic  cooling  and 
heating  systems,  have  been  conducted  in  the  past.  Earlier  tests  were 
conducted  with  polymer  solutions  (e.g.  [5,6]),  but  the  basic  shortcoming  of 
polymer  additives  is  the  rapid  permanent  degradation  they  experience  in 
recirculating  systems.  Recognition  that  surfactants  are  also  good  drag- 
reducing  additives,  but  without  the  sensitivity  to  permanent  degradation 
provided  an  incentive  for  more  tests  with  surfactant  solutions.  Not 
surprisingly,  early  efforts  were  focused  on  large  primary  distribution  loops 
in  district  heating  systems.  These  are  very  favorable  applications  for  drag- 
reducing  additives  because  the  system  involves  primarily  long  straight 
pipes,  with  few  fittings  and  few  heat  exchangers.  In  such  conditions,  the 
overall  drag  reduction  is  expected  to  come  close  to  the  80%  or  85%  that 
can  be  readily  achieved  in  fully-developed  flow  in  straight  pipes.  Much  of 
this  work  was  conducted  in  Europe  where  large  district  systems  are  much 
more  common  than  in  the  US.  Extensive  large-scale  tests  in  Germany  [7], 
for  example,  in  a  district  heating  system  showed  indeed  80%  total  pressure 
drop  reduction.  The  total  heat  transfer  capacity  of  the  plate  heat  exchanger 
was  reduced  by  only  up  to  15%  A  similar  test  in  Denmark  [8]  with  the 
same  additive  showed  75%  total  drag  reduction. 

The  system  we  conducted  our  field  test  in  is  a  smaller  yet  more 
complex  HVAC  system  in  a  building.  We  chose  this  system  as  a  test  bed 
because  it  includes  all  the  main  features  of  other  types  of  recirculating 
systems.  Some  tests  in  building  systems  were  conducted  previously,  but 
because  of  the  complexity  of  such  systems  the  apparent  savings  in 


281 


pumping  power  were  lower  than  in  district  heating  systems,  and  the  results 
also  more  difficult  to  interpret.  Rose  et  al.  [9],  for  example,  tested 
surfactant-drag  reducers  in  a  building  heating  system.  They  observed  the 
expected  level  of  drag  reduction  in  straight  portions  of  the  pipes,  but  noted 
that  the  overall  drag  reduction  was  smaller.  Young  [10]  reported  results  of 
his  test  in  a  system  consisting  of  a  short  chilled  water  loop  with  a  large  air 
coil.  After  introduction  of  a  surfactant  additive,  the  flow  rate  increased  by 
a  factor  corresponding  to  a  total  drag  reduction  level  of  34%,  but  it  is  likely 
that  because  of  the  short  pipe  length  this  drag  reduction  resulted  largely 
from  the  reductions  in  friction  in  the  two  heat  exchangers  themselves.  The 
heat  transfer  coefficient  of  the  chiller  was  reduced  by  up  to  55%,  and  that 
of  air  coils  by  up  to  35%.  Pollert  et  al.  [1 1]  tested  the  surfactant  Habon, 
used  in  previous  tests  in  Germany,  in  a  secondary  distribution  loop  of  a 
district  heating  system  in  the  Czech  Republic.  The  distribution  side  of  that 
district  system  is  similar  to  a  single  building  system,  with  many  fittings 
and  branching,  and  a  large  number  of  heat  exchangers.  They  observed  an 
increase  in  flow  rate  corresponding  to  about  30%  total  drag  reduction  and 
about  20%  of  heat  transfer  reduction  in  the  tube-in-tube  heat  exchanger. 

It  is  important  to  note  the  significant  difference  in  results  achieved  in 
the  district  systems,  characterized  by  long  runs  of  straight  pipes,  on  the  one 
hand,  and  the  building  systems  where  many  valves  and  fittings  may 
interfere  with  drag  reduction,  on  the  other.  Unfortunately,  whereas  a  good 
empirical  knowledge  of  the  drag  reduction  phenomenon  has  been  achieved 
for  fully-developed  conditions  in  straight  pipe,  we  have  much  less 
information  about  flow  in  the  more  complex  components  of  a  typical 
hydronic  circulation  systems  (e.g.  fittings,  pumps,  valves,  heat  exchangers 
etc).  We  have  therefore  endeavored  to  obtain  such  information,  and  in 
particular  in  a  manner  that  is  general  enough  in  scope  and  fundamental 
enough  in  nature  to  be  applicable  to  other  processes  involving  fluid 
transportation  and  heat  exchange  for  drag-reducing  surfactant  solutions.  In 
this  article,  however,  we  limit  ourselves  to  a  description  of  some  of  the 
results  obtained  in  our  field  tests. 

2.  COOLING  SYSTEM  OVERVIEW 

Our  feasibility  study  suggested  that  larger  relative  (and  of  course 
absolute)  savings  would  be  achieved  in  larger  buildings  (because  most  of 
the  total  pressure  drop  corresponds  then  to  straight  pipes  where  high  drag 
reduction  can  be  achieved),  but  it  is  more  convenient  to  conduct  tests  first 
in  a  smaller  system,  that  one  can  keep  better  control  of,  and  where  the 
hardware  is  of  smaller  size  and  the  fluid  quantities  to  handle  are  more 
limited.  Typically,  a  smaller  system  will  nevertheless  involve  all  the  issues 
that  will  also  be  encountered  in  large  systems.  If  the  effects  on  all  the 
components  are  thoroughly  analyzed,  the  results  can  then  be  extrapolated 
readily  to  larger  systems..  The  building  chosen  for  our  test  (the  Engineering 
2  building  at  UCSB)  has  three  floors,  each  with  two  cooled  wings.  A 
layout  of  the  chilled  water  loop  is  shown  in  Figure  1.  There  are  typically 
about  5  or  6  rooms  cooled  in  each  wing,  with  one  cooling  coil  per  room, 
for  a  total  of  34  cooled  rooms,  all  laboratories.  The  total  area  of  the  cooled 
space  is  about  2800  m2  (30,000  ft2),  far  less  than  the  size  of  buildings 
thought  to  be  best-suited  for  the  use  of  drag-reducing  additives.  The 
chilled  water  is  cooled  in  a  200  tons  (700  kW  thermal  power)  chiller  and 
circulated  by  one  of  two  pumps  in  constant  flow  rate  mode.  The  pumps, 
chiller,  cooling  towers,  fans,  are  all  located  on  the  penthouse  floor.  (More 
detailed  technical  specifications  for  the  main  pieces  of  equipment  and  the 
piping  can  be  found  in  [12].  An  individual  room  air  temperature  is 
controlled  by  a  thermostat  located  in  the  room.  The  thermostat  operates 
two  valves,  one  on  the  hot  water  coil  (there  is  also  a  hot  water  distribution 
system  similar  to  the  chilled  water  system  described  here),  and  one  on  the 
cold  water  coil.  The  main  control  valves  in  the  chilled  water  system  are 
three-way  valves,  which  control  the  water  flow  through  the  coil  depending 
on  the  cooling  demand,  while  maintaining  the  total  flow  through  the  valve 
approximately  constant  through  diversion  of  cold  water  in  a  bypass  line  in 
parallel  with  the  coil  and  including  also  a  balancing  valve. 

For  balancing  purposes,  there  is  also  one  circuit-setter  valve  in  the 
return  line  of  each  coil  assembly.  In  addition,  there  are  also  2  butterfly 
valves  (1  normally  fully  open)  in  each  of  the  6  main  flow  branches  (2 
wings,  3  floors  each)  for  balancing  between  branches  (Fig.  1).  (Our 


analysis  of  the  system  showed  cases  of  poor  balancing  and  general 
overthrottling,  however.)  Finally,  there  is  also  one  main  throttling  valve 
downstream  of  each  pump  that  is  provided  for  final  adjustment  of  the 
water  flow  rate.  These  valves  are  also  partially  closed  in  the  case  of  our 
system,  but  provide  relatively  small  throttling. 

3.  FIELD  TEST  STRATEGY  AND  IMPLEMENTATION 

The  field  test  was  divided  in  two  phases,  each  having  a  different 
main  objective.  In  the  first  test  we  used  an  asymptotic  fluid,  i.e.  a  fluid 
which  provided  maximum  drag-reducing  effect  in  all  components  of  the 
system.  This  fluid,  however,  provided  also  maximum  heat  transfer 
reductions  in  all  heat  exchangers.  In  many  cases  (e.g.  systems  where  good 
heat  transfer  is  needed  in  the  types  of  heat  exchangers  which  are  affected 
by  drag-reducing  additives)  this  may  not  be  acceptable.  This  is  the  case  for 
this  particular  cooling  system,  but  it  was  necessary  to  quantify  in  this  test 
the  maximum  overall  drag  reduction  achievable. 

In  the  second  phase  of  the  test,  a  different  fluid  was  used  in  order  to 
eliminate  the  unwanted  heat  transfer  reduction  in  heat  exchangers  by 
intentional  degradation,  i.e.  temporaiy  elimination  of  the  drag-reducing 
ability  of  the  fluid.  Under  these  conditions,  the  total  drag  reduction  and 
pumping  power  savings  achieved  were  necessarily  smaller  than  in  the  first 
phase. 

In  addition  to  drag  and  heat  transfer  reductions,  several  other  aspects 
of  additive  use  were  addressed  in  both  tests,  such  as  operability, 
maintenance,  compatibility  with  the  materials  in  the  system,  chemical 
stability  of  the  additive,  safety,  etc. 

3.1  Drag  reduction  and  pumping  power  savings 

At  a  given  flow  rate,  the  reduction  in  pressure  drop  is  proportional  to 
the  reduction  in  pumping  power.  For  better  analysis  of  the  results,  it  is 
preferable  to  maintain  the  same  flow  rate  in  the  system  after  introduction  of 
surfactant  additive  as  it  was  with  water.  (This  is  also  needed  to  achieve 
actual  savings  in  pumping  power.)  As  this  system  was  designed  as  a 
constant  flow  rate  system,  we  had  to  install  a  variable-speed  drive  on  the 
chilled  water  circulation  pump  so  that  a  reduced  speed  can  be  used  to 
maintain  the  nominal  flow  rate  when  the  pressure  drop  in  the  system 
decreases.  The  comparison  between  pump  heads  in  operation  for 
surfactant  solution  and  water  at  the  same  flow  rate  should  therefore  give  us 
total  drag  reduction  and  pumping  power  savings.  It  is  important,  however, 
to  keep  all  valves  in  the  system  at  the  same  degree  of  opening,  for  a 
meaningful  comparison  to  be  achieved.  (In  this  case,  the  pressure  drop  on 
all  control  valves  will  remain  the  same  as  for  water,  at  the  given  -nominal- 
flow  rate  through  the  heat  exchangers.  It  is  indeed  necessary  for  good 
control  and  balancing  that  a  certain  amount  of  the  total  pump  head  be  used 
for  pressure  drop  on  valves).  Some  valves,  such  as  the  balancing  valves, 
are  maintained  in  a  fixed  position  to  provide  proper  distribution  of  chilled 
liquid  in  the  system.  There  are,  however,  also  control  valves,  one  for  each 
room  or  coil  unit.  In  order  to  keep  all  the  control  valves  in  the  same 
position,  we  allowed  the  chilled  water  temperature  to  rise  to  the  ambient 
temperature  (with  the  chiller  compressor  turned  off)  and  let  the  control 
system  open  all  valves  fully  in  a  (futile)  attempt  to  cool  the  rooms  to  the 
preset  temperature.  No  heat  transfer  measurement  is  possible,  of  course, 
under  such  conditions,  however.  (Theoretically,  this  approach  would  not 
be  necessary  for  three-way  control  valves  such  as  those  used  in  this 
building,  which  should  provide  a  constant  total  flow  rate  through  the  heat 
exchanger  and  the  by-pass  at  all  positions,  but  this  was  not  the  case,  as  our 
measurements  have  shown). 

Besides  the  pump  head  measurement,  we  also  measured  the  electrical 
power  used  by  the  electric  motor  driving  the  pump  as  another 
quantification  of  the  total  drag  reduction,  but  this  power  depends  on 
additional  parameters  such  as  efficiency  of  the  motor  and  pump  which  can 
vary  with  load  and  speed.  In  addition  to  the  total  drag  (or  pumping  power) 
reduction  in  the  whole  system,  we  also  measured  local  drag  reduction  in 
many  locations  in  the  system.  The  parts  of  the  system  in  which  drag 
reduction  was  measured  vary  in  size  from  a  whole  wing  to  a  vety  short 
section  of  piping.  The  pressure  drop  as  a  function  of  the  flow  rate  was  also 
measured  for  all  the  typical  valves  in  the  system  (i.e.  balancing  valves, 
circuit  setters,  and  bypass  valve  through  the  coils)  as  well  as  for  the 


282 


evaporator  and  some  typical  coils.  We  also  calculated  the  total  drag 
reduction  in  the  system  from  the  measured  local  drag  reduction  in  typical 
components  and  sections  by  integration  over  the  whole  system,  in  order  to 
see  if  the  calculation  matched  the  total  drag  reduction  measured.  A  good 
match  between  the  total  drag  reduction  obtained  in  these  two  ways  would 
indeed  be  a  strong  indication  that  measurements  are  appropriate  and  that 
no  unknown  or  unanticipated  effect  significantly  affected  the  results. 

Another  issue  of  interest  was  the  level  of  drag  reduction  that  can  be 
achieved  in  large  size  fittings.  There  was  indeed  very  little  information 
available  about  this  issue,  and  we  wanted  to  make  some  measurements  to 
investigate  this  question.  We  had  seen  earlier  in  the  laboratory  that  a  1/2" 
threaded  elbow  exhibited  no  drag  reduction  and  even  some  increase  in 
pressure  drop  at  low  Reynolds  numbers,  but  our  analysis  at  that  time 
suggested  the  possibility  that  there  may  well  be  some  drag  reduction 
present  in  elbows  of  larger  size,  and  especially  so  for  smoother  welded 
elbows.  Accordingly,  we  chose  a  section  of  the  6"  pipe  at  the  outlet  of  the 
evaporator  which  contains  3  elbows  and  some  sections  of  straight  pipe  for 
our  measurements  in  these  elbows.  Pressure  taps  of  a  special  design  that 
allow  averaging  of  3  pressure  measurements  at  each  connection  were  used 
to  minimize  the  effect  of  viscoelastic  pressure  hole  error,  since  these  may 
be  significant  because  of  the  very  low  pressure  differences  measured. 

3.2  Heat  transfer  capacity  of  the  heat  exchangers 

There  are  two  types  of  heat  exchangers  in  this  cooling  system.  One  is 
a  large  shell-and-tube  exchanger  which  serves  as  the  chiller's  evaporator,  in 
which  the  refrigerant  evaporates  on  the  shell  side  and  the  circulating 
chilled  water  or  solution  is  cooled  on  the  tube  side.  There  are  also  34  coils, 
one  for  each  cooled  room,  in  which  the  chilled  water  cools  incoming  air. 
The  coils  are  in  parallel  arrangement  with  the  evaporator,  so  that  the  chilled 
water  passes  once  through  the  evaporator  and  only  once  through  one  of  the 
coils,  for  each  cycle  afound  the  loop.  The  coils  are  m&de  of  finned  copper 
tubes,  with  the  air  flowing  on  the  outer  side  of  the  pipes,  and  the  chilled 
water  solution  inside  the  tubes.  The  coil  tubes  go  through  several  passes 
across  the  air  flow,  each  pass  starting  with  a  180°  elbow. 

Reduced  heat  transfer  on  the  surfactant  side  would  result  in  an 
increase  in  the  temperature  difference  needed  to  transfer  a  given  amount  of 
heat,  which  in  turn  would  reduce  the  overall  system  thermodynamic 
efficiency.  There  is  some  difference  between  the  two  types  of  heat 
exchangers,  however.  The  secondary  fluid  in  the  coils  is  air,  which  has 
poor  heat  transfer  properties  compared  to  water.  As  a  consequence,  the 
dominant  resistance  to  heat  transfer  is  usually  on  the  air  side  for  these  coils 
(even  considering  the  fins),  which  means  that  any  reduction  in  heat  transfer 
on  the  surfactant  side  will  affect  the  total  heat  transfer  to  a  smaller  extent, 
as  our  tests  in  the  laboratory  had  already  shown.  For  the  evaporator,  the 
corresponding  situation  was  much  less  clear,  because  the  heat  transfer  to 
the  evaporating  refrigerant  depends  considerably  on  the  design  of  the  heat 
exchanger. 

A  major  difficulty  we  encountered  in  our  measurements  of  the  heat 
transfer  capacity  of  the  evaporator  was  that  the  chiller  was  operating  most 
of  the  time  in  unsteady  mode,  which  would  introduce  large  errors  in  the 
measurements.  We  had  therefore  to  increase  artificially  the  cooling  load  in 
order  to  overcome  this  problem  and  to  achieve  a  steady  operation  with  high 
thermal  loads.  This  was  accomplished  by  running  the  hot  water  boiler 
simultaneously  with  the  chiller.  For  a  number  of  cooling  coils,  the  control 
valves  were  disconnected  from  the  thermostatic  control  and  blocked 
manually  in  the  fully-open-to-the-coil  position.  This  ensured  full  cooling 
load  on  those  coils.  The  air  supplied  to  the  rooms  was  then  maintained  at 
the  desired  temperature  by  the  normal  thermostatic  control  action  on  the 
heating  coils.  We  could  measure  in  this  fashion  the  heat  transfer  capacity 
of  the  evaporator  in  steady  conditions  at  any  load.  This  technique  was  a 
major  improvement  in  the  measurement  procedure.  Not  only  were  results 
more  accurate  at  high  thermal  loads,  but  this  approach  enabled  us  to  ran 
and  test  the  cooling  system  at  any  load,  even  during  the  winter  time.  The 
temperature  measurements  for  water  were  achieved  by  direct  immersion  of 
thermoresistors,  whereas  the  refrigerant  saturation  temperature  was 
calculated  from  measured  saturation  pressure  in  the  evaporator  shell.  (The 
effects  of  superheat  and  subcooling  can  be  neglected  for  purpose  of 
comparison  between  water  and  surfactant  solution  operation,  at  the  same 


load  and  the  same  operating  conditions.) 

The  extent  of  a  possible  reduction  in  heat  transfer  will  likely  be 
greater  in  the  coils  with  longer  straight  tubes,  because  the  flow  will  have  a 
greater  opportunity  to  develop  downstream  of  the  entrance  and  of  the  180° 
bends.  Accordingly,  to  quantify  the  worst  possible  case,  we  have  identified 
the  largest  coil  with  the  longest  straight  exchanger  tubes  and  instrumented 
it  with  all  the  necessary  sensors  for  water  and  air  temperature 
measurements.  The  heat  flux  was  measured  on  the  water  side,  because 
water  flow  rate  measurements  are  more  accurate.  This  flow  rate  was 
obtained  from  an  orifice  meter  in  the  branch  with  all  the  other  coils  shut 
off.  The  air  flow  rate  is  kept  essentially  constant  in  this  system,  which 
simplifies  the  measurements.  The  air  velocity  was  measured  in  the  center 
of  the  duct  with  a  Pitot  tube.  This  measurement  alone  can  not  be  used  for 
air  flow  calculations,  but  can  be  used  for  comparison  purposes  since  it 
should  remain  constant  for  a  given  flow  rate.  The  air  flow  rate  was  then 
calculated  from  the  heat  balance.  Reliable  measurements  could  be 
obtained  only  under  steady  conditions,  and  achieving  these  was  done  in  a 
fashion  similar  to  that  used  for  the  evaporator  measurements. 

3.3  Measurement  techniques  and  accuracy 

Variable  reluctance  pressure  transducers  were  used  for  pressure 
measurements  at  various  locations  in  the  system.  These  feature 
interchangeable  diaphragms  to  cover  wide  measurement  ranges  with  good 
accuracy.  With  appropriate  calibration,  they  are  capable  of  1  %  accuracy 
for  pressure  difference  measurements  in  the  upper  1/4  of  any  diaphragm 
range.  The  instrumentation  of  the  main  6"  distribution  pipe  was 
challenging,  however,  because  of  the  very  low  level  of  measured  pressure 
differences.  This  is  because  of  the  large  diameter  and  the  short  sections  of 
pipe  over  which  the  pressure  differences  are  measured.  The  problem  is 
compounded  for  the  flow  of  surfactant  solution,  for  which  the  errors  due  to 
viscoelastic  effects  (also  known  sometimes  as  hole  pressure  errors)  may 
become  relatively  large.  This  may  be  so  even  for  differential  pressure 
measurements  if  there  are  imperfections  in  the  holes  such  as  burrs  or 
deviations  in  shape.  To  alleviate  the  problem,  several  pressure  taps  were 
installed  at  each  of  a  couple  of  axial  locations  in  the  longest  straight  run  of 
pipe.  The  use  of  several  taps  and  averaging  at  a  given  axial  location 
increases  greatly  the  accuracy  of  these  small  pressure  difference 
measurements. 

A  total  flow  measuring  device  was  installed  at  the  pump  discharge. 
It  is  a  non-magnetic  impeller-based  sensor  which  provides  a  frequency 
signal  proportional  to  the  flow  rate.  The  manufacturer  lists  the  sensor  as 
having  a  1%  accuracy.  There  may,  however,  be  a  greater  error  when 
measuring  the  flow  rate  of  our  surfactant  solutions  because  of  the 
viscoelastic  nature  of  the  fluid.  Our  laboratory  experience  with  similar 
flow  measuring  devices  suggested  that  the  deviations  in  flow  rate 
measurements  relative  to  water  are  mostly  due  to  viscosity,  and  less  so  due 
to  differences  in  velocity  profile.  However,  as  will  be  discussed  later,  the 
surfactant  solution  prepared  from  the  particular  batch  used  for  this  test  did 
not  show  any  increase  in  viscosity  relative  to  water.  This  reduced  the 
problem  of  flow  measurement  error  due  to  the  different  fluid  properties  for 
water  and  the  surfactant  solution.  Accordingly,  we  can  consider  the  total 
flow  rate  measurement,  both  for  water  and  surfactant  solution  to  be 
comparatively  repeatable  within  about  3%  (and  underestimated  for  the 
surfactant  solution,  meaning  that  the  power  savings  estimates  will  also  be 
underestimated). 

In  addition  to  this  total  flow  sensor,  each  of  the  six  branches  has  also 
an  orifice-type  flow  sensor  installed.  Calibration  data  have  been  obtained 
that  enable  us  to  convert  the  measured  pressure  drop  to  a  flow  rate.  These 
orifice  meters  are  rated  at  1%  accuracy  with  water,  but  the  same 
considerations  regarding  the  measurement  of  flow  rate  of  a  surfactant 
solution  mentioned  for  the  impeller  flow  meter  apply  here  as  well.  Paddle 
wheel  flowmeters  were  also  used  for  some  local  drag  reduction 
measurements.  Their  accuracy  is  about  4%  after  calibration,  which  is  less 
than  the  installed  impeller  and  orifice  flowmeters.  This  reduced  accuracy 
is  of  lesser  importance,  because  these  flowmeters  are  used  only  for  local 
drag  reduction  measurements,  and  not  for  the  total  energy  savings 
measurements. 

Analyzing  the  uncertainty  of  the  pressure  drop  measurements,  one 


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should  consider  that  a  meaningful  comparison  of  pressure  drops  for  runs 
with  water  and  drag-reducing  solution  must  be  conducted  at  the  same  flow 
rate.  Consequently,  a  major  uncertainty  factor  is  that  of  the  flow  rate 
measurements,  not  only  because  this  uncertainty  is  higher  than  the 
uncertainty  in  pressure  drop  measurements,  but  also  because  the  pressure 
drop  is  function  of  the  velocity  squared.  Overall,  for  water  runs,  the 
uncertainty  of  pressure  drop  measurements  is  +3%/-3%  of  the  actual 
quantity  measured;  and  for  surfactant  solution  +3%/-7%,  taking  into 
account  the  uncertainty  in  underlying  flow  rate  measurements. 

Fluid  temperature  measurements  were  obtained  from  1/8"  sheathed 
thermoresistor  sensors.  An  exception  is  the  refrigerant  temperature  in  the 
evaporator  which  is  calculated  from  saturation  pressure  measurements.  All 
temperature  measurements  were  interfaced  to  a  computerized  data 
acquisition  system.  The  nominal  accuracy  of  the  thermoresistors  used  for 
the  temperature  measurements  is  0.1  °C,  but  careful  calibration  gave  us  a 
proven  accuracy  of  better  than  0.05°C,  including  a  negligible  error  in 
resistance  measurement.  The  uncertainty  in  the  heat  transfer  capacity 
calculation  for  the  heat  exchangers  is  mostly  due  to  the  uncertainty  in  the 
temperature  difference  measurements  (and  to  a  lesser  degree  due  to  the 
flow  rate  measurements).  The  uncertainty  in  the  heat  transfer  capacity  of 
the  air  cooling  coil  is  +5%/-5%  for  the  water  runs,  and  +5%/-7%  for  the 
surfactant  solution  runs.  For  the  evaporator,  the  uncertainty  in  heat 
transfer  capacity  is  somewhat  higher  than  for  the  air  coil  (because  the 
saturation  temperature  is  calculated  from  saturation  pressure 
measurement),  namely  about  +7%,  -7%  of  the  measurement,  for  both 
water  and  surfactant  runs.  Those  uncertainty  limits  refer  to  the  nominal 
(maximum)  thermal  loads  (in  contrast  to  pressure  drop  measurements),  and 
remain  the  same  in  absolute  values  at  lower  thermal  loads. 

4.  RESULTS  AND  DISCUSSION 

We  will  present  separately  the  results  for  the  first  and  the  second 
phases  of  the  test,  because  very  different  objectives  were  aimed  at  and 
significantly  different  fluids  were  used.  In  the  presentation  of  results  for 
the  first  phase  the  focus  will  be  on  drag  reduction  measurements,  whereas 
for  the  second  phase  we  will  emphasize  the  heat  transfer  results.  The 
reader  should  keep  in  mind  that  one  can  not  achieve  maximum  drag 
reduction  (as  in  the  first  phase)  and  an  unimpaired  heat  transfer  (as  in  the 
second  phase)  at  the  same  time.  An  optimum  should  be  found  for  any 
particular  system,  and  a  fluid  with  appropriate  degradation  characteristics 
should  be  used. 

4.1  First  Phase  of  the  field  test:  Maximum  Drag  Reduction 

The  measurements  were  first  conducted  with  water  and  then  repeated 
with  the  surfactant  solution.  The  drag-reducing  surfactant  additive  used  in 
the  test  was  Ethoquad  T 13-50  by  AKZO  Chemicals.  The  surfactant  is  tris 
(2-hydroxyethyl)  tallowalkyl  ammonium  acetate  (tallowalkyl- 
N(C2H4)OH)3Ac).  We  used  as  counterion  2-hydroxyl  benzoate  (sodium 
salicylate)  from  Aceto,  Inc.  in  a  1  :  2.5  molar  ratio  of  surfactant  to 
counterion  salt.  The  solvent  used  for  the  surfactant  solution  was  tap  water. 
The  numbers  used  hereafter  for  solution  concentration  refer  to  the 
surfactant,  with  an  assumed  constant  2.5  molar  ratio  of  NaSal  to  surfactant. 
Drag  reduction  was  continuously  measured  during  the  whole  test  period  at 
a  flow  velocity  of  1.5  to  2  m/s  in  a  15  mm  pipe  we  installed  for  that 
purpose  on  the  second  floor.  This  is  the  average  chilled  water  velocity  in 
pipes  throughout  the  system.  At  that  velocity,  the  drag  reduction  level  in 
that  pipe  was  about  75%  (i.e.  about  asymptotic)  for  a  concentration  of 
1000  ppm  to  1200  ppm,  which  suggested  that  asymptotic  drag  reduction  is 
likely  in  all  straight  pipes  in  the  system  for  fully-developed  conditions. 
(We  know  from  laboratory  tests  that  drag  reduction  measured  in  pipes  of 
different  diameters  for  this  type  of  fluid  scales  with  bulk  velocity  within 
5%,  for  pipes  with  diameters  larger  than  10  mm  [13]  which  allows  us  to 
evaluate  the  drag  reduction  level  in  bigger  pipes.)  However,  this  particular 
solution  showed  problems  of  chemical  instability,  particularly  at  low 
concentrations,  and  we  increased  the  concentration  further  to  about  2300 
ppm  of  surfactant,  maintaining  the  same  molar  ratio  of  counterion  to 
surfactant  of  2.5.  In  this  manner  we  achieved  maximum  drag  reduction 
effects  for  this  system,  but  had  to  leave  the  heat  transfer  control  test  for  the 
second  phase,  when  another,  more  chemically  stable  surfactant  was  used. 


4.1.1  Drag  reduction  and  pumping  power  savings 

We  have  measured  the  pump  head  for  water  and  surfactant  solutions, 
while  keeping  all  control  valves  in  the  fully  open  to  the  coils  position  and 
varying  the  flow  rate  by  adjustment  of  the  variable  speed  drive.  Some 
results  are  shown  in  Fig.  2.  The  hydraulic  pumping  power  can  be 
calculated  from  the  flow  rate  and  pump  head  for  both  water  and  surfactant 
solution.  The  comparison  of  the  pump  heads  at  the  same  flow  rate  gives 
then  a  direct  measure  of  pumping  power  savings.  We  see  that  the  pump 
head  and  therefore  the  hydraulic  pumping  power  was  reduced  by  about 
30%  over  the  entire  range  of  measurements. 

We  also  measured  the  electrical  power  used  by  the  pump  motor.  The 
reduction  in  electrical  power  used  by  the  pump  motor  was  about  25%,  or 
slightly  less  than  the  reduction  in  hydraulic  pumping  power.  Interestingly, 
both  numbers  are  very  close  to  the  original  pre-test  estimates  (25%) 
generated  by  assuming  asymptotic  drag  reduction  in  straight  pipes,  and  no 
drag  reduction  in  fittings  and  valves. 

In  addition  to  overall  pressure  drop  reduction,  we  also  measured  the 
drag  reduction  level  in  many  singular  components  of  the  system,  as  well  as 
in  one  entire  wing.  These  data  were  then  used  to  calculate  the  overall  drag 
reduction  by  summing  contributions  of  each  sub-system.  In  this  cooling 
system,  about  20%  to  30%  of  the  total  pump  head  results  from  the  pressure 
drop  in  the  fittings,  and  we  were  therefore  particularly  interested  in 
measuring  the  pressure  drop  in  some  large  fittings  which  could  not  be 
tested  readily  in  our  laboratory.  Although  the  fittings  are  of  various  types, 
elbows  and  tees  are  the  most  common  in  the  system  and  may  be  looked  at 
as  "representative"  fittings.  We  have  therefore  measured  the  pressure  drop 
for  a  series  of  three  6"  elbows  for  water  and  surfactant  solution.  Over 
velocities  ranging  from  0.5  m/s  to  2  m/s,  the  pressure  drop  coefficient  for 
the  series  of  3  elbows  was  found  to  be  reduced  by  about  40%  relative  to 
water.  More  details  on  the  results  and  experimental  configuration  can  be 
found  in  [12].  Considering  that  a  significant  portion  of  the  pressure  drop 
in  the  system  may  be  due  to  the  pressure  drop  in  fittings,  the  drag  reduction 
in  large  fittings  may  then  contribute  significantly  to  the  overall  drag 
reduction  for  the  whole  system. 

The  drag  reduction  level  was  also  measured  in  the  return  line  of  one 
of  the  six  horizontal  chilled  water  distribution  loops,  namely  the  north 
wing  of  the  second  floor.  This  wing  plus  the  other  five  constitute  most  of 
the  chilled  water  pipe  system  (besides  a  short  section  of  6"  pipe  supplying 
the  chiller  and  the  vertical  distribution  lines).  A  more  complete  analysis  of 
these  measurements  can  be  found  elsewhere  [12]  as  well.  The  drag 
reduction  levels  measured  in  this  line  at  the  nominal  flow  rate  were  55%, 
37%  and  34%,  depending  on  flow  distribution  in  the  coils.  We  can  then 
use  these  results  of  local  drag  reduction  to  predict  the  overall  drag 
reduction  for  the  whole  system.  The  37%  corresponds  to  a  flow 
configuration  which  is  a  good  approximation  for  the  pressure  drops  in  the 
return  loops  of  all  coils.  (The  circuit  setters  may  be  on  average  slightly 
more  closed  in  the  coils  closer  to  the  vertical  main  to  compensate  for  less 
pressure  drop  in  the  horizontal  main.)  The  supply  lines  are  very  similar  to 
the  return  lines  and  the  same  drag  reduction  level  is  to  be  expected  there. 
The  other  components  in  the  horizontal  distribution  lines  of  the  6  wings 
that  are  still  not  accounted  for  are  the  coil  control  valves,  the  coils 
themselves,  and  the  butterfly  balancing  valves  (one  in  each  wing).  There  is 
no  drag  reduction  in  the  valves  and  only  little  drag  reduction  in  the  coils 
(see  below).  Since  about  one  third  of  the  total  pressure  drop  in  horizontal 
distribution  corresponds  to  the  pressure  drop  in  these  components,  our 
average  drag  reduction  gets  reduced  to  about  26%.  However,  to  complete 
the  picture  we  still  have  to  consider  the  vertical  portion  of  the  distribution 
system,  and  the  evaporator.  About  50%  drag  reduction  was  measured  in 
the  evaporator  (see  below)  and  similar  drag  reduction  is  expected  in  the 
vertical  pipes  (which  actually  contribute  very  little  to  the  total  pressure 
drop).  About  80%  of  the  total  pressure  drop  in  the  system  (2.6  105  Pa  with 
water)  is  due  to  the  horizontal  distribution  lines  and  only  20%  to  the 
vertical  distribution  lines  and  evaporator.  Our  estimate  of  the  total  drag 
reduction  becomes  then  about  30%,  which  is  about  the  reduction  in  pump 
head  actually  measured,  a  confirmation  of  the  general  validity  of  our 
analysis. 


284 


4.1.2  Heat  transfer  reduction 

The  heat  transfer  capacities  (U)  of  the  evaporator  and  coil  were 
calculated  from  measurements,  as  described  below,  for  water  and  for  the 
surfactant  solution.  They  are  defined  as  the  amount  of  heat  transferred 
from  one  fluid  to  another,  for  a  unit  logarithmic  temperature  difference. 
For  the  evaporator,  the  logarithmic  temperature  difference  is  calculated 
from  the  measured  inlet  and  outlet  chilled  water  (or  solution)  temperature 
and  the  saturation  temperature  of  the  refrigerant.  The  temperatures  of  the 
chilled  liquid  were  measured  directly,  whereas  the  refrigerant  temperature 
was  taken  to  be  the  saturation  temperature  corresponding  to  the  refrigerant 
pressure  measured  in  the  evaporator  (with  supercooling  of  the  refrigerant 
assumed  negligible).  The  results  for  the  chiller  thermal  capacity  per  unit 
logarithmic  mean  temperature  difference  across  the  evaporator  are  shown 
in  Fig.  3.  As  can  be  seen,  the  reduction  in  thermal  capacity  of  the 
evaporator  is  about  30%  for  the  range  of  thermal  load  covered  (from  about 
1 20  kW  to  3 10  kW).  The  lower  limit  is  the  lowest  load  achievable  with  the 
current  chiller  control  setup.  (The  chiller  can  not  safely  operate  below  this 
limit,  because  hot  gas  bypass  which  would  allow  operation  at  very  low  load 
is  not  provided  in  this  unit).  On  the  other  hand,  we  could  not  run  the 
chiller  beyond  310  kW  of  thermal  load,  because  the  overcurrent  protection 
for  the  compressor  motor  shuts  the  system  off  at  that  point  (even  though 
this  is  less  than  the  nominal  thermal  load,  mainly  because  of  the  relatively 
poor  condition  of  the  cooling  tower).  The  pressure  drop  of  the  chilled 
liquid  (water  or  surfactant  solution)  in  the  evaporator  was  also  measured  at 
various  flow  rates.  About  60%  drag  reduction  was  achieved  with  the 
surfactant  solution  over  the  whole  range  of  flow  rates.  The  evaporator  tubes 
are  about  15.5  mm  in  diameter  and  4  m  long,  but  the  drag  reduction 
measured  under  fully-developed  conditions  in  a  custom  1/2"  pipe  (15.7 
mm)  loop  added  immediately  downstream  of  the  evaporator  showed  75%, 
however.  The  difference  can  be  attributed  to  undeveloped  flow  conditions 
in  the  upstream  part  of  the  evaporator  tubes  and  to  entry  effects.  The  fact 
that  the  measured  total  heat  transfer  reduction  in  the  evaporator  is  only 
30%  can  be  explained  by  a  larger  heat  transfer  resistance  on  the  refrigerant 
side  than  on  the  chilled  liquid  side.  This  is  an  important  point,  because  it 
illustrates  that  the  anticipated  large  heat  transfer  reduction  on  the  surfactant 
side  of  the  heat  exchangers  may  not  necessarily  translate  into 
correspondingly  large  decreases  in  overall  heat  exchanger  performance  - 
which  would  likely  render  the  systems  inoperable  without  further 
intervention. 

The  largest  coil  heat  exchanger  was  also  instrumented  for  heat 
capacity  reduction  measurements.  The  overall  heat  transfer  capacity  of  this 
coil  was  measured  in  two  regimes:  with  constant  water  flow  (varying  the 
air  flow)  and  with  constant  air  flow  (varying  the  water  flow).  Figure  4 
shows  the  heat  transfer  capacity  of  the  coil  per  unit  logarithmic 
temperature  difference  (calculated  in  the  same  way  as  for  the  evaporator) 
for  various  liquid  flow  rates,  but  with  constant  air  flow  rate.  The  air  flow 
rate  is  maintained  as  high  as  possible  (about  3  times  higher  than  normal)  to 
make  the  effect  of  heat  transfer  reduction  on  the  liquid  side  more  apparent. 
At  the  maximum  liquid  flow  rate,  the  reduction  in  thermal  capacity  of  the 
coil,  when  running  the  surfactant  solution  instead  of  water,  is  20%.  When 
the  liquid  flow  rate  is  reduced  the  reduction  becomes  slightly  larger,  up  to 
30%.  These  results  are  similar  to  those  obtained  during  our  tests  of  a 
similar  air  coil  in  the  laboratory  [3]. 

Pressure  drop  measurements  for  the  same  coil,  for  both  water  and  the 
surfactant  solution  showed  drag  reduction  ranging  from  0%  to  35%, 
depending  on  the  solution  flow  rate.  This  is  significantly  less  than  the  60% 
drag  reduction  measured  in  the  evaporator  and  the  75%  measured  in  fully- 
developed  flow  conditions.  The  likely  reason  for  this  low  drag  reduction 
level  is  that  the  flow  could  not  develop  fully  in  the  short  sections  of  straight 
coil  tubes  between  the  180°  elbows. 

4.2  Second  phase  of  the  field  test:  Heat  transfer  control 

The  primary  objective  for  the  second  phase  of  the  field  test  was  to 
prove  that  the  heat  transfer  in  all  heat  exchangers  can  be  maintained  at 
the  same  level  as  for  water  by  proper  choice  of  the  surfactant  solution 
and  by  relying  on  intentional  temporary  degradation.  An  extensive 
investigation  of  the  nature  and  phenomenology  of  the  temporary 
degradation  and  recovery  of  surfactant  solutions  was  first  undertaken  in 


the  laboratory.  Various  surfactant  solutions  were  tested  to  determine  the 
chemical  characteristics  of  the  phenomena.  As  a  result  of  those  tests  we 
decided  to  use  a  new  nonionic  surfactant  solution  (SPE95285), 
developed  for  us  by  Dr.  M.  Hellsten  of  Akzo  Nobel  Chemicals,  in  a 
concentration  of  around  2500  ppm.  This  solution  was  thought  to 
provide  good  control  of  heat  transfer  in  both  heat  exchangers  and  also 
high  enough  drag  reduction  in  the  rest  of  the  system  to  provide 
satisfactory  pumping  power  savings. 

In  addition  to  the  measurements  used  in  the  first  phase  of  the  field 
test,  we  developed  for  the  second  phase  some  portable  devices  that 
enabled  us  to  measure  the  fluid  characteristics  at  practically  any  location 
in  the  system,  which  in  turn  allowed  us  to  ascertain  the  average  drag 
reduction  and  heat  transfer  reduction  in  every  section.  To  achieve  this, 
we  measured  drag  reduction  in  customized  2  mm  and  5  mm  inner 
diameter  portable  characterization  test  pipes.  The  corresponding  fluid 
was  diverted  from  the  system  though  the  test  pipes  by  special  fittings 
which  provided  a  smooth  cone-shaped  entry  so  that  the  fluid  entered  the 
pipe  ‘as  is*  and  was  not  temporarily  degraded  by  the  entry.  The  drag 
reduction  ability  of  the  fluid  was  calculated  by  measuring  the  pressure 
drop  and  flow  rate  in  the  characterization  pipe,  which  gave  us 
information  on  the  drag  reduction  in  the  system  at  that  location.  To 
facilitate  this  comparison,  the  fluid  velocity  in  the  characterization  pipe 
was  kept  equal  to  the  fluid  velocity  in  the  main  system,  in  order  to 
eliminate  diameter  effects.  From  the  drag  reduction  ability  of  the  fluid 
we  can  then  estimate  the  heat  transfer  reduction  using  the  DR  /  HTR 
relationships  we  developed.  We  were  therefore  able  to  generate  a  map  of 
the  local  drag  reduction  in  the  whole  building,  and  then  to  integrate 
these  measurements  to  obtain  the  total  drag  reduction  and  pumping 
power  savings.  We  can  also  calculate  the  heat  transfer  on  the  surfactant 
solution  (water)  side,  and  consequently  the  overall  heat  transfer  in  the 
heat  exchangers  knowing  the  relationship  between  the  heat  transfer 
resistances  on  both  sides  of  the  heat  exchanger.  This  approach  is  not 
only  more  accurate  than  the  integral  measurements  of  the  overall  heat 
transfer  capacity,  but  also  more  general,  and  the  results  can  be  readily 
applied  to  other  systems  of  different  size  and  heat  exchangers 
characteristics. 

4.2.1  Drag  reduction  and  pumping  power  savings 

At  the  nominal  flow  rate  the  pump  head  in  the  system  was  reduced 
by  about  12%  (Figure  2).  The  reduction  in  electrical  power  used  by  the 
pump  motor  was  also  measured  at  about  12%.  The  difference  with  the 
30%  reduction  in  total  head  measured  in  the  first  phase  is  due  to  the  loss  of 
drag  reduction  in  the  heat  exchangers  and  in  the  pipes  downstream  of  the 
heat  exchangers. 

In  addition  to  the  overall  pressure  drop  reduction,  we  also 
measured  the  drag  reduction  level  in  many  singular  components  of  the 
system,  as  well  as  in  one  entire  wing.  These  data  were  then  used  to 
calculate  the  overall  drag  reduction  by  summing  contributions  of  each 
sub-system,  as  was  done  in  the  first  phase.  We  calculated  the  expected 
overall  level  of  drag  reduction  for  the  system  and  obtained  a  good  match 
with  the  total  drag  reduction  measurements.  Both  the  direct 
measurements  and  the  integration  of  local  measurements  showed  an 
overall  pressure  drop-i.e.  power-  reduction  of  about  10  to  15%,  with  a 
slightly  greater  reduction  at  high  thermal  loads  because  of  the  effect  of 
temperature  on  the  drag-reducing  ability  of  the  solution.  A  full  report 
on  local  drag  reduction  measurements  will  be  published  elsewhere. 
Figure  5  shows  a  distribution  of  drag-reducing  effects  in  the  whole 
system. 

4.2.2  Heat  transfer  control 

The  heat  transfer  control  used  in  this  field  test  works  on  the 
principle  of  temporary  fluid  degradation  and  subsequent  recovery.  The 
recovery  as  a  function  of  time,  as  well  as  the  level  of  degradation  caused 
by  a  given  pressure  drop  on  the  degrading  device,  depends  on  the 
temperature.  In  our  case,  the  temperature  difference  between  the  supply 
and  return  was  about  3°C  at  full  thermal  load,  but  in  other  systems  it 
could  be  5°C,  which  is  a  common  design  practice  value.  For  the  fluid 
temporary  degradation  upstream  of  the  evaporator,  the  fluid  has  to  be 
degraded  at  the  higher  temperature  level,  which  means  higher 


285 


degradation  is  needed.  Fortunately,  high  degradation  is  taking  place  in 
the  pump  itself.  If  the  pump  hydraulic  efficiency  is  70%,  it  means  that 
30%  of  the  total  pumping  power  -or  42%  of  the  effective  pumping 
power-  is  dissipated  in  the  pump  itself.  This  translates  to  an  equivalent 
pressure  drop  of  42%  of  the  actual  pump  head,  or  in  our  case  about  17 
psi  worth  of  degradation,  which  is  much  more  than  any  other  discrete 
degrading  component  in  the  system.  In  the  case  of  the  coil,  the  situation 
is  different.  The  fluid  must  be  degraded  at  lower  temperature,  which 
means  a  lower  pressure  drop  is  needed.  The  recovery  in  the  case  of  the 
cold  fluid  is  also  slower,  and  the  distance  between  the  degrading  valve 
and  the  coil  is  therefore  less  critical. 

Degradation  devices  with  large  discrete  pressure  drop  are  available 
at  proper  locations  to  be  used  for  our  heat  transfer  control  purposes,  but 
on  the  other  hand  —given  proper  choice  of  the  fluid-there  is  no  other 
location  in  the  system  with  discrete  pressure  drops  that  is  high  enough 
to  cause  undesired  temporary  degradation  of  the  fluid.  In  principle,  it  is 
possible  to  tailor  the  degradation  and  recovery  characteristics  of  a 
surfactant  system  by  varying  one  or  more  of  the  influential  parameters. 
A  12%  of  drag  reduction  capability  was  measured  with  the  5  mm  pipe  at 
the  evaporator  exit  .  The  overall  drag  reduction  in  the  evaporator  at 
nominal  flow  rate  is  measured  at  between  4  and  6%,  with  increasing 
drag  reduction  at  higher  average  temperatures.  From  the  6%  drag 
reduction  in  the  evaporator  we  would  expect  about  10%  heat  transfer 
reduction  on  the  fluid  side  based  on  the  fixed  heat  transfer/drag 
reduction  ratios  we  identified.  Indeed,  the  actual  heat  transfer 
measurements  (Fig.  3)  show  that  the  overall  heat  transfer  reduction  in 
the  evaporator  is  essentially  zero  within  the  experimental  uncertainty 
which  is  estimated  to  be  ±4%  maximum,  because  there  is  about  4  times 
higher  heat  transfer  resistance  on  the  refrigerant  (Freon)  side  than  on  the 
solution  (water)  side. 

In  the  building  tested,  the  control  valves  as  well  as  the  balancing 
valves  are  located  downstream  of  the  coils.  For  our  purposes  it  is  better 
to  have  the  control  valve  upstream  of  the  coil  to  provide  temporary  fluid 
degradation  and  to  eliminate  the  possible  heat  transfer  reduction.  Since 
these  valves  exhibit  a  pressure  drop  of  about  5  psi  at  nominal  flow  rate 
to  the  coil  -which  is  normally  enough  for  degradation-  heat  transfer 
control  on  the  coil  can  then  be  achieved  without  additional  throttling. 
To  provide  and  investigate  fluid  degradation  at  the  coil  entry,  we  used 
an  existing  shut-off  valve  upstream  of  the  coil  for  flow  control,  with 
similar  effects.  This  valve  was  manually  throttled  to  generate  a  pressure 
drop  of  approximately  5  psi.  The  overall  drag  reduction  in  the  coil  for 
the  relevant  temperature  range  was  then  between  5%  and  12% 
depending  on  the  mean  temperature.  Local  measurements  of  solution 
properties  conducted  with  the  5  mm  pipe  indicated  that  the  drag 
reduction  ability  was  about  5%  to  35%  (depending  on  temperature)  at 
the  coil  exit,  and  no  drag-reducing  ability  or  total  degradation  at  the  coil 
inlet.  The  measured  overall  hfcat  transfer  reduction  when  the  fluid  was 
degraded  by  the  upstream  valve  is  negligible  (Figure  4).  In  fact,  looking 
at  the  overall  drag  reduction  we  would  indeed  expect  an  overall  heat 
transfer  reduction  of  only  about  2%  in  the  coil.  This  estimate  is  based 
on  the  known  drag/heat  transfer  reductions  ratio  and  the  ratio  between 
air  and  water  side  heat  transfer  resistances,  which  ranges  from  about  5 
to  10  depending  on  the  conditions  (as  can  be  seen  from  the  data 
corresponding  to  changing  air  velocities  for  water  during  phases  1  and  2 
in  Figure  4). 

5.  SUMMARY  AND  CONCLUSIONS 

We  conducted  a  field  test  of  surfactant  additives  in  a  complex 
recirculating  hydronic  system  in  a  building  that  includes  all  the  main 
components  likely  to  be  found  in  other  hydronic  systems  that  could  benefit 
from  the  drag  reduction  technology.  In  addition  to  an  improved 
understanding  of  the  fluid  /  flow  and  fluid  /  hardware  interactions,  specific 
objectives  could  be  energy  savings,  pump  and  pipe  size  reduction,  an 
increase  in  flow  rate  or  heat  transfer,  or  an  increase  in  system  length.  One 
could  also  combine  some  of  these  features.  In  this  case,  we  focused  on 
energy  savings,  and  paid  particular  attention  to  the  connection  between 
local  and  system  wide  engineering  issues  and  analyses.  The  test  was 


divided  in  two  phases. 

In  the  first  one,  we  measured  the  overall  decrease  in  pressure  drop 
across  the  system  using  a  fluid  giving  maximum  drag  reduction.  The 
pump  head  (and  therefore  the  pumping  power)  was  found  to  decrease  by 
about  30%.  This  number  is  relatively  low  because  of  the  presence  of  many 
valves  and  fittings  in  this  relatively  small  yet  complex  system.  Much 
higher  savings  could  be  obtained  in  bigger  or  simpler  systems.  The  system 
was  found  to  remain  operational,  but  the  heat  exchangers  suffered  from 
significant  decreases  in  thermal  capacity. 

In  the  second  phase  of  the  test,  we  focused  therefore  on  the  issue  of 
elimination  of  these  heat  transfer  reductions,  and  we  were  indeed  able  to 
eliminate  completely  the  undesirable  heat  transfer  limitations  through 
appropriate  choice  of  the  fluid  and  temporary  fluid  degradation  at 
necessary  locations.  This  elimination  has  to  be  accompanied  by  lower  drag 
reduction  in  the  heat  exchangers,  however,  and  the  net  overall  pressure 
drop  reduction  was  smaller.  Again,  proportionally  greater  savings  would 
be  achieved  in  a  bigger  /  simpler  system  or  with  a  more  optimized  fluid. 
Alternatively,  one  could  also  achieve  hardware  size  reduction,  increased 
flow  rate  and  heat  transfer,  or  increased  system  length.  As  in  the  first 
phase  of  the  test,  the  implementation  of  the  technology  was  simple,  and  no 
maintenance,  corrosion,  operability,  performance,  nor  control  difficulties 
were  found. 

This  large-scale  field  study  was  very  successful  and  shows 
conclusively  that  it  is  indeed  possible  in  practice  to  use  surfactant  drag- 
reducing  additives  in  complex  recirculating  systems,  even  those  involving 
heat  exchangers.  The  new  results  and  understanding  generated  should 
bring  us  much  closer  to  the  stage  of  widespread  implementation  of  the  drag 
reduction  technology  in  many  types  of  recirculating  industrial,  commercial, 
and  military  fluid  systems. 

ACKNOWLEDGEMENTS 

The  authors  gratefully  acknowledge  financial  support  by  the 
California  Institute  for  Energy  Efficiency  (contract  No.  4902610  to  EFM) 
the  California  Energy  Commission  (contract  No.  500-94-022  to  EFM),  and 
the  University  of  California;  the  assistance  provided  by  the  Facilities 
Management  personnel  at  UCSB;  laboratory  work  by  Mr.  G.  Aguilar;  and 
the  additives  samples  and  chemistry  information  kindly  provided  by  Drs. 
S.  Shapiro  and  M.  Hellsten  (AKZO  Nobel  Chemicals). 

REFERENCES 

1.  Gasljevic  K.  and  E.F.  Matthys,  1993,  "On  saving  pumping  power  in 
hydronic  thermal  distribution  systems  through  the  use  of  drag-reducing 
additives".  Energy  and  Buildings,  Vol.  20,  pp.  45-56. 

2.  Gasljevic  K.  and  E.F.  Matthys,  1992,  "Effect  of  drag-reducing 
surfactant  solutions  on  centrifugal  pumps  performance",  In  Recent 
advances  in  non-Newtonian  flows,  AMD-Vol.153,  ASME  Pub.,  pp.  49-56. 

3.  Gasljevic  K.  and  E.F.  Matthys  ,1993,  ''Effect  of  drag-reducing  additives 
on  heat  exchangers".  In  Developments  in  non-Newtonian  flows,  AMD- 
Vol.  175,  ASME  Pub.,  pp.  101-108. 

4.  Gasljevic  K.  and  E.F.  Matthys.  1997.  Experimental  investigation  of 
thermal  and  hydrodynamic  development  regions  for  drag-reducing 
surfactant  solutions.  Journal  of  Heat  Transfer  vol.  119,  No.  1,  pp.  80- 
88. 

5.  Leca  A.  and  M.  Leca,  1984,  "Drag  Reduction  and  Heat  Transfer 
Measurements  with  Polyacrylamides  on  a  Model  of  a  District  Heating 
System,"  In  Drag  Reduction  (Proc.  of  the  3rd  International  Conference  on 
Drag  Reduction,  R.  Sellin  and  R.  Moses  eds),  IAHR  Pub.,  paper  D8. 

6.  Martischius  F.D.  and  W.  Heide,  1984,  "Drag  Reduction  in  Heating 
Systems:  Stabilization  of  Polyacrylamide  Solutions  up  to  Temperatures  of 
150°C,"  In  Drag  Reduction  (Proc.  of  the  3rd  International  Conference  on 
Drag  Reduction,  R.  Sellin  and  R.  Moses  eds),  IAHR  Pub.,  paper  D9. 

7.  Steiff  A.,  W.  Althaus,  M.  Weber  and  P.  Weinspach;  1989. 
"Application  of  drag-reducing  additives  in  district  heating  systems",  In 
Drag  Reduction  in  Fluid  Flow:  Techniques  for  friction  control  (eds:  R.H. 
Sellin  and  R.T.  Moses),  Ellis  Horwood  Pub.,  Chichester,  pp.  247-254. 

8.  Hammer  F.,  1993,  "Smooth  water  in  district  heating",  Femwarme 
International.  Vol.  22  (4),  pp.  142-150. 


286 


9.  Rose  G.D.,  K.L.  Foster,  V.L.  Slocum,  and  J.G.  Lenhart;  1984.  "Drag 
Reduction  and  Heat  Transfer  Characteristics  of  Viscoelastic  Surfactant 
Formations."  In  Drag  Reduction  (Proc.  of  the  3rd  International  Conference 
on  Drag  Reduction,  R.  Sellin  and  R.  Moses  eds),  IAHR  Pub.,  paper  D6. 

10.  Young  C.O'C.  J.,  1994,  "Drag  reduction  in  chilled  water  distribution 
system  of  a  200-ton  absorption  chiller",  Proc.  of  the  85th  International 
District  Heating  and  Cooling  Association  Conf.,  IDHCA  Pub.,  Vol.  85, 
pp.  301-317. 

1 1 .  Pollert  J.,  J.  Zakin,  J.  Myska,  and  P.  Kratochvil,  1994,  "Use  of  friction 
reducing  additives  in  district  heating  system  field  test  at  Kladno  - 
Krocehlavy,  Czech  Republic",  Proc.  85th  International  District  Heating 
and  Cooling  Association  Conf.",  IDHCA  Pub..  Vol.  85,  pp.  141-156. 

12.  Gasljevic  K.  and  E.F.  Matthys.  1996.  “Field  test  of  a  drag- 
reducing  surfactant  additive  in  a  hydronic  cooling  system”,  In  Drag 
Reduction  and  Turbulence  Modification,  vol.  FED-237;  vol.  2,  pp.  249- 
260;  ASME,  NY. 

13.  Gasljevic  K.  and  E.F.  Matthys.  1995.  “On  the  Diameter  Effect  for 
Turbulent  Flow  of  Drag-Reducing  Surfactant  Solutions.”  In 
Development  and  Applications  of  Non-Newtonian  Flows  ID,  Vol.  FED- 
231,  pp.  237-243,  ASME  Pub,  Washington  D.C. 


Fig.  2  Pump  head  for  water  and  for  the  2  surfactant  solutions. 


Fig.  1  Schematic  of  the  chilled  water  system.  The  chilled  water  is 
distributed  to  3  floors  of  the  building,  with  two  cooled  wings  at  each  floor. 
There  are  on  average  4  to  5  cooling  coils  in  each  wing  (some  shown  here 
only  on  the  third  floor  north  wing  for  clarity).  Butterfly  valves  are  used  to 
balance  the  water  flow  rate  between  the  wings.  F  stands  for  flow  rate 
sensor. 


chilluc.jnb 


Thermal  Load  [kW] 


Figure  3  :  Overall  heat  transfer  capacity  of  the  evaporator  as  a  function 
of  thermal  load  at  a  nominal  fluid  flow  rate  of  28.5  1/s,  for  both  water 
and  the  2  surfactant  solutions. 


287 


coiluc.jnb 


Figure  4  :  Heat  transfer  capacity  of  the  cooling  coil  for  water  and  the  2 
surfactant  solutions. 


2500  pnm 

savings  [psi] : 

(Total=  7  psi  or 

18%  DR) 

Recovery  time  and 
DR  w.r.t.  distance : 

© 

_ |_  | _ 0.25 _ |  2.0  |l.2|0.(j  2.3  _ j_  0.6 

7  i  _ LM _ i _ i 

ni  i 

1  ,  '  recovery  time 

|  •  .  'v  :  :  40  s  to  60% 

1  . 1 . 1 

^  20  s  to  60% 

30% 

2QQ0  ppm 

savings  [psi] : 

(Total=  6  psi  or 

15%  DR) 

Recovery  and  DR 
with  distance  : 

— n  i  r  r  i  i  i 

W  |  |  0.15  |  1.6  |l.lM  2.0  1  06  1 

III  III  1  1 

n  i  n 

:  j  ]  60s  to  60% 

I  1 . 1 

I  y  30  s  to  60% 

....'  10% 

Pressure  drop  for 
Water  [psi] : 

III  i 

f\  i  Jl  4  l2 

j  \  6.5  psi  in 
evaporator 

1  .  14  psi  control  &  I 

|  /  balancing  Valve  | 

/  2  psi  in  cooling  coil 

A  1  1 

2' .  4  j,  | 

0.3  1  | 

Fluid 

Temperature : 

1  1;  «"C  1  | 

|  j  1  1 

S-:  1. . . . . A . 

1  1  1 

J_. . . 1 „,,J 

12°C 

vc 

pipe  diameters 
and  lengths  : 

1  6”  2”  1.5”  2”  6”  1 

p  36m  60m  6  6m  60m  40m  j 

!  I  Evaporator  I  1  1  _  .  1  1 

•  .  Branch 

11/  1  Branch  1  1  1  balancing  V.  \  |  ! 

_ -i/'  balancing  v.  Ljjn| _ Nj _ . 

- - re 

5  Q>ntrol  and  : 

:  Pump  balancing  valves' 

Supply 

x - ~ 

\  Cooling  coil 

Return 

Figure  5  :  System  temperature  and  pressure  distribution  as  a  function  of 
distance  downstream  of  the  pump. 


288 


PRACTICAL  APPLICATIONS  OF  DILUTE  POLYMER  ADDITIVES  FOR  WATER  CRAFT 

Tadeusz  Kowalski  ,Ph.D.  Professor  Emeritus, 

Department  of  Ocean. Engineering, 

University  of  Rhode  Island  . 

Abstract  -  Effect  of  long  chain  . polymers  on.  drag  of  bodies  moving  through,  water  or  water  moving  inside  pipes  is  well  established.  In.  the 
1960’s  and.  1 970’ s  there  was  a  substantial  research  conducted. in  many  countries.  The  interest  in. the  use  of  polymer  additives  decreased. in 
subsequent  years  due  to  technical  difficulties  of  injection,  and.due  to  the  costs  associated  with. continuous  injection.  Research. of  the  effect  of 
polymer  additives  on.turbulent  drag  is  described. leading  to  a  number  of  significant  findings  and  possible  explanation  of  the  mechanism  of  drag 
reduction.  Tests  of  the  turbulence  characteristics  in  the  boundary  layer  with.  and  .  without  the  polymer  injection  were  conducted  ,  and.  marked  , 
changes  in.  the  structure  of  the  turbulent  eddies  were  measured.  Suppression  of  small  scale  eddies  and.  shift  of  the  turbulence  spectrum 
towards  the  larger  eddy  sizes  were  observed.  Injection. methods  were  tested  by  varying  the  angle  of  the  injection,  slots  to  the  flow  in.  the 
boundary  layer.  The  optimum  injection  was  with. the  slots  at  five  degrees  inclination. to  the  flow,  producing  almost  tangential  stream  of  polymer 
entering  the  boundary  layer.  Discovery  of  the  polymer  persistence  effect  in.  the  boundary  layer  during  drag  reduction,  tests  substantially 
reduced  the  expenditure  of  polymer  additives.  It  was  found. that  a  pulsed. injection. of  one  second. duration. followed  by  fifteen,  second. pause 
retained  . its  drag  reduction,  effect  at  a  substantial  decrease  of  the  amount  of  polymer.  Examples  of  some  practical  drag  reduction. applications 
of  polymer  additives  in  external  flows  are  given  together  with  suggestions  for  future  research. 


I.  INTRODUCTION 

The  objectives  of  the  investigation,  were  to  explore  the 
phenomenon  of  drag  reduction,  due  to  the  presence  of  polymer 
additives  in.  the  boundary  layer  and  .  to  obtain,  an  insight  into  the 
mechanism  of  the  drag  reduction. 

The  scope  of  the  research  was  to: 

i)  investigate  the  turbulence  changes  in  the  boundary  layer 
caused  . by  the  injection  of  polymer  additives 

ii)  develop  a  probable  mechanism  of  the  drag  reduction, 
including  a  molecular  entanglement  hypothesis 

iii)  investigate  persistence  effect  of  additives  in  the 
boundary  layer  leading  to  the  polymer  pulsing  injection  method 

iv)  test  the  effect  of  polymer  on  propeller 

v)  test  the  effect  of  polymer  additives  on  . sound  propagation 

in.  water 

vi)  suggest  possible  applications  of  the  drag  reduction 
phenomena 

II.  EXPERIMENTAL  RESULTS  AND  DISCUSSION 

A  dramatic  change  in.  the  character  of  the  turbulence  was 
observed  . in.  the  boundary  layer  each  time  dilute  solution  of  the  polymer 
additive  was  injected.  The  small  amplitude  (high,  frequency)  turbulent 
velocity  fluctuations  disappeared,  and  the  large  amplitude  (low 
frequency)  fluctuations  were  enhanced.  The  change  in.  the  distribution 
of  eddy  sizes  was  confirmed  . by  observation  using  two  methods. 

First,  using  strip  chart  records  of  the  velocity  fluctuations.  Figure 
1  shows  a  typical  record.  Stretching  the  record’s  time  base  shows  the 
effect  quite  clearly.  Curve  (a)  represents  the  turbulent  fluctuations  in. 
water  and.  curve  (b)  with,  polymer  additives.  These  records  allowed, 
the  calculations  of  microscale  of  turbulence  by  the  zero  crossing 
technique.  When  polymer  was  injected,  the  size  of  the  eddies 
increased  . up  to  100  %  near  the  solid. boundary:  The  top  part  of  Fig.  1 
shows  an.  unexpected  phenomenon,  of  the  persistence  effect  of 
polymer.  Injection. was  pulsed,  for  lsec.  followed. by  a  15  sec  pause 
and.  the  effect  on.  the  microscale  of  the  turbulent  eddies  decreased, 
slowly.  Later, experiments  with,  a  flat  plate  confirmed  this  persistence 
effect. 

Secondr  using  measured  ,  energy  density  spectra  and  .  energy  - 
dissipation,  spectra.  Figure  2  shows  typical  curves  of  both  spectra. 
The  figure  shown  refers  to  20  ppm  injection. of  Polyox  WSR  301  of 

average  molecular  weight  of  4x10  6.  The  hot  film  probe  was  located  . 3 
feet  downstream  from  the  injection,  slot  and.  0.05  inches  above  the 

bottom  of  a  flume.  F  refers  to  the  energy  density  and  n^F  to  the 
energy  dissipation.  The  dissipation,  curves  give  a  clear  picture  of  the 
effect  of  the  polymer  additive  since  the  areas  under  them  represent 
part  of  the  viscous  dissipation.in.the  flow  (confined  .to  the  u-component 
of  the  turbulent  velocities  in  these  tests).  The  curves  indicate  the 
change  of  scale  of  the  microeddies  by  the  shift  of  the  peak  of  the  curve 
for  the  flow  with  polymer  towards  the  lower  frequency  end.  of  the 
spectrum.  Since  the  viscous  dissipation. for  one-dimensional  spectra  is 
proportional  to  the  areas  under  the  dissipation,  curves  integration  was 
performed,  to  show  the  effect  of  polymer  additives  on.  energy  losses. 
The  areas  under  the  dissipation  spectra  curves,  at  two  locations 
downstream  and.  a  number  of  heights  inside  the  boundary  layer,  are 
shown. in. Fig.  3.  The  substantial  reduction. in. the  dissipation. of  energy 
across  the  boundary  layer  is  evident.  Although,  the  measurements 
could  not  be  taken. close  to  the  viscous  sublayer  (the  size  of  the  hot 


film  probe  did  not  allow  this)  it  can.be  observed. from  the  trends  of  the 
curves  that  the  maximum  dissipation  area  has  been  substantially 
affected. by  the  presence  of  polymer  additives.  The  peak  of  the  curve 
that  existed. in.  the  case  of  water  has  disappeared.  The  polymer  curve 
is  also  a  flatter  one.  This  indicates  that  the  additive  is  most  effective 
near  the  position,  of  maximum  turbulence  production,  in.  the  boundary 
layer.  The  largest  relative  increase  in  microscale  occurred. close  to  the 
boundary.  For  optimum  practical  application,  the  polymer  should, 
therefore,  be  injected. and. retained. close  to  the  boundary.  Associating 
eddy  sizes  with,  the  geometry  of  the  boundary  layer  an  increase  in. 
microscale  close  to  the  boundary  will  increase  the  thickness  of  the 
sublayer.  A  thicker  boundary  sublayer  reduces  the  velocity  profile 
gradient  at  and.  near  the  wall.  Since  the  wall  shear  stress  is 
proportional  to  the  velocity  -gradient  at  the  wall  the  frictional  drag  at  the 
surface  will  also  decrease. 

Another  turbulence  characteristic  investigated  was  the  uv  (x  and  y 
direction  velocity  fluctuations)  component  of  the  Reynolds  shear  stress 
tensor.  The  presence  of  polymer  in.  the  boundary  layer  drastically 
decreased  the  shear  stress  component.  The  curves  of  turbulent  shear 
correlation. coefficient  versus  frequency;  Fig.  4,  show  that  the  turbulent 
shear,  which,  together  with  the  velocity  gradient  is  responsible  for  the 
production,  of  turbulence  is  considerably  lower  when  polymer  is 
injected.  This  indicates  that  the  transfer  of  momentum  from  the  mean 
flow  to  the  turbulence  is  reduced .  by  the  action,  of  the  polymer  and, 
thus,  conserves  energy  of  the  mean,  motion.  This  occurs  over  the 
whole  range  of  frequencies  and  not  only  at  the  higher  range  as  in.  the 
energy  density  spectrum.  The  polymer  molecules  seem  to  act  as 
barriers  restricting  communication  across  the  boundary-  layer  and. 
forcing  the  liquid,  to  flow  in.  a  semi-laminar  manner.  The  resistance  in 
such,  a  flow  would.be  expected,  to  be  lower.  It  is  suggested,  that  the 
polymer  molecules  entangle  and. form  macromolecular  networks  which, 
become  stretched. and  oriented  . in  . the  direction,  of  the  main  flow  under 
the  action,  of  shear  stresses.  Such,  a  physical  model  could. explain  the 
reduced  momentum  transfer  across  the  boundary  layer.  Figure  5  gives 
the  distribution,  of  the  turbulent  shear  correlation,  coefficient  with,  the 
distance  from  the  wall.  The  results  for  water  and.  for  polymer  show 
opposite  correlation,  trends.  The  correlation. for  the  polymer  is  much, 
reduced,  close  to  the  wall  indicative  of  velocity  profiles  near 
separation,  and.  of  reduced  . wall  shear  stresses.  It  thus  appears  that  the 
action,  of  the  polymer  suppresses  the  turbulence  energy  within,  the 
boundary  layer  and  reduces  the  wall  shear  stresses,  Kowalski  (1) 

A  possible  model  of  the  interaction. between. polymer  molecules 
and.  the  fine  structure  of  turbulence,  the  so-called,  dissipative  eddies, 
can  be  suggested.  Physically  only  like-size  material  objects  can 
produce  sufficient  interaction  to  cause  substantial  transfers  of 
momentum  between,  them.  It  is  therefore  to  be  expected,  that  the 
interference  of  polymer  additives  with,  the  turbulent  eddies  will  be 
noticeable  when,  the  molecular  sizes  of  the  additives  are  of  the  same 
order  of  magnitude  as  the  dissipative  eddies.  The  sizes  of  the 
dissipative  eddies  in.water,  in.these  experiments,  can  be  estimated.from 
Kolmogorov’s  hypothesis  about  the  eddy  scales,  Hinze  (2).  The 
calculations  gave  the  maximum  dissipation  eddy  scale  as  0.01  im 

The  size  of  the  polymer  molecule  in.  a  randomly  coiled 
configuration,  is  givenfry: 

Length,  of  a  monomer  times  square  root  of  number  of 
monomers  in  a  chain. 

For  the  Polyox  WSR  301  Diameter  of  coiled. molecule  = 


289 


0.00004  in*  Length,  of  uncoiled  molecule  =  0.004  in* 

The  diameter  of  the  polymer  molecule  is  of  the  most  common  molecule 
in  the  solution*  Since  the  polymer  consists  of  a  distribution  of  molecular 
weights,  sizes  of  molecules  are  distributed  around  the  predominant  or 
most  common  size.  It  is  therefore  unlikely  that  the  polymers  of 
presently  available  molecular  weights  can.  theoretically  have  any  direct 
effect  on.  the  drag  or  the  turbulence  characteristics  of  the  flow.  The 
experimental  evidence  however  indicates  that  there  is  an.  effect. 

The  eddy  structure  in.  the  boundary  layer  is  constantly  changing 
with. large  eddies  being  continuously  created  by  the  interaction  of  shear 
stress  tensor  and.  the  mean,  velocity  gradient.  These  then,  decompose 
into  smaller  and  smaller  eddies  until  they  reach,  the  size  of  the 
dissipative  ones  that  turn  into  thermal  energy.  At  any  time,  at  any  place 
there  are  eddies  of  all  sizes  present  in. the  flow. 

A  given. polymer  additive  of  a  certain. molecular  weight  and. 
chemical  composition  can  be  characterized  by  the  size  of  its  molecule, 
the  chain,  arrangement,  the  energy  of  the  chain,  entanglement,  and. 
possibly  by  the  chemical  or  hydrogen,  bonding  between  the  chains. 
Under  the  influence  of  turbulent  motions,  which.can.be  characterized, 
by  the  intensity  of  the  turbulence  and  the  sizes  of  the  dissipative  eddies, 
there  is  a  level  of  mixing  in.  the  flow  to  produce  certain,  sizes  of 
macromolecular  networks.  The  drag  reduction  will  then  begin,  at  a 
specific  range  of  values  for  those  parameters.  A  functional  statement 
for  this  threshold  . of  polymer  action  .can.be  expressed  by  combining  the 
following  parameters: 

Diameter  of  coiled  molecule  of  polymer  or  its  radius 
of  gyration. 

Concentration  . of  polymer  in  the  flow 
Hydrodynamic  and  flow  perturbation. properties  of 
molecule 

Internal  friction,  coefficient  of  a  molecule 
Viscosity  of  solvent 
Kinematic  viscosity 
Wave  number  of  dissipative  eddies 
Intensity  of  turbulence 

The  result  is  a  function,  that  describes  the  effects  of  the  polymer 
additive  on  the  threshold  of  polymer  action  in  defining  the  onset  of  drag 
reduction*  This  function,  can  be  split  into  two  parts;  the  first  part 
depends  on. the  polymer  additive,  the  second. part  on. the  characteristics 
of  the  turbulent  flow.  For  detailed,  discussion,  of  the  polymer 
entanglement  hypothesis  see  Kowalski  (3). 

Velocity  Profiles 

Very  marked. differences  in. the  velocity  profiles  were  observed 
when  polymer  was  injected.  The  typical  blunt  profile  of  the  turbulent 
flow  became  a  sharp  laminar- type  with. a  hint  of  inflection,  suggesting 
approach  to  a  separation  type  profile.  Figure  6  shows  the  velocity 
profiles  at  two  different  positions  downstream  from  the  injection  point. 
The  shapes  of  the  profiles  indicate  that  they  are  still  developing  and 
have  not  reached  the  equilibrium  stage.  The  change  in.  the  velocity 
profiles  shows  that  the  polymer  slows  down  the  velocity  near  the 
boundary,  producing  a  smaller  velocity  gradient  at  the  wall,  and. 
speeds  it  up  away  from  the  boundary.  A  smaller  velocity  gradient  at 
the  wall  implies  a  thicker  viscous  sublayer  confirming  the  results  of  the 
turbulence  characteristics  measurements.  Calculations  of  velocity 
profile  parameters  gave  additional  indication,  of  the  large  changes 
caused. by  the  polymer  in. the  boundary  layer.  The  shape  factor  for 
water  or  air  has  a  theoretical  value  of  1.4  (experimental  results  gave 
the  value  of  1.5  and  .  remained  reasonably  constant)  the  H  values  for 
the  flow  with.the  polymer  additives  varied  from  2.6  to  3,7.  These  are 
well  into  the  conventional  separation  velocity  profile  range.  The  larger 
value  of  H  occurred.  1  ft  and.  the  smaller  3  ft  downstream  from  the 
injection  point.  This  can  be  the  result  of  dilution,  of  the  additive  as  it 
flows  downstream. 

Flat  Plate  Drag  Reduction 

Experiments  with. a  flat  plate  in.a  flume  gave  significant  results 
regarding  the  optimization  of  the  injection  techniques  in  external  flows. 
The  results  are  shown  in  Figs.  7  and. 8  .  They  show  the  drag  reduction 
effect  of  dilute  polymer  solutions  of  different  concentrations.  Each, 
concentration. produced. a  different  degree  of  drag  reduction*  Starting 
with  very  dilute  solution  of  20  ppm  the  drag  reduction. increases  for  30, 
50  and  100  ppm.  The  peak,  of  the  drag  reduction,  is  progressively 
higher  but  requires  an.  increased  expenditure  of  polymer  additives. 
There  seems  to  be  a  limit  to  the  solution  concentration,  effect  as  the 
curves  of  Fig.  8  show  a  leveling  trend,  of  drag  reduction,  for 


concentrations  of  200,  300  and.  500  ppm.  This  may  indicate  a 
saturation.of  the  near  boundary  region  and  pushing  of  the  excess  of  the 
additive  into  the  outer  region,  of  the  boundary  layer  or  even,  into  the 
main.  flow.  In  addition,  at  high  polymer  concentrations  the  injected, 
additive  may  not  have  time  to  properly  dissolve  in  the  near  boundary 
region,  before  it  is  diffused,  away  from  the  boundary.The  curves 
indicate  that  it  is  better  to  use  smaller  injection,  rates  of  higher 
concentration  solutions.  The  5  degree  inclination. of  the  injection,  slots 
used  in.  these  test  is  considered. to  be  a  practical  manufacturing  limit. 
Therefore  the  only  way  to  keep  the  additive  closer  to  the  boundary  is 
to  operate  at  low  injection, rates  and. as  the  flow  velocity  increases  to 
have  an.  increasing  number  of  injection  slots  distributed  in  the  flow 
direction*  In  this  way  sufficient  polymer  additives  will  be  kept  close  to 
the  boundary  for  longer  distances  along  the  surface,  Kowalski  (4) 

Effect  of  polymers  on  . sound  propagation  in  water 

Suppression  of  small  scale  eddy  sizes  in  the  flow  due  to  presence 
of  polymer  lead,  to  the  question  of  polymer’s  influence  on  the  sound 
propagation*  Tests  were  conducted. with,  a  sound  transducer  immersed, 
in.a  polymer  solution  in.a  dome  shaped. container  which.was  placed.in. 
a  flume  with,  water  flowing  round,  the  dome.  Marked  effects  were 
observed. especially  on.  the  white  noise  spectrum.  It  is  suggested  that 
the  suppression. of  smaller  turbulent  eddies  resulting  in. drag  reduction, 
also  suppresses  the  noisy  part  of  the  sound  . spectrum.  This  leads  to  the 
conclusion  that  polymer  additives  could  be  used  to  tailor  the  sound, 
spectrum  either  by  injection. on  . the  outside  the  sonar  dome  or  by  filling 
the  dome  with  polymer  solution* 

III.  POSSIBLE  APPLICATIONS  FOR  POLYMER 
ADDITIVES 

Full  scale  tests 

Drag  reduction  due  to  the  injection  of  long  chain  polymer  additives 
has  been.well  established  on. the  laboratory  scale.  There  is  not  yet  a  lot 
of  information,  on.  frill  scale  tests.  The  author  conducted,  some 
comparative  tests  on.  sailing  yawls  in.  Chesapeake  Bay;  Two  yawls 
were  used  running  on  parallel  course  matching  their  speeds.  Polymer 
solution.was  injected.through.a  1/2  inch.plastic  tubing  wrapped. around, 
the  under-water  part  of  the  bow  1/10  boat  length.aft  of  the  waterline  at 
the  bow.  Noticeable  increase  in.  speed,  was  observed,  (not  measured) 
over  the  companion  sailboat.  While  this  was  not  a  proper  instrumented 
test  a  satisfactory  confirmation  . of  full  scale  effect  of  polymer  additives 
in. salt  water  was  obtained. 

An.  instrumented,  test  was  carried,  out  by  the  AE.W.Haslar  on.  a 
coastal  minesweeper  in.  the  English.  Channel.  Drag  reduction,  was 
measured,  but  of  smaller  percentage  then,  the  laboratory  tests  would, 
indicate.  This  is  explained  by  the  fact  that  polymer  was  injected, 
through  external  piping  wrapped  . outside  the  hull  at  one  station. close  to 
the  bow.  The  polymer  additive  missed  . the  viscous  sublayer  where  the 
maximum  drag  reduction,  takes  place  and.  aft  parts  of  the  wetted, 
surface  of  the  hull  must  have  been  missed  altogether.  Tests  of  the 
author’s  pulsed. injection  method,  although,  scheduled. at  the  end. of  the 
trials,  could. not  be  carried  . out  because  of  inclement  weather  and  .  some 
delays  in  the  main  part  of  the  test,  cut  the  trials  short. 

Hydrofoil  boat  application. 

Hydrofoil  boats  exhibit  a  characteristic  curve  of  Drag  versus 
Speed!  The  drag  increases  with  the  speed  to  a  maximum  at  the  take¬ 
off  speed,  and  then. drops  down  to  frilly  foil-borne  values.  Temporary 
injection  of  polymer  additives  while  hull-borne  will  reduce  the  drag 
and  eliminate  the  hump  in.  the  dag  curve.  Tests  with. hydrofoil  boat 
model  in  a  towing  tank,  at  the  U.S .Naval  Academy,  Annapolis 
performed  by  the  author  confirmed  this  effect.  The  tests  were 
performed  with  uniformly  dissolved  . polymer  in  the  towing  tank  .water 
giving  a  20  ppm  concentration..  The  drag  reduction  on  the  hull  was  not 
as  high. as  was  expected.  At  that  time  it  was  not  realized  ,  that  polymer 
affects  detrimentally  the  lift  force  of  the  lifting  surfaces. 

Application. to  torpedoes 

Another  short  duration  use  of  the  polymer  additives  could.be 
to  increase  the  speed  or  the  running  distance  of  torpedoes.  However, 
this  will  not  apply  to  torpedoes  with  laminar  boundary  layer  flows 

Effect  of  polymer  on.  the  propeller  performance 

Tests  were  conducted,  on  a  model  propeller  in  a  flume  and. a 
decreased  ,  efficiency  was  measured.  This  was  thought  to  be  caused  . by 
the  effect  of  the  polymer  on. the  thrust  and  .torque  of  the  propeller.  The 


290 


model  propeller  must  have  been,  operating  in.  laminar  flow  regime 
where  the  polymer  increases  the  drag,  hence  higher  torque;  and.  the 
lift  of  the  propeller  could,  also  be  adversely  affected,  by  the  polymer, 
hence  lower  thrust.  Full  scale  propeller  trials  should.be  run  to  confirm 
this  explanation.  This  is  an. important  issue  since  some  of  the  injected, 
polymer  will  eventually  reach,  the  propeller. 

IV.  SUGGESTIONS  FOR  FUTURE  RESEARCH 

Full  scale  trials  axe  essential  to  prove  different  applications  of 
polymer  drag  reduction. 

1.  Optimization  ,  of  injection  .methods  which  ,  should  ,  include 
the  injection. nozzle  design,  distribution,  of  nozzles  along  the  wetted, 
surface,  concentration.of  polymer  additive  and  the  pulsing  method  of 
injection.  These  tests  should,  be  performed,  on.  surface  ships, 
catamarans,  SWATH  ships,  torpedoes  W. submarines 

2.  Large  scale,  high  Reynolds  numbers,  tests  of  propeller 
operating  in  a  dilute  polymer  solution. 

3.  Tests  with  underwater  transducers  to  determine  the 
possibility' of  enhancing  the  operation,  of  sonars.  The  injection,  of 
polymer  on  the  outside  of  the  hull  of  submarines  could  possibly  alter 
their  acoustic  signature  or  alter  it  at  will  during  combat  situation. 

V.  REFERENCES 

1.  T.  Kowalski  “Ph.D.  Dissertation  *  Department  of  Mechanical 
Engineering,  University  of  Waterloo,  Canada,  1969 

2.  J.CXHinze  “Turbulence”  McGraw-Hill 

3.  T.Kowalski  “Macromolecular  Entanglement  Hypothesis  in.  Drag 
Reduction. Flows”  Cambridge  University,  International  Conference  on. 
Drag  Reduction,  September  1974 

4.  TTCowalski  “Turbulence  Suppression. and  Viscous  Drag  Reduction 
by  Non-Newtonian  Additives”  Transaction  of  the  Royal  Institution  .of 
Naval  Architects,  1968 


291 


p.~-pyfn 

Figure  7.  Flat  Plate  Drag  Reduction  -  Low  Concentration 


•  O - 


o 


o 


X 


o 


CONCENTRATION  OF  INJECTED  SOLUTION 


®  100  ppm 

o  200  ppm 

x  300  ppm 

©  500  ppm 


P.  PP™ 

Figure  8.  Flat  Plate  Drag  Reduction  -  High  Concentration 


293 


EXPERIMENTAL  RESEARCH  OF  THE  INFLUENCE  OF  CONDITIONS  OF  POLYMER 
ADMISSION  TO  THE  BOUNDARY  LAYER  ON  A  DROP  OF  TURBULENT  FRICTION 


Vladimir  G.  Pogrebnyak 

Ecological  Center  of  scientific  and  applied 
researches  31,  Shorsa  Street,  Donetsk, 
340050,  Ukraine  Fax-(0622)-92-83- 1 6 
bvn@dgci.  donetsk.ua 


Yuri  F.  Ivanyuta 

A.N.  Krylov  Central  research 
Institute 

44,  Moskovskoye  Shosse, 
Saint-Petersburg,  196158,  Russia 


Abstract  -  Results  on  injection  using  under-slot  chambers  with  changing  angle  of  entrance  into  the  slit,  attest  that 
when  the  polymer  solution  is  supplied  to  the  body  surface,  angles  of  entrance  into  the  slit  being  small,  the 
reduction  of  tangential  stresses  of  friction  shows  itself  practically  immediately  following  the  area  of  introducing 
polymer  into  the  flow.  If  the  polymer  solution  is  supplied  into  the  boundaiy  layer  through  the  slit  with  a  big 
entrance  angle,  there  takes  place  a  delayed  manifestation  of  hydrodynamic  activity  of  polymer  molecules.  It  has 
been  shown  that  polymer  solutions  flow  through  the  under-slot  chamber  in  the  supercritical  mode,  with 
generation  of  dynamic  structures  having  relatively  big  time  of  structure  relaxation  in  them.  The  formation  of 
supermolecular  structures  is  connected  with  deformation  action  of  hydrodynamic  field  on  macromolecules  which 
causes  the  change  of  their  thermodynamic  state,  promoting  supermolecular  structure-formation  in  semi-diluted  and 
moderately  concentrated  polymer  solutions.  The  consequence  of  this  is  the  appearance  of  an  area  with  reduced 
hydrodynamic  activity  of  the  polymer  on  the  body  surface  following  the  place  of  introducing  the  polymer  solution  into 
the  boundary  layer. 


INTRODUCTION 

Among  known  methods  of  the  artificial  effect  on  a 
boundary  layer  (BL)  of  objects  of  shipbuilding  with  the 
purpose  of  decreasing  hydrodynamic  resistance  of  friction,  the 
method  of  supplying  solutions  of  polymers  is  almost  unique, 
in  the  field  of  development  of  which  certain  practical 
progress  has  been  reached.  The  research,  conducted  in  this 
direction,  concerned  improvement  of  hydrodynamics  of 
external  flow  of  bodies  by  a  polymeric  solution  as  well  as 
problems  of  perfecting  mixing  devices.  To  problems  of 
hydrodynamics  of  polymeric  solutions  in  elements  of  systems 
of  input  of  polymers  in  a  boundary  layer  of  a  streamline  body 
was  not  given  due  attention. 

It  is  considered,  that  in  case  of  current  of  solutions  of 
polymers  through  slots  and  other  elements  of  systems  of 
input,  essential  "anomalies",  which  could  considerably 
affect  Toms  effect,  cannot  be  observed.  Such  a  conclusion 
follows  from  the  analysis  of  the  data,  obtained  when 
researching  shift  laminar  currents,  for  which  the  effects  of 
elastic  deformations  are  insignificant.  In  the  systems  of  input, 
as  a  rule,  complex  current,  consisting  of  a  superposition  of 
shift  current  and  mainly  longitudinal  one  (with  stretching)  is 
realized.  In  case  of  a  complex  current  the  effects  of  elastic 
deformations  become  so  great,  that  neglecting  them  should 
in  most  cases  result  in  the  fact  that  the  potential  capabilities 
of  the  polymeric  components  are  used  not  completely, 
especially  this  should  be  noticeable  at  large  speeds  of  motion 
of  objects  of  a  ship-building  profile. 

In  the  given  paper  regularities  and  manifestations  of 
elastic  deformations  were  investigated  in  case  of  a  current  of 
solutions  of  polymers  in  conditions,  characteristic  of  internal 
and  external  problems  with  reference  to  objects  of 
shipbuilding. 


EXPERIMERNTAL 

We  have  used  a  special  hydrodynamic  bench,  permitting 
to  realize  the  exhaust  velocities  of  water  flow  through  a 
channel  up  to  35m/s;  the  channel  had  length  of  8,5  m.  Orifices 
for  measuring  pressure  and  the  sensors  of  force  of  friction 
were  placed  on  the  lower  wall  of  the  channel.  The  system  of 
injection  consisted  of  a  dosator,  underslot  chamber  with 
varying  conditions  of  deforming  the  polymeric  solution  in  the 


input  area  of  the  slot.  The  angle  of  declination  of  the  injected 
polymeric  jet  in  relation  to  a  wall  did  not  vary.  In  the 
experiments  there  varied:  angle  of  opening  the  slot, 
concentration  of  injected  polymeric  solution,  speed  of 
injection,  molecular  mass  and  kind  of  polymer  as  well  as  the 
speed  of  a  filling  flow  (water). 

RESULTS  AND  DISCUSSION 

On  Fig.l  the  experimental  data  describing  features  of 
current  of  water  solutions  polyethylene  oxide  (PEO  )  in  the 
underslot  camera  are  indicated. 


Fig.  1 .  Influence  of  U  and  angle  of  entrance  into  a  slot 
onthe  relative  pressure  differential:  1-9°,  2-13°,  3-22°, 
4-34°.  CPeo=Q.1%,  Mpeo=4-106 


It  can  be  seen,  that  the  phenomena,  unusual  for  purely 
viscous  mediums  are  characteristic  of  such  currents.  At  certain 
critical  (threshold)  values  of  average  exhaust  velocity  U  the 
relative  pressure  differential  begins  sharply  to  increase,  and  it 
is  the  sharper  the  more  is  the  concentration  of  polymer  in  a 
solution.  The  marked  character  of  dependence  £  =  f  (U) 
testifies  about  high  dissipation  of  energy  during  the  course  of 


295 


solutions  of  polymers  through  an  injector  i.e.  the  increased 
hydrodynamic  resistance  on  supercritical  flow  rates  is 
observed. 

The  considered  experimental  data  agree  with  the  results 
obtained  when  researching  currents  of  polymeric  solutions  in 
model  conditions  of  elements  of  systems  of  input  (through 
short  capillary  tubes  and  a  slot).  Such  currents  are  in  detail 
investigated  by  us  in  papers  [1  -  5].  Here  we  shall  mark  the 
most  important  moments  of  manifestation  of  effects  of  elastic 
strains  in  case  of  a  current  with  expansion  of  solutions  of 
polymers.  Transition  to  a  mode  of  current  with  an  increased 
dissipation  of  energy  is  accompanied  by  formation  of  the 
source  flooded  jet  as  "cord"  or  "fillet"  enclosed  by  secondary 
currents  in  the  shape  of  a  ring-shaped  vortex.  In  case  of 
supercritical  mode  of  current  for  area  of  the  concentration 
lying  between  very  diluted  and  moderately  concentrated 
solutions  of  polymers,  there  happens  rather  strong 
deformation  effect  of  a  hydrodynamic  field  on  molecular 
chains.  The  deployment  degree  of  a  polymeric  chain  reaches 
60%.  In  half-diluted  and  moderately  concentrated  solutions  of 
polymers,  the  relaxation  times  of  the  developed  circuits  and 
weakly-deformed  individual  chains  differ  more,  than  by  2 
orders. 

The  reason  for  so  large  time  of  swerving  is 
supermolecular  structures  generated  under  an  operation  of  a 
hydrodynamic  field  in  a  polymeric  solution.  The  last 
circumstance  should  be  essentially  reflected  in  decrease  of 
turbulent  friction,  if  the  time  of  life  of  supermolecular 
formations  originating  in  a  polymeric  of  supplying  solution  in 
a  moment  it  in  boundary  layer,  is  comparable  to  the  tine  of 
stay  at  a  surface  of  a  streamline  body. 

The  results  on  injection  onto  the  lower  wall  of  the  channel 
with  application  of  underslot  chambers  with  a  varying  angle 
of  entrance  in  a  slot  testify  (Fig.2), 


Fig2.  Influence  of  an  angle  of  entrance  on  the 
distribution  of  decrease  of  tangent  voltages  along  the 
lower  wall  of  the  channel  for  injections  of  solution 
PEO  mass  2-106,V0=16.5m/s,  Q=50sm3/s,  CPEo=0.3%; 
P°:  1-7.8°,  2-165°. 


that  when  the  polymeric  solution  is  supplied  to  the  surface  of 
a  streamline  body  at  small  angles  of  an  entrance  in  a  slot,  the 
drop  of  tangent  stresses  of  friction  is  exhibited  practically  at 
once  behind  the  place  of  introduction  of  a  polymer  in  the 
flow. 

If  the  polymeric  solution  is  introduced  into  a  boundary 
layer  through  the  chamber  with  a  large  angle  of  an  entrance, 
delay  of  development  of  hydrodynamic  activity  of  polymer 
molecules  takes  place. 

It  should  be  mentioned  that  the  distribution  of  tangent 
voltages  and  relative  pressure  losses  along  the  length  of  the 
channel  correlate  among  themselves.  From  Fig.2  it  follows, 
that  the  modification  of  a  mode  of  a  course  of  a  polymeric 


solution  through  the  underslot  camera  from  poorly  dissipative 
one  up  to  hardly  dissipative  one  at  the  expense  of 
modifications  of  conditions  of  entrance  results  in  lowering 
general  effect  of  friction  resistance  decrease(reduction)  (on  a 
three-meter  long  plot  of  a  streamline  surface)  almost  by  2 
times. 

There  has  been  (Fig.3)  registered  a  considerably  greater 
separation  of  curves  of  dependence  of  a  drop  of  resistance 
from  Y=Q-CpEo/ft-V0  (where  Q  -is  speed  of  injection,  Cpeo  - 
concentration  of  injected  polymeric  solution,  Q -moistened 
surface,  Vo  -is  speed  of  a  filling  flow)  on  concentration  of 
polymer  CPE0  in  case  of  admitting  the  polymer  onto  the 
surface  of  a  streamline  body  in  conditions  of  strong 
deformation  effect  of  the  hydrodynamic  field  on  the  injected 
solution,  than  in  conditions  of  weak  gradient  effect. 


Fig.3.  Dependence  of  general  pressure  losses  in  the 
channel  from  the  indicated  concentration  of  PEO  mass 
2T06,  V0:  •  =16.5m/s,  O  =25m/s;  j3°=7.8°(  1,2,3), 
p°=165°(4,5,6);  CPE0  :  land  4-0.05%  ,  2  and  5  -  0.1%  , 
3  and  6  -  0.3%. 


The  visualization  of  currents  of  a  polymeric  solution  in  an 
underslot  chamber  testifies,  that  the  conditions  of  entrance 
render  influence  on  the  drop  of  hydrodynamic  resistance  only 
in  case,  when  there  is  loss  of  stability  of  current,  stipulated, 
as  was  shown  by  us  earlier[l-3],  by  the  formation  of  dynamic 
supermolecular  structures,  causing  sharp  increase  of  current 
dissipativities.  The  reduction  of  efficiency  of  a  polymeric 
solution  at  the  expense  of  the  deformation  effect  on  it,  in  the 
input  system  reached  25  %  and  above  at  Vo>15m/s. 
Increase  of  filling  flow  speed  results  in  the  extension  of  the 
area  with  reduced  hydrodynamic  activity  of  a  polymer.  The 
role  of  the  area  with  reduced  hydrodynamic  activity  of 
polymer  introduced  into  the  boundary  layer  is  the  more 
significant,  the  less  is  the  length  of  a  streamlined  body.  It  is 
easy  to  explain  this  if  you  remember,  that  time  of  life  of 
derivated  structures  in  conditions  of  stretching  current  are  of 
the  order  of  0,1 -0,2  s  and  more  than  [4].  This  is  the  time, 
during  which  polymer,  which  has  left  a  slot,  has  reduced 
activity  stipulated  by  its  memory.  Obviously,  the  more  there 
will  be  the  velocity  of  the  main  stream,  the  larger  is  the  area 
behind  a  slot  filled  in  with  a  polymeric  solution  in  this 
condition,  and  its  sizes  will  be  evaluated  as  U~0sw’Vo, 
where  0SW  -  by  the  time  of  structural  relaxation  of 
supermolecular  formations.  Then,  for  example,  for  velocity 
of  filling  stream  of  25  m/s  this  area  should  be  distributed 


296 


downwards  along  a  stream  up  to  2,5  m,  if  0SW  -  0,1s.  The 
estimated  sizes  of  area  of  reduced  hydrodynamic  activity  of 
polymer  will  quite  agree  with  experimentally  obtained  results. 

From  comparison  of  results  of  experiments  for 
injections  of  polymeric  solutions  of  various  concentration 
through  the  underslot  camera  with  a  changed  angle  of 
entrance  (Fig.3  y  =  QCpe0/^  -V0,  where  Q  is  speed  of 
injection,  Cpeo  -  concentration  of  injected  polymeric 
solution,  Q  -  moistened  surfaces  ,V0  -speed  of  a  filling 
flow)  follows,  that  for  want  specific  average  concentration  of 
polymer  in  the  boundary  layer  the  efficiency  of  a  diminution 
of  resistance  is  reduced  with  growth  of  concentration  of  the 
injected  polymeric  solution  and  it  is  the  stronger  the  higher  is 
the  angle  of  entrance.  In  [6]  there  was  put  forward  a 
hypothesis  that  viscoelastic  effects  (swelling  of  a  jet)  near  a 
slot  strengthen  a  dagging  of  a  solution  of  polymer  by  the 
external  boundary  layer  and  result  in  a  faster 
decrease(reduction)  of  concentration  of  polymer  on  the  a 
surface  of  a  streamline  body.  The  results  of  papers  [7,8]  force 
to  reconsider  this  hypothesis,  as  visualization  of  current 
behind  a  slot  [7]  and  measurement  of  concentration  of 
polymer  in  the  boundary  layer  [8]  have  not  shown 
amplifications  of  a  diffusion  of  polymer.  Most  acceptable  is 
the  explanation  based  on  the  influence  of  effective  viscosity 
(if  you  understand  it  in  a  broad  sense)  which  does  not 
contradict  the  results  describing  dependence  of  hydrodynamic 
activity  of  polymer  from  conditions  of  supplying  of  a 
polymeric  solution  to  the  surface  of  a  streamline  body.  The 
dynamic  structures  formed  under  an  operation  of  a 
hydrodynamic  field  in  a  polymeric  solution  call  its  densening 
[1,3],  and  this,  naturally,  should  diminution  of  a  diffusion  of 
polymer  in  the  boundary  layer. 

The  detected  regularities  of  the  manifestation  of  elastic 
deformations  when  admitting  polymer  solution  onto  the 
surface  of  a  streamline  body  allows  to  offer  a  way  to  evaluate 
resistance  of  bodies  of  revolution.  Resistance  of  streamline 
bodies  of  revolution  when  admitting  polymeric  solution  to  the 
boundary  layer  accounting  for  the  effects  of  elastic 
deformations  thus  arising  can  be  determined  as: 


X  - 


'A 

f  Z(x)rwodx  + 
0 


\z(x)rwldx  , 

h 


where  x  IS  perimeter  of  object,  xw0  and  tw!  -  tangential 
stresses  with  supply  and  with  no  supply  of  polymer  to  a 
boundary  layer,  L-  length  of  object,  1^=0SW  •  Vq  (0sw-  time  of 
structural  relaxation  of  super-molecular  formations, V0  -speed 
of  the  body). 


CONCLUSION 

The  data  obtained  in  this  paper  testify,  that  when  solving 
problem  on  drop  of  resistance  to  the  motion  of  a  body  by 
means  of  injecting  polymeric  solutions  in  a  boundary  layer  in 
a  part  of  development  of  optimum  versions  of  systems  of 
admission,  it  is  necessary  to  take  into  account  the  possible 
development  of  effects  of  elastic  deformations  in  them. 

The  drop  of  effect  of  reduction  of  resistance  to  motion  when 
supplying  polymeric  solution  into  a  boundary  layer  of  the 
object  results  from  the  combination  of  deformation  effect  of  a 
longitudinal  hydrodynamic  field,  realized  in  the  system  of 
supply  and  of  the  molecular  -concentration  characteristics  of 
a  polymeric  solution. 


REFERENCES 

1.  Pogrebnyak  V.G.,Ivanyuta  Y.F.,Frenkel  S.Y.”  The  Structure 
of  the  Hydrodynamic  Field  and  Distorsions  of  the 
Molecular  Shape  of  Flexible  Polymers  under  Free-Converging 
Flow  Conditions”  Polymer  Science  USSR  ,1992,  vol.34, 
No.3.  p.270-273. 

2.  Pogrebnyak  V.G.,Ivanyuta  Y.F.,Naymchuk  N.V.,  and 
Tverdokhleb  S.V  “Experimental  investigation  of  solutions  of 
polymers  under  near-the-wall  turbulence  simulated 
conditions”  Interfacial  Layers  under  Complex  Conditions, 
Ed.  By  Mironov  B.P.,  Novosibirsk, USSR,  1984,  p.120-127. 

3.  Pogrebnyak  V.G.,Ivanyuta  Y.F.,Naymchuk  N.V., 
Tverdokhleb  S.V.,  and  Frenkel  S.Y.  “Flow  structure  of 
polyethylene  oxide  solutions  in  the  input  zone  of  a  short 
capillary”  Inzh.-Fiz.  Zh.,  1985,  vol.49,  No.4,  p.614-621. 

4.  .Pogrebnyak  V.G.  “Deformation  relaxation  time  of 
polymers’  solutions”  Hydro  and  gasdynamics  of  flows  with 
heat  and  mass  transfer,  Ed.  By  Nikulin  V.A.,  Izhevsk,  USSR, 
1989, Issue  3,  p.143-149. 

5.  Pogrebnyak  V.G.,  Naymchuk  N.V.,  and  Tverdokhleb  S.V, 
’’Dynamic  structureformation  in  the  solutions  of 
hydrodynamically  active  polymers”  Inzh.-Fiz.  Zh.,  1992, 
vol.63,  No.2.  p.147-150. 

6.  Wu.  I.,  Fruman  D.H.,  Tulin  M.P.  “  Drag  reduction  by 
polymer  diffusion  at  high  Reynolds  numbers  ”  J.  of 
Hydronautics.,  1978,  vol.  12,  Juli,  p- 1 34-136. 

7. Fruman  D.H.  and  Galivel  P.  “Anomalous  effects  connected 
with  ejection  of  polymer,  reducing  resistance,  in  turbulent 
boundary  layers  of  pure  water”  Technical  papers  from  the 
Symposium  on  Viscous  Drag  Reduction  ,Ed.  By  Gary  R. 
Hough,  Vought  Advanced  Technology  Center,  Dallas, 
Texas,  vol. 72,  November  1979. 

8.  Vdovin  A.V.  and  Smolyakov  A.V.  ’’Diffusion  of  solutions 
in  a  turbulent  boundary  layer”  Zh.  Prikl.  meh.  i  teh.  Fiz.1978, 
No2, p.66-73. 


297 


Drag  reduction  dynamics 


V.M.Kulik 

Institute  of  Thermophysics,  Russian  Academy  of  Sciences, 
Novosibirsk,  630090,  Russia 


It  was  experimentally  shown  that  solution  of  PEO  changes  its  drag  reduction  (DR)  efficiency  during  the  process  of  flow  in  tube 
or  between  coaxial  cylinders.  DR  initially  increases,  then  reaches  its  maximum  value  and  then  decreases.  It  is  explained  by  change 
of  solution  properties  during  the  process  of  turbulent  flow.  The  maximum  DR  corresponds  to  the  Virk  ultimate  value.  To  describe 
this  universal  dependence  the  simple  formula  is  suggested.  It  was  shown  that  solution  of  PEO  can  work  very  effectively  in 
conditions  of  high  shear  stresses. 

The  method  of  DR  determination  by  pressure  drop  was  analysed  and  corrected.  It  was  noted  that  neglect  of  a  flow  kinetic 
energy  change  can  lead  to  considerable  error  in  DR  value.  Neglect  of  DR  dynamics  lowers  real  possibilities  of  PEO-solution.  The 
method  of  action  on  DR  dynamics  decreasing  the  growth  stage  and  prolonging  the  zone  of  maximum  efficiency  is  suggested. 

The  resumption  of  DR  growth  when  flow  restarted  after  short  stop  was  obtained.  The  explanation  of  DR  decrease  in  tubes  of 
large  diameter  is  suggested. 


In  the  earliest  work  on  DR  by  polymer  solution  (Fabula,  1963)  it 
was  obtained  that  DR  differs  on  the  tube  length.  But  the  author 
analysed  only  the  results  for  the  second  half  of  the  test  tube  and 
approximated  the  pressure  distribution  along  the  tube  by  a  straight 
line.  After  this  work  all  authors  began  to  ascribe  some  certain  DR 
value  to  each  hydrodynamics  regime  of  polymer  solution  flow.  There 
are  a  lot  of  works  on  the  DR  dependence  on  different  parameters: 
sort  of  polymer,  its  molecular  weight,  concentration,  temperature, 
pH-factor  of  medium,  shear  stresses,  flow  velosity,  tube  diameter, 
etc:  see  reviews  of  Hoit  (1972),  Virk  (1975),  Berman  (1978),  Sellin 
(1982). 

It  is  well  known  that  in  a  turbulent  flow  the  polymer  solution 
properties  change  (Balakrishnan  &  Gordon,  1975;  Berman,  1980; 
Kalashnikov  &  Tsiklauri,  1990).  Globule-like  supermolecular 
structures  consisted  of  many  linked  macromolecules  are  destroyed. 
The  number  of  binding  and  linking  is  reduced.  Macromolecules  are 
aligned  and  elongated.  Macromolecules,  which  are  close  enough, 
begin  to  crystallize  and  give  insoluble  dust.  It  means  that  drag 
reduction  is  not  constant  value  but  depends  on  interaction  time  of 
macromolecules  with  shift,  elongation  shears  and  pulsation  stresses. 

In  our  investigation  two  setups  were  used.  The  first  one  with 
rotating  coaxial  cylinders  has  an  advantage  that  it  directly  shows 
time  dependence  Of  DR  change  of  fluid  volume  between  the 
cylinders  (Kulik  &  Semenov,  1991).  The  experimental  points  (fig.l) 
obtained  for  concentration  of  PEO  from  4  to  100  ppm  lay  on  one 
curve,  if  the  ratio  of  the  interaction  time  to  concentration  is  used  as 
an  abscissa.  This  fact  is  in  a  good  agreement  with  Belokon  & 
Kalashnikov  (1977)  and  confirms  the  hypothesis  of  the 
concentration-time  analogy.  But  unlike  preceding  investigation, 
where  the  authors  had  observed  in  detail  only  monotonous  decrease 
of  DR,  in  given  case  the  initial  time  interval  with  the  DR  growth  is 
found,  and  the  maximum  DR  is  fixed.  It  must  be  specially  noted  the 
DR  decrease  is  sharper  as  the  solution  concentration  increases  further 
c>200  ppm,  and  the  concentration-  time  analogy  is  infringed. 

As  it  is  well-known,  high-molecular  polymers  are  able  to  form 
supermolecular  structures  in  a  static  concentrated  solution,  which  are 
the  colloid  particles.  The  process  of  association  leads  to  a  significant 
decrease  of  concentration  of  effectively  working  macromolecules.  As 
energy  of  the  Van-der-Vaals  interaction  is,  at  least,  by  the  factor  of 
10-20  less  then  energy  of  chemical  polymerization  bonds,  the 
process  of  the  supermolecular  formation  disintegration  must 
predominate  over  the  process  of  the  breaking  up  of  molecules  at  first, 
if  one  considers  the  number  of  dissociations.  That’s  why  on  the 
certain  stage  the  degradation  of  macromolecules  accompanying  by 
the  process  of  the  breaking  up  of  the  colloid  particles  has  the  least 
action  on  the  DR  change  then  the  dissociation  of  supermolecular 
structures. 

For  studying  DR  dynamics  when  c<100  ppm  the  second  setup 
(fig.2)  was  made.  The  duration  of  a  single  pass  of  the  fixed  liquid 
volume  trough  the  smooth  tubes  of  different  length  and  inner 
diameter  £>=2.0  mm  were  measured.  The  length  of  the  longest  tube 
1=4  m  corresponds  to  L/D=4  000.  Every  next  tube  was  twice  as  long 
as  previous  one.  The  minimum  length  of  the  tube  was  equal  to  0.25 
m  (L/D=l  25)  in  the  first  series  of  experiments  and  0.125  m 
(L/D=6 2.5)  in  the  second  one.  To  attain  a  turbulent  flow  with  large 
Re  the  tank  can  operate  under  a  high  pressure  of  16  MPa.  It  makes 
possible  to  pass  water  trough  the  longest  tube  at  velocity  U- 40  m/s 


(Re  =8104).  Compressed  air  enters  trough  a  solenoid  valve  into  the 
tank  and  dissipates  by  a  set  of  screens  to  reduce  a  disturbance  of 
horizontal  liquid  surface.  The  platinum  electrodes  of  diameter  0.5 
mm  react  on  medium  conductance  between  them  and  the  body  of 
tank.  The  top  gauge  controls  by  start  of  the  timer,  the  lower  gauge 
controls  by  stop  of  the  timer  and  a  valve  closing.  Liquid  volume 
between  electrodes  V0~642  sm3,  volume  of  tank  -  1/ .  An  effluence 
of  liquid  situated  upon  the  top  electrode  (volume  0.25  0  ensures  the 
stability  regime  of  flow  before  a  start  of  the  timer. 

All  tubes  and  the  tank  were  thermostated  with  constant 
temperature  25°  C.  The  basic  solution  of  2%  -concentration  was 
prepared  a  week  before  the  measurements.  The  dilute  solutions  were 
prepared  a  day  before  its  testing.  The  water  distillate  was  used  for  the 
solutions  preparation.  Just  before  the  measurements  1  ml  of  0.5% 
NaCl  solution  was  added  to  1/  of  tested  solution  in  order  to  guarantee 
the  sufficient  electric  conductivity  of  medium. 

The  measurements  were  carried  out  in  range  of  Reynolds 
number  from  6-103  to  8- 104  (fig. 3).  It  is  easy  to  see  that  drag 
reduction  varies  along  the  tube,  therefore  efficiency  of  a  solution 
action  can't  be  determined  correctly  by  only  one  number  -  it  is  a 
function  of  time  and  intensity  of  interaction  between  polymer 
macromolecules  and  a  turbulent  flow.  There  are  three  regions  with 
different  behavior  of  drag  reduction.  The  first  one  is  characterized  by 
a  drag  reduction  increase  along  the  tube.  This  region  at  small 
velocities  and  large  concentrations  occupies  the  largest  part  of  the 
tube.  So,  at  U= 3  m/s  and  c=100  ppm  the  drag  reduction  growth  is 
observed  along  the  all  length  of  the  tube.  The  second  zone  is 
determined  by  maximum  drag  reduction.  This  region,  as  the  first  one, 
is  observed  here  for  some  but  not  all  regimes.  The  increase  of  a  flow 
velocity  moves  the  place  of  maximum  drag  reduction  appearance  to 
the  beginning  of  the  tube,  and  the  solution  concentration  growth 
moves  it  to  the  tube  end.  For  example,  when  c=20  ppm  maximum 
drag  reduction  at  U=5  m/s  appears  within  the  range  1  -2  m,  but  at  U  = 
13  m/s  -  within  the  range  0.5-1  m.  And,  at  last,  on  the  third  region 
the  efficiency  of  drag  reduction  decreases.  This  behavior  of  Toms 
phenomenon  is  typical  for  weak  concentration  and  high  velocity  of  a 
flow. 

The  ultimate  possible  drag  reduction  (according  by  Virk)  are 
shown  in  fig.4  and  in  fig.3  by  dash  lines.  We  can  see  the  good 
agreement  between  the  measured  data  of  maximum  drag  reduction 
and  calculated  ones.  The  dependence  of  ultimate  drag  reduction  on 
Re  can  be  described  by  following  formula: 

'K,  =  0.554  arctg  (0.024  ^Re  ).  (1 ) 

Size  of  the  tubes  and  possibility  of  setup  allowed  to  determine 
maximum  drag  reduction  for  not  all  solution  concentration  and  flow 
velocities.  So,  when  U=  3  m/s  the  tube  is  too  short  to  find  maximum 
drag  reduction  for  solution  with  c  =  100  ppm.  For  solutions  with  c  = 
1  ppm  and  c  =  2  ppm  maximum  drag  reduction  can't  be  measured 
correctly  for  some  velocity  because  a  place  of  them  appearance  is  on 
the  initial  part  of  their  tube  (0  +  125)  D. 


299 


Sedov  etal.  (1979)  drew  the  conclusion  about  a  drag  reduction 
decrease  when  r  >  80  N/m2.  But  when  the  overall  picture  of  drag 
reduction  change  is  shown  this  conclusion  is  not  confirmed  (see 
fig. 5).  A  decrease  in  drag-reducing  efficiency  was  not  found  even  for 
very  high  shear  stresses  rp  =  z0  (1  -  ¥?  -  800  N/m2  as  it  is  shown  in 
fig.3(d).  Growth  of  shear  stressed  increases  a  rate  of  drag  reduction 
change  and  shifts  a  place  of  maximum  drag  reduction  appearance  to 
a  tube  beginning.  It  seems  likely  that  it  is  the  main  reason  of  the 
slope  of  the  efficiency  obtained  them. 

In  the  second  series  of  experiments  DR  dynamics  was  studied 
for  4  samples  of  PEO  with  different  molecular  weights:  0.3- 106  ([t}J 
-  2.2  dl/g  ),  0.8*  106  (5  dl/g  ),  1.93  106  (10  dl/g)  and  3.25*1 06  (15 
dl/g).  The  results  of  measurement  are  shown  in  fig.6.  Here,  as  before, 
there  are  three  regions  with  different  behaviour  of  drag  reduction:  a 
growth,  maximum  value  and  a  slope  down.  The  region  of  growth  is 
especially  noticeable  at  low  velocity  (see  figs.6(a),(b))  and  becomes 
more  considerable  with  increase  of  molecular  weight. 


*0  ** 

J  vQ‘ u0  (1-y,; /R0')d(y;/R;)=  J  v'u*(l-y/R*)d(y/R*) 

0  0 

the  usual  two  -  layer  profile  of  velocity  for  water 

ao+  =  y0+  y0+<11.6  (5) 

u0+  =  2.5  lgy0+  +  5.5  11,6  <y0+  <  R0 + , 

and  Virk'  velocity  profile 

u  =y  y+  <  15 

u+  =  11.7  lgy+  -17  15  <  y+  <  y+  (6) 

u+=2.5lgy+  +  B  y  +  <  y+  <  R+ , 


The  region  of  maximum  drag  reduction  is  removed  to  the  tube 
beginning  with  increase  of  velocity  or  decrease  of  Mw.  So  at  U~  3m/s 
and  Mh> 0.8  min  [see  fig.6(a)]  the  growth  of  drag-reducing  efficiency 
is  observed  along  all  the  tube,  i.e.  the  tube  is  too  short  to  show 
maximum  drag  reduction.  But  at  U  =5  m/s  maximum  drag  reduction 
is  reached  on  the  distance  0.5  t  1  m  for  solution  with  Mw=0.S  min 
[fig.6(b)],  on  1  -  2  m  for  M„=  1.93  min  and  for  M„=3.25  min  beyond 
the  tube  limit.  At  10  m/s  [see  fig.6(c)]  maximum  drag  reduction  is 
reached  on  distance  0.25  *  0.5  m  for  solution  with  Mw- 0.8  min  and 
so  on.  Maximum  values  of  drag  reduction  are  near  the  ultimate  drag 
reduction  determined  by  formula  (1). 

From  these  figures  it  can  immediately  be  seen  that  maximum 
drag  reduction  does  not  depend  on  molecular  weight  if  weight  is 
more  then  certain  value.  So  solution  with  Mw=0.3  min  can  not  reach 
the  ultimate  drag  reduction.  However,  at  the  large  Reynolds  numbers 
the  measured  values  of  maximum  drag  reduction  are  more  then 
ultimate  ones  [see  figs.6(d),(e)]. 

With  the  aim  of  determination  the  reason  of  Virk's  maximum 
drag  reduction  law  violation  let's  analyse  the  method  of 
hydrodynamic  friction  calculation  from  pressure  drop  measuring. 
According  to  Bernoulli  equation,  pressure  drop  is  required  to  work 
against  friction  and  to  change  kinetic  energy  of  a  flow 


where  u+~u  h\  R+=Rv'/v,  v*-  shear  velocity,  v-kinematic  viscosity, 
y-  radial  distance  from  pipe  wall,  y+~y  v*/v. 

Determined  velocity  profile  was  substituted  in  Eq.(3)  and  next 
formula  was  used 

J  x"  bim  xdx  =  —  2J-\)k («+  \Mm- l)...(m- k  + 1)  w  . 


The  calculated  results  are  shown  in  fig.7.  Coefficient  of  kinetic 
energy  flow  a  is  changed  greatly  at  small  Re  and  large  XR.  It  is  worth 
noting  that  coefficient  a  for  laminar  flow  (Poiseulle  velocity  profile) 
is  equal  to  2,  but  with  growth  of  Re  and  ^coefficient  a  tends  to  1, 
not  to  2,  as  one  may  suggest  because  of  laminarization  action  of 
polymer  additions. 

Let’s  consider  our  typical  case  for  the  first  measuring  part: 

D=2R  =  2*1 0'3  m,  U=  20  m/s, 

x/D  =  62.5-5-125,  ^,=0.7,  ^2=0.6,  ¥/=0.5(f'1+r2)=  0.65. 

From  Fig.8  we  have  aj  =  a^.?)  =  1  -27,  a2  =  a^g) “  IT 6. 

Using  Blasius  formula  for  water 

ro  =  Q3l6  ( Re)  l/4pU 2, 


21 

A  =  —  r  +  0.5pU~(ct2  -  a,)  . 
R 


(2) 


Here  a  -  coefficient  of  kinetic  energy  which  takes  into  account 
the  distribution  of  velocity  u  at  tube  cross-section  area  S\ 


8 

Eq.(2)  is  transformed  into: 

A  =—  To[(l-  'P)  +  -i-L  (Re)'*(a,  -  a,)]  (7) 

R  0.3164/ 

After  substitution  our  data  in  Eq.(7) 


R 

ju*dS  2x  ju3  (R  -  y)dy 

(j  —  A— - -  r=  - - - — - =r 

orr  3  R 

kR  2  2  J  u  (l  -  y/R)d{y/R) 

0 

For  usual  turbulent  flow,  when  velocity  profile  does  not  change, 
respectively  kinetic  energy  doesn’t  change  and  usual  formula  holds: 

A  =2/r. 

R 

A  situation  may  be  significantly  changed  when  liquid  is  non- 
Newtonian  fluid. 

For  determining  the  relationship  between  A  and  r  it  is 
necessary  first  to  know  the  dependence  of  a  on  Re  and  Y.  For  this 
task  a  velocity  profile  for  fixed  Re  and  W  was  found  using  the 
condition  for  equality  of  a  volume  velocities  for  water  and  a  polymer 
solution 


21 

A  s  ~  t0 (0.35  -  0.08). 

R 

We  have  that  the  contribution  from  a  kinetic  energy  change  to 
pressure  drop  is  equal  to  22.5%  of  friction  one.  Without  this 
contribution  drag  reduction  is  8%  above  the  true  value.  If  a  decrease 
in  hydrodynamic  efficiency  takes  a  place  on  a  measuring  part  of  a 
tube  (in  a  cases  of  weak  solution  concentration  or  high  flow  velocity) 
the  contribution  from  a  kinetic  energy  change  has  opposite  sign. 

As  we  can  see  from  an  analysis  Eq.(7),  the  influence  of  a  kinetic 
energy  flow  change  becomes  significant  in  two  cases: 

-  large  drag  reduction  Q¥  >  0.5)  when  the  first  term  in  square 
brackets  is  decreased; 

-  velocity  profile  is  strongly  changed.  Because  velocity  profile 
depends  on  local  drag  reduction,  this  influence  is  pronounced  at  the 
beginning  tube  part  (Kulik,  1992). 


300 


W=(AP0  -  APp)/AP0 , 


Generally  for  correct  measurement  of  friction  stress  it  is 
necessary  to  measure  not  only  pressure  drop  but  the  velocity  profiles 
on  the  limits  of  the  measuring  tube  part.  In  fig.6  corrected  value  of 
drag  reduction  is  shown  by  the  dark  sings.  Correction  was  made  only 
for  the  first  measuring  tube  part,  because  its  value  on  the  second 
section  is  significantly  smaller.  As  indicated  by  these  figures  the 
correction  reduces  the  slope  angles  for  growth  and  loss  of  drag 
reduction.  Finally  the  most  interesting  fact:  the  corrected  drag 
reduction  never  exceed  the  ultimate  value.  This  result  widens  the 
region  of  application  of  Virk’  ultimate  drag  reduction  low. 

Neglect  of  a  change  of  flow  kinetic  energy  may  be  the  reason 
why  drag  reduction  exceeds  the  ultimate  value  (Beversdorff,  1993; 
Zakin  et  al.,1996).  Unfortunately,  in  those  papers  drag  reduction 
dynamics  were  not  studied  but  from  dependence  of  *F  on  Re  it  may 
be  safely  suggested  that  was  strongly  varied  along  a  tube, 
consequently,  a  contribution  not  taken  into  account  may  be 
important.  Ramu  &  Tullis  (1976)  obtained  the  pronounced  change  of 
drag-reducing  efficiency  on  the  initial  part  of  canal  was  obtained.  It 
is  the  fine  illustration  of  necessity  to  correct  obtained  here  extremely 
high  value  of  drag  reduction  (*P-  0.95)  and  to  reduce  it. 

In  Toms'  phenomenon  papers  the  dependencies  of 
hydrodynamics  efficiency  on  different  parameters  (concentration, 
molecular  weight,  temperature,  wall  shear  stress  and  so  on)  usually 
were  given.  For  correct  understanding  of  the  obtained  results  it  is 
necessary  to  take  into  account  drag  reduction  change  during  the 
process  of  a  flow,  i.e.  the  strong  dependence  of  results  on  location  of 
a  measuring  tube  part  and  on  a  method  of  measurement.  On  small 
diameter  tubes  the  duration  of  pass  of  fixed  liquid  volume  is 
measured.  This  method  gives  a  mean  value  of  drag  reduction  on  the 
whole  tube  length 


measure 


ylviOdl- 
L  0 


(8) 


It  is  clear  that  drag  reduction  defined  by  this  method  is  less  than 
maximum  drag  reduction  and  real  dependencies  of  efficiency  upon 
polymer  properties  and  turbulent  flow  parameters  will  be  connected 
in  complicated  manner. 

Using  tubes  with  bigger  diameter  one  can  measure  local  pressure 
drops  on  several  distances  from  the  tube  inlet.  However,  to  determine 
a  drag  reduction  dynamics  one  must  have  very  long  tube  with 
L/D>  103  which  involves  reasonable  difficulties.  For  example,  if  D  - 
5  sm  a  tube  must  be  as  long  as  50  m.  Usually  experiments  are  carried 
out  using  shorter  tubes  and  tested  solution  must  be  passed  through  a 
tube  several  times.  Yet  this  method  is  not  enough  correct.  At  the  first, 
a  neglected  dissipation  of  kinetic  energy  of  the  flow  by  small-scale 
addies  takes  a  place  after  passing  through  a  tube.  It  leads  to 
additional  destruction.  At  the  second,  in  time  intervals  between  the 
passes  the  supermolecular  structures  are  formed  in  solution  because 
of  partial  reversibility  of  drag  reduction  growth  (Semenov  et 
al.,1990).  Fisher  &  Rodriguez  (1971)  confirmed  nonequivalence  of 
action  of  several  passes  to  one  pass  through  a  tube  with  length 
divisible  to  number  of  passes  was  shown.  If  a  setup  has  a  closed 
circuit  there  are  the  same  drawbacks:  additional  destruction  of 
solution  happens  in  a  pump  and  a  partially  relaxation  -  in  expanded 
sections  of  a  tube. 


Besides,  the  next  important  fact  must  be  taken  into  account.  The 
value  of  drag  reduction  is  defined  as 


W=(To  -  xp)/x0, 

where  x  p  and  r0  -  the  shear  stresses  for  solution  and  water  at 
the  same  Re  value,  in  other  words,  at  the  same  volume  velocity  of 
flow  in  constant  diameter  tube.  However,  drag  reduction  in  pipe  flow 
is  customarily  quantified  by  comparing  friction  coefficient  values 
and  the  next  formula  is  really  use 


where  APp  and  APa  -  are  pressure  drops  on  the  measuring  part  of 
a  tube  with  and  without  polymer  respectively. 

Consequently  for  correct  comparison  of  experimental  results  it  is 
necessary  to  define  the  correct  relationship  between  AP  and  r. 

Obtained  results  of  drag-reducing  efficiency  during  a  flowing  of 
polymer  solutions  somewhat  modify  the  traditional  understanding 
about  Toms  phenomenon  action.  Local  drag  reduction  is  changed 
along  a  tube  and  it  is  necessary  to  see  the  three  stages  of  this  process: 
growth,  maximum  and  slope  down,  in  other  words  to  study  the  drag 
reduction  dynamics.  This  dynamics  should  be  taken  into  account  for 
determination  of  various  parameters  influence  (temperature, 
concentration,  molecular  weight,  conditions  of  preparation  and  so 
on).  It  can  add  significant  corrections  to  existing  dependence. 

In  particular,  it  may  be  deduced  that  some  part  of  tube  exists 
where  drag  reduction  is  near  the  ultimate  value  for  wide  region  of 
concentration  and  molecular  weight  of  polymer.  This  ultimate  drag 
reduction  depends  only  on  Re.  Consequently,  the  concept  of  a 
“optimum”  concentration  should  be  only  used  in  a  narrow  sense. 

The  problem  of  test  of  different  polymer  samples  should  be 
transformed  too.  Different  marks  may  be  described  by  angles  of 
slope  up,  by  persistence  of  maximum  drag  reduction  and  by  intensity 
of  slope  down.  A  study  of  action  methods  on  Toms  phenomenon 
dynamics  which  make  faster  a  drag  reduction  growth  and  prolong 
time  of  its  maximum  value  is  perspective. 

Addition  of  low-molecular  substance  is  one  of  methods  of  action 
on  drag  reduction  dynamics.  Initial  stage  is  resumed  again  when  flow 
restarts  after  stop.  However  if  the  solution  is  subjected  to  stress  for  a 
extended  time,  which  includes  the  destruction,  a  resumption  of 
growth  stage  is  not  shown  practically.  In  our  experiments  near-ideal 
resumption  of  growth  stage  was  obtained  after  one  minute  of  rest.  It 
seems  likely  that  this  time  of  recreation  must  be  considerably  shorter 
and  be  determined  by  time  of  conformation  realignment  of  stretched 
macrqmolecules  into  the  state  of  minimum  potential  energy. 

Existence  of  growth  stage  explains  the  reason  why  polymer 
solutions  in  tube  of  large  diameter  have  low  efficiency.  In  tube  with 
small  diameter  (D<5sm)  all  molecules  are  in  zone  of  intensive 
turbulent  interaction,  because  elastic  sublayer  may  cover  all  sectional 
area  of  tube.  With  increase  of  tube  diameter  this  sublayer  takes  up 
only  small  part  of  section.  The  convection  mass  transfer  brings  a 
“fresh”  polymer  additives  into  the  zone  responsible  for  drag 
reduction.  These  macromolecules  have  no  time  to  pass  through  the 
growth  stage  and  diffuse  in  the  core  of  a  flow.  When  these 
macromolecules  will  be  again  in  near-wall  area  the  drag  reduction 
will  increase  beginning  from  low  initial  value.  Almost  the  same  takes 
place  when  polymer  solution  is  injected  into  a  boundary  layer  over 
moving  body.  But  in  this  case  macromolecules  diffused  out  from 
boundary  layer  waste  without  results. 


References 

A.G.  Fabula,  “The  Toms  phenomenon  in  the  turbulent  flow  of 
very  dilute  polymer  solutions,”  Proc.  4th  Intemat.  Congr.  Rheol. 
1963. 

J.W.  Hoyt,  "The  effect  of  additives  on  fluid  friction,"  ASME  J. 
Basic  Eng.  94,  258  (1972). 

P.S.  Virk,  "Drag  reduction  fundamentals,"  AIChE  J.  21,  625 
(1975). 

N.S.  Berman,  "Drag  reduction  by  polymers,"  An.  Rev.  Fluid 
Mech.  10,  47(1978). 

R.H.J.  Sellin,  J.W.  Hoyt  and  O.  Scrivener,"  The  effect  of  drag- 
reducing  additives  on  fluid  flows  and  their  industrial  applications," 
J.  Hydraulic  Research  20,  29  (1982). 

C.  Balakrishnan  and  R.J.  Gordon,  "Influence  of  molecular 
conformation  and  intermolecular  interactions  on  turbulent  drag 
reduction,"  J.  App.  Polymer  Science  19,909(1975). 

N.S.  Berman,  "Evidence  for  molecular  interactions  in  drag 
reductions  in  turbulent  pipe  flow,"  Polymer  Eng.  and  Science  20, 
451  (1980). 

V.N.  Kalashnikov  and  M.G.  Tsiklauri,  "Above-molecular 
structure  of  dilute  solutions  of  high-molecular  polymers  exhibing 
decreased  turbulent  friction,"  J.  Engineering  Physics  58,  49  (1990). 


301 


in  Recent  Developments  in  Turbulence  Management,  edited  by 
K.-S.  Choi  (Kluwer  Academic  Publishers,  1991),  pp.  309-321. 

V.S.  Belokon  and  V.N.  Kalashnikov,  “Hydrodynamics  drag  and 
degradation  of  dilute  polymer  solutions  in  turbulent  rotating  flow 
between  the  coaxial  cylinders”.  Preprint  91,  Institute  for  Problems  in 
Mechanics,  Moscow,  1977. 

L.I.  Sedov,  V.A.  Ioselevich,  V.N.  Pilipenko  and  N.G. 
Vasetskaya,  “Turbulent  diffusion  and  degradation  of  polymer 
molecules  in  a  pipe  and  boundary  layer,”  J.  Fluid  Mech.  94,  561 
(1979). 

V.M.  Kulik,  ’’Dynamics  of  the  Toms  phenomenon  effect  in 
polyethylene  oxide  solution  tube  flow,”  J.  of  Engineering  Physics 
62,  228  (1992). 

H.-W.  Beversdorff,  ’’Turbulence  structure  of  dilute  polymer 
and  surfactant  solution  in  artificially  roughness  pipes,”  Appl.  Sci. 
Research  50,  347  (1993). 

J.L.  Zakin,  J.  Myska  and  Z.  Chara,  "New  limiting  drag  reduction 
and  velocity  profile  asymptotes  for  Nonpolymeric  additives 
systems,"  AIChE  J.  42,  3544  (1996).  K.L.V.  Ramu  and  J.P.  Tullis, 
"Drag  reduction  and  velocity  distribution  in  developing  pipe  flow," 
J.  Hydronautics  10,  55  (1976). 

B.N.  Semenov,  A.I.  Amirov,  V.M.  Kulik  and  O.N. 
Marennikova,  "Effect  of  supermolecular  structures  in  PEO-solutions 
on  drag  reduction,"  Archiv  Mech.  42,  639  (1990). 

D.H.  Fisher  and  F.  Rodriguez,  "Degradation  of  drag-reducing 
polymers,"  J.  Appl.  Polym.  Sci.  15, 2975  (1971). 


Fig.2.  Scheme  of  setup. 


Fig.3.  Drag  reduction  change  along  the  tube. 


302 


Drag  reduction,  °/o 


ON  THE  HYDRODYNAMICAL  SMOOTHNESS  IN  POLYMER  SOLUTIONS 


Walter  B.  Anifilokhiev 

Saint-Petersburg  State  Marine  Technical  University 
Department  of  Hydromechanics 
190008  Lotsmanskaya  street,  3, 
Saint-Petersburg,  Russia 


Kirill  M.  Mazaev 

Saint-Petersburg  State  Marine  Technical  University 
Department  of  Hydromechanics 
190008  Lotsmanskaya  street,  3, 
Saint-Petersburg,  Russia 


Abstract  -  As  it  is  known,  at  small  heights  of  hills  of  rough  surface  it  appears  hydro  dynamically  smooth  because  hills  are  wholly 
shipped  in  viscous  sublayer  and  do  not  render  any  influence  on  to  friction  resistance.  In  dilute  polymer  solutions  viscous  sublayer  and 
the  buffer  zone  is  significant  thicker  than  in  pure  solvent.  Thus,  surfaces,  which  were  rough  in  water,  in  a  polymer  solution  can  appear 
hydrodynamically  smooth.  On  the  basis  of  a  developed  numerical  research  of  an  internal  and  external  problem  about  hydrodynamic 
smoothness  of  a  rough  surface  it  is  shown  that  hydrodynamic  smothness  depends  on  a  type  of  polymer,  concentration  of  solution,  kind 
of  roughness  and  its  size  and  Reynolds  number. 


One  of  active  (i.e.  connected  with  expenses  of  energy  or  sub¬ 
stance)  ways  of  viscous  drag  reduction  is  use  of  the  polymer  addi¬ 
tives.  It  is  established  at  present  that  the  additives  of  many  natural 
and  synthetic  polymers  have  property  to  reduce  friction  resistance 
of  turbulent  flows  essentially  (up  to  five  times)  at  extremely  low 
concentrations,  thousandths  or  even  ten-thousandths  of  percent.  In 
this  method  the  question  on  interaction  of  polymer  with  a  rough 
surface  is  especially  important  for  practice.  The  importance  grows 
if  one  takes  into  consideration  that  the  majority  of  experiments 
with  rough  surfaces  (including  classical  experiments  by  Nikuradse 
with  rough  pipes)  were  carried  out  with  artificial  (“grainy"  or 
"sandy")  roughness,  the  influence  of  which  to  a  flow  differs  from 
influence  of  technical  one  strongly. 

I.  ACCOUNT  OF  POLYMERS  INFLUENCE 

The  fact  is  experimentally  established,  that  on  some  distance 
from  a  wet  surface  the  undimensional  near- wall  average  velocity 
profile  in  a  polymer  solution  can  be  expressed  with  the  universal 
logarithmic  law  of  a  wall: 


1 

(p  =  —  In  T|  +  B , 

K 


(1) 


where  (p =u/u^,  u-u(y)  -  dimensional  longitudinal  velocity, 
wWTw/P  *  s^ear  velocity,  -  shear  stress  on  a  wall,  k=0,4  - 


The  quantity  a  can  be  connected  with  the  turbulent  relaxation  time 

0  [3,4]: 


Ao  +  4p0  2pG 


a  .  <a<l,  po  =- 

mm 


(4) 


(5) 


where  0  depends  on  properties  of  polymer  and  concentration  of 
solution. 

The  function  of  polymer  influence  B  (3)  is  formally  similar  to 
well  known  roughness  function  [2]  with  that  difference,  that,  being 
included  in  the  universal  logarithmic  law  (1),  it  lifts  the  line  (p(r[) 
concerning  the  law  for  a  Newtonian  liquid  at  a  smooth  wall 


(p  =  — Z«t|  +  B0. 

K 


(6) 


while  the  influence  of  a  roughness  lowers  the  line  (1)  comparative 
to  (6).  Then  the  roughness  function  can  be  present  in  the  form, 
similar  (3): 


B 


■■  24,6  Zn(a.  +4) -34,4, 


(7) 


the  first  constant  of  a  turbulence,  r|=wty/v  -  normal  to  a  wall  undi¬ 
mensional  dynamic  coordinate,  y  -  appropriate  dimensional  coordi¬ 
nate,  p  and  v  -  density  and  kinematic  viscosity  of  a  liquid,  B  - 
function  of  polymer  influence,  which  must  pass  in  the  second 
constant  of  a  turbulence  (for  a  smooth  surface)  in  case  of  a  New¬ 
tonian  liquid  flow,i.e.  in  the  flow  of  pure  solvent  -  water.  The 
formula  that  was  offered  in  [1]  is  in  accordance  with 


where  ar<l  -  parameter,  taking  into  account  influence  of  a  rough¬ 
ness.  The  function  of  joint  roughness  and  polymers  influence  takes 
the  form 


B  =  24,6  ln\ 


JL+4 


-34,4, 


(8) 


B  =  B0  +  V2 1 


■ 

(  \ 

■ 

A 

40  Ig 

—  +4 

-28 

<Ao  ) 

(2) 


where  a  looks  like  (4),  and  ar  can  be  obtained  by  comparison  (7) 
with  any  known  roughness  function. 


where  B0=5,2  -  second  constant  of  a  turbulence,  26  -  constant 
by  Van-Drist  (the  numerical  meanings  of  AQ  and  BQ  are  not  inde- 
pended,  they  correspond  each  other  [2]),  A=AQ/ a  -  parameter, 
similar  to  a  constant,  but  taking  into  account  polymer  effect.  It 
gives  the  appropriate  meaning  of  B  for  (1).  Taking  into  account  the 
connection  between  A  and  AQ,  it  is  possible  to  present  formula  (2)  as 


II.  ACCOUNT  OF  ROUGHNESS  INFLUENCE 

The  roughness  function  [5]  that  corresponds  to  the  half- 
empirical  theory  of  turbulence  by  Millionshchikov  [6]  is  used  in 
the  numerical  method.  This  theory  is  one  of  few  ones  in  which  the 
roughness  is  characterized  with  not  one  but  two  geometrical  pa¬ 
rameters:  average  hills  height  of  roughness  (mathematical  expecta¬ 
tion)  k  and  root-mean- square  deviation  (root  square  of  disper¬ 
sion):  a  - 


B  =  24.6  In 


—  +  4 


-34.4  , 


(3) 


j  /  2  1  Z  2 

k  =  -jykdx,  a  =-j(yk-k)  dx, 


(9) 


l  , 


l  , 


305 


where  yk  ( x )  -  curve  of  surface  profilogram,  l  -  length  of  a  pro- 
filogram.  Such  description  of  a  roughness  allows  to  calculated 
(without  using  an  additional  empirical  data)  rather  wide  class  of 
rough  surfaces.  So,  the  small  value  of  the  ratio  elk  corresponds  to 
a  uniform  roughness  (in  [6]  it  is  shown,  that  at  elk- 0,2  ...0,3 
Nikuradse  experiments  are  well  described),  the  growth  of  e/h* 
correspondsto  increase  of  roughness  ununiformity  (for  ship  sur¬ 
faces  elk  «1,1...1,4). 

In  the  Millionshchikov’s  theory  the  principle  of  a  superposi¬ 
tion  of  three  parts  of  total  viscosity  is  postulated  for  near-wall 
layer  with  constant  shear  stress  near  a  rough  surface.  This  parts  are 
molecular  and  two  turbulent  ones.  The  first  of  the  callers,  as  usual, 
is  connected  with  distance  from  a  wall,  and  the  second  depends  on 
a  size  of  hills  of  roughness,  leaning  out  of  a  viscous  sublayer: 

* 

v^=v+KwT(y-60)+Kw^(fe  -80),  (10) 

where  8Q  -  thickness  of  a  sublayer,  outside  of  which  turbulence 

has  place,  k *  -  meanprobabilitstic  height  of  hills,  leaning  out  of  a 
this  sublayer.  The  equation 


du 

T  =  pvz  —  =  const  =  %w 

dy 


(11) 


after  integration  gives 


Meanprobabilistic  height  of  hills,  leaning  out  of  a  sublayer 
80,  is  found  with  help  of  a  probability  density  p: 


Jr,”*** 

Ja>^ 


(17) 


If  to  consider,  that  the  distribution  of  hills  heights  yk  submits 
to  the  normal  law,  then 


where 

q  =  [(l  -  erffej  exp(h  )] 


Po  TU 


■n*  =7i* 


(18) 


(19) 


n,  =5owt/v' 

1rJ11  +  K(l1~P°;  +  K(l1*~|3°J  ,  H  -n  >  ft  (12> 
«T  In  ;  ^Po  ’  Tl>Po' 

K  1  +  KfTlj-PoJ 

*  *  * 

where  T\k  =  k  and  at  <pQ  a  hydrodynamical  smooth 

* 

regime  takes  place  (Tj^ -PQ=0)  and 

q=—ln[  1  +K(ri-p0)7+p0.  (13) 

K 


The  last  fomiula  allows  to  'find  numerical  meaning  pQ,  since  at 
large  T\  it  passes  in  the  universal  logarithmic  law  of  a  wall 


<p= — lnr\+ — /nK+p0 

K  K 


(14) 


1 

Since  BQ~ 5,2  and  k=0,4,  it  is  obvious  that  P0=#o - /«K=7,5. 

K 

At  rather  large  r|  it  is  possible  to  obtain  [5]  from  (12): 


11  1  *  „ 
cp  =  —In  ti  +  —In  K  +  pQ - ln[l  +  K(T\k-$Q)],  (15) 

K  K  K 


i.e.  the  profile  in  the  form  (1),  where 

B  =  B0  +  A B,  30  =  —  In  K  +  p0  =  5,2, 

K 

AB=-i/„fl  +  K(Tli-Po)7 

K 


(16) 


B 

|  | 

\  j 

!  \  I  * 

V 

- i 

1 - 1 

\K 

- j - p - ! 

-10  12  3  4 

Fig.  1.  The  universal  roughness  function. 


Fig.  2.  The  family  of  roughness  functions. 


306 


In  result  the  universal  form  of  the  expression  of  roughness 
function  that  is  in  accordance  with  eq.  (16)  (fig.  1),  can  be 

developped  into  the  family  of  functions  (fig.  2),  and  curves 

of  this  family  will  be  different  depend  on  value  of  parameter  of 
non-uniformity  c/k\ 


1 

B  - ln{  1  +  k/tl 


1  +  - 


&]-P07 }. 


(20) 


For  the  proof  of  admissibility  of  roughness  function  (16)  boundary 
layers  of  plates  with  a  regular  roughness  [5]  and  rotating  disks 
with  a  technological  roughness  [7]  were  calculated.  In  both  cases  it 
occurs  that  the  calculated  results  were  in  good  accordance  with  the 
experimental  ones. 

III.  JOINT  INFLUENCE  OF  POLYMERS  AND  ROUGHNESS 
In  the  case  of  polymer  solution  flow  at  a  rough  surface  it  is 
necessary  to  replace  the  roughness  function  (7)  by  function  of  joint 
polymers  and  roughness  influence  (8).  Firstly  it  is  necessar  to 
obtain  a  formula  for  0^.  It  is  possible  by  comparing  of  roughness 
functions  in  the  forms  (7)  and  (16): 


ar 


(21) 


secondly,  one  has  to  take  into  account  a  thickening  of  a  viscous 
sublayer  according  to  polymer  effect  for  that  to  present  function 
A B,  appearing  in  (16),  as 


A B 


-K  1  lh[l+K(t\k  -  Tl*  >P 

o.  \  <  p. 


(22) 


The  second  limit  for  p  can  be  obtained  from  an  asymptote 
[8],  which  corresponds  to  the  maximum  drag  reduction  at 
Ru%/v>  100  [3],  where  R  -  radius  of  a  pipe  or  boundary  layer  thick¬ 
ness,  - 


1 

q  =  — In  r j  +  32 .  (27) 

K 


Comparison  (27)  with  (24)  gives  Pmax=41,3,  then  from  (26)  one 
can  get  a  .  =0,092. 

The  shape  of  of  universal  functions  of  joint  polymers  and 
* 

roughness  influence  B(r\k)  (the  formula  (8)  with  the  account  (4), 
(21)  and  (22)  and  with  a  simplify  hypothesis  p=PQ/a)  at  several 

meanings  a =const  is  shown  in  fig.  3.  At  transition  to  usual  coordi¬ 
nates  B(r\k)  each  of  these  curves  gives  family  of  functions  differed 

one  from  the  other  by  meaning  of  c/k,  as  it  was  visible  in  fig.  1 
and  fig.  2  for  usual  roughness  in  water.  The  minimum  meaning 
a^0,l  corresponds  to  a  case  of  limiting  drag  reduction,  meaning 

a=l  -  to  a  case  of  water  flow.  In  fig.  3.  it  is  visible,  that  the  for- 
* 

mally  constructed  curves  J5(T(a)  at  a<l  cross  usual  roughness 

function  Br  =  B(r\k  j|  aasl  ,  leaving  in  area  of  smaller  numerical 

meanings.  However,  resistance  in  a  solution  should  be  less,  than  in 
water,  or  -  in  an  extreme  case  of  a  square-law  regime  -  the  same. 

Therefore  the  functions  of  joint  influence  (8)  should  use  only  so 

* 

long  as  their  meanings  are  more,  than  meaning  Br  at  the  same  r^. 

* 

The  coordinates  of  crossing  points  B(V[k)  and  Br  correspond  to 
approximate  dependence 


( 


TUO  =  eXP\ 


3.39  +  - 


0,147 


(28) 


Here  p  -  undimensional  sublayer  thickness  in  a  flow  of  a  solution. 
For  its  definition  it  is  possible  to  take  into  account  that  the  formu¬ 
las  (16)  and  (22)  have  the  same  form,  but  with  p  instead  of  pQ.  In 
result  instead  of  (15)  it  is  received: 

1  1  1  *  „ 

(p  =  —  lnr\  +  —  lmc  +  p - ln[l  +  -  fi)]. .  (23) 

K  K  K 

In  the  case  of  a  smooth  surface  the  last  formula  turns  in 
1  1 

(p  =  —  lnr\  +  —  Zhk+P  (24) 

K  K 

and  it  has  to  coincide  with  an  expression  (1)  provided  that  B  is  the 
function  of  polymer  influence  on  a  smooth  surface,  i.e.  is  deter¬ 
mined  by  expression  (3): 


1  1 


24,6/«( — +4)-34,4= — /«K+p. 
a  k 


In  result 


/ 


1 


P  =  24,6  ln\ 


—  + 
a 


4-32,1, 


that  gives  p~7,5=p0  when  oc=l. 


(25) 


(26) 


2  3  3  4  4 

Fig.  3.  Functions  of  joint  polymers  and  roughness 
influence. 


IV.  HYDRODYNAMIC  SMOOTHNESS  IN  WATER. 

As  it  was  shown  above,  the  roughness  function  B  for  water 
can  be  represented  as  (16).  Thus  the  condition  of  a  hydrodynamic 
smoothness  can  be  written  down  so: 


307 


\  =7-5* 


(29) 


* 

where  r\k  is  defined  with  the  formulas  (19).  Reynolds  number  on 
roughness  hills  height  can  be  presented  as  r\k 


n*  = 


(30) 


where  X  -  hydraulic  factor  of  friction,  k  -  k  /  d ,  Re=VdN ,  V  - 
mean  (bulk)  velocity,  d=2R  -  pipe  diameter.  Thus,  the  meaning  of 
permissible  roughness  hills  height  kpos  depends  on  Re  and  pa¬ 
rameter  of  non-uniformity  c/k.  Using  the  Coles  profile  for  a 
smooth  pipe  with  31=0,1 

u  1  u  y  II  2  3 

—  =  -/n-U-  +  B0+  —  (6y  r4 y  ).  (31) 

U%  K  V  K 


and  integrating  it  pie  cross  section,  it  is  possible  to  find  the  resis¬ 
tance  law  as 


V 


1 

=  —  ln\ 


u „  2  RV 


{  V  2v  ) 


3 

+  S0 - +  0,15 

2k 


or,  in  an  undimensional  form,  - 


Then  from  (29),  (19)  and  (30)  follows 


( 

a  i 

|7  ] 

Re 

hi 

K  J 

(32) 


(33) 


(34) 


From  the  equations  (33)  and  (34)  connection  kpos  with  Re 

can  be  found.  Results  of  accounts  for  pipes  (the  internal  problem) 
are  shown  in  fig.  4. 


Dependences  of  permissible  roughness  hills  height  from  Re  in 
logarithmic  scale  represent  practically  parallel  straight  lines.  Influ¬ 
ence  of  a  parameter  of  roughness  non-uniformity  a/k  can  be  seen 
clearly:  with  increase  of  this  parameter  with  0,2  ("grain"  rough¬ 
ness)  up  to  2,0  (the  technical  roughness)  permissible  roughness 
hills  height  decreases. 

An  external  problem  can  be  solved  analogously.  For  this  pur¬ 
pose  a  boundary  layer  should  be  predicted,  the  size  d/2-R  is  re¬ 
placed  with  boundary  layer  thickness  8;  instead  of  V  it  is  possible 
to  use  velocity  uQ  on  outer  border  of  a  boundary  layer,  and  ^X  /  8 

can  be  replaced  with  /  2  ,  where 

Cf2V(PMo2> 

is  local  friction  factor.  Then  the  formulas  similar  to  (33)  and  (34) 
will  define  a  local  hydrodynamic  smoothness.  However,  in  practice 
a  general  hydrodynamic  smoothness  has  the  greater  interest.  It 
connects  with  full  friction  resistance  coefficient 


l 


o 

where  x  -x/L,  x  -  longitudinal  coordinate  in  a  boundary  layer,  L  - 
length  of  a  body.  In  this  case  the  hydrodynamic  smoothness  has 
not  so  much  physical,  how  many  quantitative  sense,  as  along  a 
wetted  surface,  on  different  parts  of  it,  in  accordance  with  growth 
of  a  boundary  layer,  there  will  be  all  three  regimes  of  roughness 
display  (square-law,  transitive  and  hydro  dynamic  ally  smooth).  By 
setting  acceptable  accuracy  of  account  (i.g.  0,5  %),  the  regime  of  a 
general  hydrodynamic  smoothness  can  be  found  for  definite  o/k 
and  k  =  k  /  L  in  result  of  calculation  of  a  curve  Cf(Re )  via  a 
point  of  its  deviation  from  the  curve  CF  for  a  smooth  surface.  Such 
calculations  were  produced  in  [9]  for  flat  plates.  In  result  connec¬ 
tion  between  k  and  Re  was  determined  and  it  can  be  seen  in 

pos 

fig.  5.  It  is  interesting  (but  natural),  that  at  dk- 0,2  the  line  k 

(Re)  does  not  practically  differ  from  one  in  [10],  where  it  was 
obtained  with  the  help  of  recalculation  of  results  of  Nikuradse 
experiments  in  pipes  to  flat  plates  (i.e.  the  line  in  [10]  is  in  con¬ 
nection  with  uniform  sand-grain  roughness). 


6  7  8  9 

Fig.  5.  Dependence  of  flat  plate  permissible  roughness 
from  Re  for  water. 


Fig.  4.  Dependence  of  permissible  roughness  from 
Reynolds  number  for  water  in  pipes 


308 


V.  HYDRODYNAMIC  SMOOTHNESS  IN  POLYMER  SOLU¬ 
TION 

The  polymer  solution  flow  near  a  rough  wall  is  determined 
by  a  condition  as  (29)  with  replacement  p0  on  p  in  accordance 
with  the  formula  (26): 


T[k  <  P  =  24.6  ln\ 


1 

\CC 


\ 

4  -32.1 


(35) 


* 

where  T\k  is  defined  as  (19). 

In  result  the  equation  placed  below  will  be  an  analogue  of 
the  formula  (30) 


,%  - 

-  *  kr,oi  '  Re 

pos 

h-j 

-■</(*) 

=  24 ,6  In 

f 1  1 

— +4 

8 

k  v 

%  j 

,a  j 

From  here  it  is  visible,  that  the  function  kpos  (Re)  turns  out  differ¬ 
ent  for  different  a.  The  resistance  law  (in  a  pipe)  still  corresponds 
to  Coles  profile  (31)  with  B  instead  £0  and  can  be  written  down  as 


where  B  -  function  of  polymer  influence  for  a  smooth  surface,  i.e.  (3). 
Using  (36)  and  (37)  one  can  get  dependence  kpos  (Re)  for 

any  given  meanings  oc  and  c/k.  Such  results  are  obtained  for  pipes 
(fig.  6)  and  can  be  compared  with  a  similar  picture,  found  earlier 
(fig.  4)  for  a  pure  solvent. 


4  5  6  7 

Fig.  6.  Dependence  of  permissible  roughness  from  Re 
for  polymer  solution  in  pipes  (-— c/k=0,2, 
~c/k=  2,0). 

CONCLUSION 

The  convenient  characteristic  of  a  hydrodynamic  smoothness 
is  dependences  kpos  (Re).  They  turn  out  different  depending  on 

meanings  c/k  (characteristics  of  the  roughness  form)  and  a 
(characteristics  of  polymer  efficiency  dependent  from  its  kind  and 
molecular  weight  and  from  concentration  of  a  solution  [4,7]).  As 
all  dependences  in  logarithmic  coordinates  are  close  to  linear,  it  is 
possible  to  establish  influence  of  parameter  a  on  meaning  kpos  at 

any  Re: 


lgkpoi\a*o/lSkpoi\a=o  =  -0,592a2  + 1,1 13a  +  0,452  (38) 


This  relation  depends  on  c/k  also. 

REFERENCES 

1.  AM(j)HjioxHeB  B.E.,  J]po6jieHKOB  B.B.  HcnoJib30Bamie 

MaTeMaraHecKHx  MOflejiefi  nojiHMepHoro  s^eicra  npn  pacnexe 
norpammHoro  cnon  HHierpajitHLiM  h  KOHeqHo-pa3HocxHHM 
MeToflaMH,  Tpydbt  JIKM,  1986,  ebin .  ” MameMammecKoe 

Modenupoeanue  u  aemoMamu3upoe  aunue  cucmeMbi  e 
cydocmpoemu” ,  c.53-60. 

2.  Oe^eBCKHH  K.K.,  THHeBCKHH  A.C.,  KoJiecHHKOB  A.B.  PacqeT 
Typ6y;ieHTHoro  norpaimqHOFo  cnon  HecxcHMaeMoii  xh^kocth,  - 
JI.:  Cydocmpoeuue,  1973,  256  c. 

3.  Mizushina  T.,  Usui  H.,  Yoshida  T.  Tyrbulent  pipe  flow  of 
dilute  polymer  solutions,  J.Chem.Eng.  of  Japan ,  1974,  v.7, 
No.3,  p.162-167. 

4.  XonopKOBCKHH  5LC.  Typ6yjieHTHoe  npucieiraoe  HBuxemie 
ynpyroB^3KOH  xh^kocth,  MHyceuepH0-<pu3mecmu  xcypncui, 
1976,  t.30,  N?l,  c.110-114. 

5.  AM^nnoxHeB  B.B.,  Ma3aeBa  H.II.  flByxnapaMeTpaqecKaq 
cxeMa  yqeia  mepoxoBaTocTH  b  pacueiax  noipaHHHHoro  cjiosi, 
Tpydbi  JIKM,  6bin.”XodKocmb  u  Mopexodnbie  muecmea  cydoe“, 
1982,  c.3-12. 

6.  Mhjuihohiuhkob  M.ff.  Typ6yjieHTHLie  Tenemui  b 
npncTeHOHHOM  cnoe  n  b  Tpybax,  AmoMuaji  suepzun,  1970, 
t.28,  bbih.3,  c.207-220. 

7.  AM(J)HJioxneB  B.B.,  Ma3aeBa  H.IT.  Bpamemie  mepoxoBaioro 
flHCKa  b  neHLioTOHOBCKOH  XHflKOCTH,  Tpydbi  JIKM,  1987, 
eunJ'MopexodHocmb  u  cma6miu3aifuji  mexuunecKux  cpedcme 
oceoeuuA  OKeaua ”,  c.30-36. 

8.  Seyer  F.A.,  Metzner  A.B.  Turbulence  phenomena  un  drag 
reducing  systems,  AIChE  Journal,  1969,  v.15,  No.3,  p.426-434. 

9.  AM^HJioxneB  B.E.,  Ma3aeBa  H.II.  PacneT 
raapo^HHaMHqecKoro  Tpemra  noBepxHocTen  c  peajibHon 
mepoxoBaTocTbio,  Mamepuajibi  no  oCMeny  onbimoM  HTO  um. 
amd.  A.H.Kpbuioea,  sun.  400  ” Coeeputeucmeoeanue  xodoebtx, 
Mopexoduux  u  Maneepenubix  muecme  cydoe",  c.4-15. 

10.  IUjiHXTHHr  T.  Teopnq  noipannuHoro  cjio.h,  M.:  Maym,  1974, 
712  c. 


309 


Turbulent  Drag  Reduction 
Methods:  Microbubble 


EXPERIMENTAL  EVIDENCE  FOR  A  LINK  BETWEEN  MICROBUBBLE  DRAG  REDUCTION 
PHENOMENA  AND  PERIODICALLY  EXCITED  WALL-BOUNDED  TURBULENT  FLOW 


Madan  Mohan  Guin 
Department  of  Mechanical  Engineering 
The  Johns  Hopkins  University 
122  Latrobe  Hall/ 3400  N.  Charles  St. 
Baltimore,  Maryland  21218,  USA 
guin@titan.me.jhu.edu 


Hiroharu  Kato 

Department  of  Naval  Architecture  & 
Ocean  Engineering 
The  University  of  Tokyo 
7-3-1  Hongo,  Bunkyo-ku 
Tokyo  113  JAPAN 
kato@fluidlab.naoe.tu-tokyo.ac.jp 


Yoshiaki  Takahashi 
Technology  Development  Department 
Shipbuilding  and  Offshore 
IHI  Ltd. 

1-1,  Toyosu  2-chome,  Koto-ku 
Tokyo  135,  JAPAN 
yoshiaki_takahashi_l  @ihi.  co.jp 


1 Abstract  -  Better  collapse  of  microbubble  drag  reduction  data  is  obtained  against  the  near-wall  bubble  concentration  otw  than  against  the 
cross-section  average  value  0Cm  in  a  turbulent  channel  flow.  This  is  primarily  because,  aw  includes  most  of  the  bubbles  participating  in 
the  drag  reduction  process,  compatible  with  a  general  view  that  the  phenomena  are  inner-region-dependent.  When  combined  with 
bubble  diameter  and  flow  velocity,  the  near-wall  concentration  yields  a  bubble  passing  frequency  (Ob .  Accordingly,  bubbles  are  pictured 
as  discrete  bodies  passing  by  a  fixed  point  at  the  wall  at  the  local  velocity.  The  channel  results  show  good  scaling  with  this  frequency 
normalized  by  the  inner  variables  Wb+.  Under  some  reasonable  assumptions,  similar  scaling  is  shown  to  hold  good  with  the  well  known 
hot-film  results  of  Madavan,  Deutsch,  and  Merkle  [J.  Fluid  Mech.  156,  237  (1985)].  In  either  case,  poor  collapse  occurs  with  CJb 
normalized  by  the  outer  variables.  Based  on  the  new  scaling,  it  is  proposed  that  the  basic  physical  mechanism  of  microbubble  drag 
reduction  may  possibly  be  a  special  case  of  wall-bounded  turbulent  flow  where  the  near-wall  region  is  subjected  to  periodic  high 
frequency  excitations  by  the  passing  bubbles  at  an  idealized  frequency  cob . 


L  INTRODUCTION 

Skin  friction  reduction  in  a  turbulent  boundary  layer  by  the 
introduction  of  small  gas  bubbles  into  the  flow  has  been  the  subject  of 
several  recent  investigations.  Laboratory  studies  in  various  test 
configurations,  injection  methods  and  flow  conditions  have  confirmed 
this  phenomenon  (e.g.  1-18).  The  skin  friction  in  a  microbubble- 
modified  boundary  layer  is  found  to  be  even  80  %  less  than  the 
undisturbed  value  under  suitable  conditions.  An  excellent  review  on 
the  subject  including  many  references  can  be  found  in  Merkle  and 
Deutsch  (11).  Considering  the  possibility  of  such  high  magnitude, 
attempts  are  currently  being  made  in  applying  this  method  in  reducing 
the  viscous  drag  of  ships  and  underwater  vehicles.  However,  to  the 
best  of  the  authors’  knowledge,  sufficient  progress  has  not  yet  been 
made  in  this  direction. 

A  clear  understanding  of  the  physical  mechanism  of  this  drag 
reduction  method  is  necessary  in  order  that  the  method  can  be 
effectively  applied  to  practical  ship  boundary  layers.  Although,  the 
process  is  argued  to  be  due  to  increase  of  effective  viscosity  in  the 
wall  region  due  to  the  presence  of  small  bubbles  (5,19-21),  other 
possibilities  cannot  be  entirely  ruled  out.  A  main  purpose  of  this 
paper  is  to  provide  evidence  for  a  possible  mechanism  in  which  skin 
friction  reduction  might  occur  due  to  excitation  of  the  near-wall  region 
by  the  passing  bubbles.  This  is  based  on  a  new  scaling  parameter 
involving  bubble  passing  frequency  0)b  normalized  by  the  inner 
variables.  These  results  are  an  outcome  of  experiments  carried  out  in  a 
two-dimensional  water  channel  reported  in  detail  in  Ref.  16  and  17. 

H.  DEPENDENCE  ON  NEAR-WALL  BUBBLE 
CONCENTRATION  aw 

The  experiments  referred  to  above  were  conducted  in  a  horizontal 
water  channel  specially  built  for  this  purpose  at  the  University  of 
Tokyo.  The  channel  had  a  width  2Sof  10  mm  and  span  b  of  100  mm 
with  the  smaller  dimension  in  the  vertical  direction  (Fig.  1).  The 
Reynolds  number  based  on  channel  height  and  mean  velocity  varied 
from  50  to  90  x  103  at  nominal  temperature  of  25°C.  A  pair  of  sintered 
plastic  porous  plates  mounted  flush  with  the  top  and  bottom  walls 
could  create  small  air  bubbles  when  dry  compressed  air  was  blown 
through  them.  The  location  of  these  plates  was  61  channel  heights 
downstream  of  a  smoothly  matching  inlet  after  a  settling  chamber  and 


contraction.  The  wall  friction  was  measured  with  a  floating-element 
transducer  with  a  5  mm  circular  sensing  disk  mounted  on  the  top  wall 
located  67  channel  heights  downstream  of  the  injection  plates.  Bubble 
diameter  was  determined  by  still  photographs  taken  through  the 
transparent  acrylic  top  wall.  The  resolution  was  sufficient  to  measure 
the  mean  bubble  diameter  to  a  reasonable  accuracy  by  projecting  the 
photographic  negative  against  a  film  analyzer  equipped  with  digital 
cross- wire  position  indicators. 

The  ratio  between  the  skin  friction  coefficients  C/  with  air  and  Cfo 
without  air  based  on  pure-water  density  was  found  at  comparable  bulk 
velocity  Um.  Use  of  pure-water  density  in  the  definition  of  C/  is 
justified  by  the  existence  of  a  bubble-free  region,  albeit  of  the  order  of 
the  viscous  sublayer  thickness  next  to  the  wall  (6,10,11)  with  the 
liquid  as  the  medium  of  momentum  exchange  with  the  wall.  Absence 
of  bubble  impingement  against  the  wall  has  been  verified  with  the  hot- 
film  signals  used  for  shear  measurements  in  Madavan,  Deutsch  and 
Merkle  (MDM2,  Ref.  4)  and  Ref.  11. 

Bubble  concentration  profiles  at  the  shear  measurement  location 
were  obtained  using  a  sampling  probe  with  a  flattened  mouth  facing 
the  flow  traversing  in  the  wall-normal  direction  (Fig.  2).  Typical 
profiles  are  given  in  Fig.  3  showing  the  ratio  of  local  concentration  a 
to  the  cross-sectional  average  value  aw  =  QJ(Q<i+2UmHbS),  where  Qa 
is  the  volumetric  injection  rate  of  air  and  Umw  is  the  bulk  velocity  of 
water.  These  profiles  clearly  show  a  dependence  on  the  flow  velocity, 
injection  orientation  with  respect  to  gravity,  and  air  quantity.  A  near¬ 
wall  bubble  concentration  aw  was  obtained  from  such  profiles  by 
averaging  within  a  wall-normal  distance  of  1  mm  from  the  top  wall. 

The  C/Cf0  values  are  plotted  in  Fig.  4(a)  against  the  cross- 
sectional  average  bubble  concentration  aw.  As  in  water-tunnel 
boundary  layers  (e.g.  MDM2),  the  skin  friction  reduction  is  found  to 
generally  increase  with  aw  within  the  range  of  these  experiments. 
However,  the  data  points  do  not  collapse  well,  notably  the  points 
corresponding  to  the  cases  with  air-injection  from  the  porous  plate 
located  at  the  bottom  wall  are  quite  apart  from  those  corresponding  to 
the  opposite  cases.  This  behavior  may  initially  appear  to  be  due  to  aw 
lacking  the  information  of  detailed  bubble  distribution  patterns  in  the 
flow.  At  the  same  time,  however,  in  Fig.  4(b),  the  C/Cfo  values 
collapse  reasonably  well  against  the  near-wall  concentration  aw  which 
also  seems  to  bear  no  systematic  relation  with  the  detailed  distribution 


1  This  work  was  carried  out  during  the  first  author  MMG’s  graduate  studies  at  the  University  of  Tokyo,  Japan 


313 


(Dimensions  in  mm) 


Figure  1 .  Schematic  diagram  of  the  channel  in  elevation 


Tn  air-wa^Qf 


Figure  2.  The  sampling-type  probe  for  measurement  of  local 
bubble  concentration. 


Figure  3.  Bubble  concentration  profiles  in  the  channel  measured  by  the  sampling  probe.  The  numbers  in  the  legend  refer  to  Qa  in  1/min.  ‘T’ 
and  ‘B*  represent  the  location  of  the  porous  plate  on  the  top  and  bottom  channel  walls  respectively,  y  =  0  corresponds  to  the  top  wall. 


of  bubbles  in  the  bulk  of  the  flow  (Fig.  3).  Therefore,  it  is  logical  to 
say  that  wall  friction  is  not  influenced  by  the  presence  or  absense  of 
bubbles  far  away  from  the  wall  and  their  distribution  patterns.  The 
main  strength  of  a*  is  that  it  comprises  most  of  the  bubbles 
contributing  to  the  drag  reduction,  irrespective  of  the  details  away 
from  the  wall.  Similarly,  the  weakness  of  Oh  is  not  that  it  is  devoid  of 
any  information  of  the  profile  variation,  but  that  it  comprises  a  large 
number  of  bubbles  not  participating  in  the  drag  reduction  process. 
These  observations  are  additional  confirmation  of  the  well-known 
concentration  profile  results  of  Pal,  Merkle  and  Deutsch  (PMD,  Ref. 
10)  showing  that  bubbles  have  to  be  present  within  about  150  viscous 
units  to  be  effective  in  the  drag  reduction  process.  Close  examination 
of  previously  obtained  results  supports  these  points  (e.g.  2,6,11). 


These  are  also  in  agreement  with  the  generally  accepted  view  that 
microbubble  drag  reduction  is  inner-region  dependent  (see  also  Ref. 
5). 

Although  somewhat  arbitrary,  the  region  of  definition  of  wall- 
concentration  used  above,  viz.  1  mm  from  the  wall,  corresponds  to  a 
y+  value  of  200  to  400,  well  within  the  logarithmic  region  including 
the  buffer  zone.  (Here,  y+  is  the  wall  coordinate  yujv,  where,  y  is  the 
dimensional  wall-normal  distance,  uT  is  the  friction  velocity  under 
drag  reducing  conditions,  and  v  is  the  kinematic  viscosity  of  pure 
water.)  This  region  is  of  the  order  of  the  y-dimension  of  the  sampling 
probe  mouth.  Although  the  nearest  position  of  the  probe-center  from 
the  wall  was  of  the  order  of  100  viscous  units,  it  is  difficult  to  assign 
too  much  confidence  on  the  local  values  in  this  rather  narrow  region 


314 


Figure  4.  Dependence  of  skin  friction  ratio  from  direct  shear 
measurements  in  the  channel  on  (a)  mean  bubble  concentration 
and  (b)  wall  bubble  concentration.  The  numbers  in  the  legend 
mean  the  bulk  water  velocity  in  m/s.  and  the  location  of  the 
porous  plate  on  the  channel  walls.  ‘T’  and  ‘B’  represent  the 
location  of  the  porous  plate  on  the  top  and  bottom  channel 
walls  respectively. 

from  the  frontal-area  averaging  inherent  in  the  sampling  method. 
Moreover,  the  bubble  size  itself  in  viscous  units  Db  ranged  from 
about  100  to  250  in  the  entire  range  of  these  experiments  (Fig.  5  and 
6).  Thus,  in  an  average,  there  can  be  at  best  one  or  two  bubble  layers 
in  the  region  of  interest.  Therefore,  it  is  somewhat  inappropriate  to 
distinguish  much  among  the  y-locations  within  a  resolution  smaller 
than  the  bubble  size.  Accordingly,  in  the  range  of  these  experiments, 
an  average  within  1  mm  is  assumed  to  be  the  best  representative  of  the 
near-wall  bubble  concentration. 

in.  NEW  SCALING  OF  CHANNEL  RESULTS  WITH  BUBBLE 
PASSING  FREQUENCY  0)b 

Since  the  phenomena  are  inner-region  dependent,  an  appropriate 
scaling  parameter  should  consider  the  fundamental  quantities 
representative  of  the  dynamics  near  the  wall,  i.e.,  the  friction  velocity 
ux  and  kinematic  viscosity  v.  It  must  be  recognized  that,  unlike  dear- 
water  flow,  another  length  scale  exists  in  the  form  of  bubble  diameter 
Db.  As  already  seen,  the  local  near- wall  bubble  concentration  has 
an  important  role.  In  one  sense,  this  quantity  is  a  passive  volume 
fraction  of  gas  irrespective  of  the  bubble  diameter  in  the  mixture  as 
would  be  measured  by  a  locally  averaging  device  like  a  sampling 
probe.  Viewed  another  way,  bubble  concentration  combined  with 
bubble  diameter  has  the  connotation  of  a  frequency.  Bubbles  can  be 
pictured  as  discrete  bodies  passing  by  a  fixed  point  at  the  wall  at  the 
local  velocity.  This  view  is  strengthened  by  considering  the  narrow 


Figure  6.  Variation  of  observed  bubble  diameter  with  velocity  for 
porous  plate  injection  methods  and  comparison  with  Hinze(22) 

(a)  Channel  (b)  PMD.  The  vertical  bars  denote  the  observed 
range  of  diameters. 

region  of  definition  of  (Av  which  can  include  at  best  one  or  two  layers 
of  bubbles  in  the  present  experiments.  Bubble  passing  velocity  is 
assumed  to  be  equal  to  the  local  velocity  of  water  which  in  this  region 
of  200  -  400  viscous  units  can  be  approximately  the  bulk  velocity  Um. 
The  local  void  fraction  is  then  converted  into  a  bubble  passing 
frequency, 

cob=2n(awUm/Db )  (1) 

The  physical  picture  is  analogous  to  the  case  of  a  wall-bounded  flow 
with  the  near-wall  region  is  subjected  to  periodic  velocity 
perturbations  at  an  idealized  frequency  given  by  (Db.  This  frequency 
combined  with  the  inner  time  scale  yields  the  normalized  frequency 
(Ob  =  (ObVlux  or  the  normalized  period  T  =  2%fo)b+.  In  addition,  a 
length  parameter  characterizing  oscillatory  viscous  flow  normalized 
by  the  inner  variables  is  the  Stokes  length  defined  as,  S+  =  u^2Jv(Ob)0'5 
which  is  also  equal  to  (2 J(Db+)0'5.  The  value  of  ux  is  taken  under  drag- 
reducing  conditions  and  v  is  the  pure-water  kinematic  viscosity.  This 


315 


1 


^0.9 

U 


0.8 


cobv/ut2 


«\8/Um 


Figure  7.  Dependence  of  local  skin  friction  ratio  on  bubble  passing  frequency  normalized  by  (a)  inner  and  (b)  outer  time  scales  from  direct 
shear  measurements  in  the  channel.  The  measured  wall  void  fraction  (Xw  is  used  in  determination  of  the  bubble  frequency.  The  legend  is 
same  as  in  Fig.  4. 


is  justified  by  the  presence  of  a  bubble-free  region  next  to  the  wall  as 
mentioned  before. 

The  measured  wall  shear  ratios  in  the  channel  are  plotted  in  Fig. 
7(a)  against  cof  evaluated  with  the  measured  quantities.  Despite 
some  scatter,  the  data  points  collapse  reasonably  well.  This  is  again  a 
confirmation  that  the  phenomena  are  inner-region-dependent.  The 
poor  collapse  in  the  frequency  normalized  by  outer  variables  (ObSlUm 
in  Fig.  7(b)  is  in  agreement  with  the  insensitiveness  of  the  phenomena 
to  the  outer  region.  Thus,  combined  with  the  physical  picture  and 
arguments  in  the  preceding  paragraphs  the  normalized  bubble  passing 
frequency  (of  appears  to  be  a  pertinent  scaling  parameter.  In  the 
following  section,  we  examine  if  similar  scaling  also  holds  good  in  the 
well  documented  case  of  the  water  tunnel  boundary  layer  with  local 
hot-film  measurements  by  MDM2. 

TV.  EXTENSION  OF  0)f  SCALING  TO  MDM2. 

The  data  examined  in  this  section  are  taken  from  figures  8  to  13  of 
the  original  reference  in  which  the  mean  local  skin  friction  ratio  was 
measured  by  hot-film  gauges  and  plotted  against  an  average  bubble 
concentration.  In  order  to  extend  the  present  scaling  to  these  results, 
information  on  wall  concentration  and  bubble  diameter  are  necessary. 

In  the  absence  of  measurements,  the  determination  of  a  most 
probable  wall  bubble  concentration  in  these  cases  is  difficult.  For 
example,  there  is  a  possibility  of  the  bubble  cloud  moving  away  from 
the  wall  in  the  plate-on-bottom  and,  to  a  lesser  extent,  in  the  plate-on- 
top  configurations  as  shown  by  PMD.  This  would  tend  to  reduce  the 
near-wall  concentration.  This  is  also  one  reason  why,  despite  gross 
likeness  in  shape,  the  bubble  distribution  patterns  obtained  in  the 
channel  in  terms  of  afoCm  shown  in  Fig.  3  may  not  be  quantitatively 
extended  to  the  case  of  MDM2  since,  in  the  former,  bubbles  stay 
within  the  thickness  of  the  channel  while  tending  to  diffuse  out  of  a 
boundary  layer.  For  the  present  purpose,  however,  a  tentative 
assumption  is  made  equating  the  local  wall  concentration  a*,-  to  the 
local  average  bubble  concentration  qai  =  QJ(Qa+U0(Si-Si*)L),  which  is 
deduced  for  each  measuring  station  i  using  the  original  boundary  layer 
properties.  Here,  Qa  is  the  volumetric  air  flow  rate,  U0  the  free-stream 
velocity,  4  and  the  local  boundary  layer  thickness  and 
displacement  thickness  respectively,  and  L  is  the  spanwise  length  of 
the  porous  plate. 

The  range  of  bubble  diameter  measured  in  the  channel  (Fig.  6a) 
and  those  reported  by  PMD  (Fig  6b)  using  also  porous  plates 
corresponding  to  their  air-flow  I  and  II  are  seen  to  agree  with  each 
other  by  the  treatment  of  Hinze(22)  predicting  the  largest  drop  size 
Dmax  stable  against  break-up 


D„ 


(2) 


where,  p  and  a  are  the  liquid  density  and  surface  tension  respectively, 
and  e  is  the  dissipation.  The  observed  diameters  closely  fall  within  the 
curves  corresponding  to  the  values  of  the  empirical  constant  Ch  of 
0.725  and  1.5.  The  first  value  is  the  one  originally  proposed  by  Hinze. 
Using  these  information  as  guideline,  the  bubble  diameter  in  the  case 
of  MDM2  is  determined.  This  method  of  extending  the  diameter 
variation  to  an  entirely  different  experiment  involves  large 
uncertainty.  But  it  seems  justified  to  some  extent,  as  the  main  flow 
velocity  and  the  shear  layer  thickness  are  comparable  among  PMD, 
MDM2  and  present  channel.  In  this  way,  local  cof  values  are 
calculated  using  Eqn.  1  and  the  CjfCf0  ratios  are  plotted  in  Fig.  8(a)  for 
the  original  data  set  of  MDM2.  The  data  indeed  correlate  very  well 
independent  of  velocity,  air-flow  rate  and  plate  orientation.  Despite 
the  uncertainties  in  bubble  diameter  and  the  wall  concentration 
involved  in  the  assumptions,  this  good  collapse  seems  surprising.  If 
the  exact  values  of  Dt  and  a*  were  used  in  calculating  cof,  such  very 
good  correlation  could  be  weakened.  In  any  case,  is  expected  to 
be  nearly  proportional  to  qai  whose  effect  would  be  to  change  the 
magnitude  of  (of  proportionately  rather  than  to  seriously  affect  the 
goodness  of  the  data  collapse.  The  plot  in  Fig.  8(b)  in  terms  of  the 
frequency  normalized  by  the  outer  variables  may  be  contrasted.  As  in 
the  channel  case  (Fig.  7b),  this  plot  again  demonstrates  that  the 
phenomenon  does  not  scale  with  outer  variables. 

Thus,  inner  variable  scaling  with  the  bubble  passing  frequency  is 
seen  to  be  quite  effective  also  in  the  case  of  a  water  tunnel  boundary 
layer  examined  above  though  under  several  assumptions.  The 
agreement  in  the  values  in  both  channel  and  the  case  of  MDM2  shown 
together  in  Fig.  9  tends  to  suggest  that  cof ,  or  the  equivalent 
parameters  S+  and  7*  shown  in  the  abscissa,  may  even  be  universal.  In 
addition  to  the  effective  bubble  concentration,  these  parameters 
establish  the  importance  of  bubble  diameter  and  the  inner  variables. 
Based  on  the  new  scaling,  although  at  present  speculative,  there  seems 
to  be  a  possibility  that  skin  friction  reduction  in  a  microbubble- 
modified  boundary  layer  could  be  due  to  the  excitation  imparted  to  the 
wall  region  by  the  passage  of  the  bubbles  in  close  proximity  to  the 
wall.  Further,  there  seems  to  be  a  threshold  frequency  around  cdt  value 
of  0.04  above  which  drag  reduction  occurs.  Interestingly,  this 


316 


(a) 


(b) 


Figure  8.  Dependence  of  local  skin  friction  ratio  on  bubble  passing  frequency  normalized  by  (a)  inner  and  (b)  outer  time  scales  from  the 
hot-film  measurements  of  MDM2.  The  first  digit  in  the  legend  implies  plate  configuration:  plate-on-top  denoted  by  T’  and  plate-on-bottom 
by  *B\  The  second  digit  is  the  hot-film  probe  position  in  increasing  order  in  the  downstream  direction. 


frequency  is  close  to  the  sublayer  burst  frequency  found  in  the 
literature. 

V.  CONCLUSIONS 

Despite  gross  uncertainties,  it  is  clear  that  the  bubble  passing 
frequency  (of  normalized  by  the  inner  variables  is  a  relevant 
nondimensional  parameter  governing  microbubble  drag  reduction 
phenomena.  The  bubble  concentration  near  the  wall  within  a  wall- 
normal  distance  comparable  to  the  bubble  dimensions  together  with 


the  diameter  and  velocity  yields  a  near-wall  bubble  passing  frequency. 
Good  collapse  of  skin  friction  ratios  with  this  quantity  is  obtained  in 
the  experiments  in  a  channel.  Similar  scaling  with  quantitative 
agreements  is  also  found  to  apply  in  the  boundary  layer  case  of 
MDM2  under  some  assumptions.  The  quantity  (Ob  can  serve  as  a 
good  design  parameter  in  applying  the  methods  to  real  ships.  More 
importantly,  from  a  physical  point  of  view,  it  brings  out  the  possibility 
that  microbubble  drag  reduction  could  be  the  outcome  of  high 
frequency  excitation  of  the  near- wall  region  by  the  passing  bubbles. 


317 


1.5 


<s 

u 


0.5 


- 

r^-“ 

s 

0  2  4  6 

i _ i - 1 - 

8  10 

1 _ t 

10  S+ 


0.5 


0.125 


0.04 


0.02  C0+ 


12.6 


50 


157 


314  T+ 


•  Present  (Direct  shear  measurements  in  channel  with  microbubbles) 

#  MDM2  (Hot-film  shear  measurements  on  flat-plate  with  microbubbles) 

Figure  9.  Comparison  of  the  scaling  between  MDM2  and 
channel.  The  value  of  of  ~  0.04  appears  to  be  a  threshold  value 
for  drag  reduction. 

There  also  seems  to  be  a  threshold  frequency  close  to  the  sublayer 
burst  frequency  above  which  drag  reduction  might  occur.  Due  to 
considerable  difficulties  of  measurements  in  the  wall  region  in  the 
presence  of  bubbles,  direct  supporting  data  has  not  been  obtained  yet. 

ACKNOWLEDGMENTS 

We  are  thankful  to  Professor  H.  Yamaguchi  for  helpful  advice, 
and  M.  Maeda,  M.  Miyanaga  and  T.  Matsuzawa  for  their  valuable 
assistance  during  the  experiments.  Encouragement  from  E.  Sugita  of 
IEM  Ltd.  Y.  Yoshida  and  A.  Masuko  of  IHI  Ltd.  is  thankfully 
acknowledged.  We  acknowledge  the  financial  support  from  the 
Ministry  of  Education,  Science,  Culture  and  Sports  of  Japan  (the 
Monbusho)  in  the  form  of  a  scholarship  to  MMG.  Useful  discussions 
with  Professor  Vijay  H.  Arakeri  of  the  Indian  Institute  of  Science, 
Bangalore,  India  during  a  visit  by  MMG  is  gratefully  acknowledged. 


REFERENCES 

1  M.  E.  McCormick  and  R.  Bhattacharyya  “Drag  reduction  of  a 
submersible  hull  by  electrolysis,”  Nav.  Eng.  J.  85, 11  (1973). 

2  V.  G.  Bogdevich,  A.  R.  Evseev,  A.  G.  Malyuga,  and  G.  S. 
Migirenko  “Gas-Saturation  effect  on  near- wall  turbulence 
characteristics,”  in  Second  lntl  Conference  on  Drag  Reduction , 
Paper  D2  (BHRA  Fluid  Eng.,  Cambridge,  England),  p.  25  (1977). 

3  N.  K.  Madavan,  S.  Deutsch,  and  C.  L.  Merkle  “Reduction  of 
turbulent  skin  friction  by  microbubbles,”  Phys.  Fluids  27,  356 
(1984). 

4  N.  K.  Madavan,  S.  Deutsch,  and  C.  L.  Merkle  “Measurements  of 
local  skin  friction  in  a  microbubble-modified  turbulent  boundary 
layer,”  J.  Fluid  Mech.  156,  237  (1985).  [referred  to  as  MDM2) 

5  N.  K.  Madavan,  S.  Deutsch,  and  C.  L.  Merkle  “Numerical 
investigations  into  the  mechanisms  of  microbubble  drag 
reduction,”  J.  Fluids  Eng.  107,  370  (1985). 

6  C.  L.  Merkle,  S.  Deutsch,  S.  Pal,  J.  Cimbala,  and  W.  Seelig 
“Microbubble  drag  reduction,”  in  Proceedings  of  the  Sixteenth 
Symposium  on  Naval  Hydrodynamics  (Berkeley,  California, 
USA),  p.  199(1986). 

7  K.  Tokunaga  “Reduction  of  frictional  resistance  of  a  flat  plate  by 
microbubbles,”  Trans.  West  Japan  Soc.  of  Nav.  Arch.  73, 79 
(1986). 


8  E.  Baba,  “Discussion  on  Merkle  et  al,6”  in  Proceedings  of  the  16th 
Symposium  on  Naval  Hydrodynamics  (Berkeley,  California, 

USA),  p.214  (1986). 

9  S.  Deutsch  and  J.  Castano  “Microbubble  skin  friction  reduction  on 
an  axisymmetric  body,”  Phys.  Fluids  29,  3590  (1986). 

10  S.  Pal,  C.  L.  Merkle,  and  S.  Deutsch  “Bubble  characteristics  and 
trajectories  in  a  microbubble  boundary  layer,”  Phys  Fluids  31, 744 
(1988).  [referred  to  as  PMD] 

11  C.  L.  Merkle  and  S.  Deutsch  “Microbubble  drag  reduction,”  in 
Frontiers  in  Experimental  Fluid  Mechanics,  Lecture  notes  in 
Eng.,  edited  by  M.  Gad-el-Hak  (Springer-Verlag  Berlin),  vol  46, 
p.  291  (1989). 

12  S.  Deutsch  and  S.  Pal  “Local  shear  stress  measurements  on  an 
axisymmetric  body  in  a  microbubble  modified  flow  field,”  Phys. 
Fluids  A  2, 2140  (1990). 

13  H.  Clark  HI  and  S.  Deutsch  “Microbubble  skin  friction  reduction 
on  an  axisymmetric  body  under  the  influence  of  applied  axial 
pressure  gradients,”  Phys.  Fluids  A  3  2948  (1991). 

14  H.  Kato,  M.  Miyanaga,  Y.  Haramoto  and  M.  M.  Guin  "Frictional 
drag  reduction  by  injecting  bubbly  water  into  a  turbulent  boundary 
layer,"  in,  ASME  Symposium  on  Cavitation  and  Gas-Liquid  flow 
in  Fluid  Machinery  and  Devices ,  FED-Vol  190,  p.  185  (1994). 

15  H.  Kato,  M.  Miyanaga,  H.  Yamaguchi  and  M.  M.  Guin  "Frictional 
drag  reduction  by  injecting  bubbly  water  into  turbulent  boundary 
layer  and  the  effect  of  plate  orientation,"  in,  Advances  in 
Multiphase  Flow  (ed.  A.  Serizawa,  T.  Fukano  and  J.  Bataille 
(Proc.  2nd  Intern.  Conf.  Multiphase  Flow,  Kyoto),  Elesevier 
Science  B.V.,  p  85  (1995). 

16  M.  M.  Guin  “Studies  on  frictional  drag  reduction  by  microbubbles 
in  turbulent  boundary  layers,”  Ph.D.  thesis,  The  University  of 
Tokyo,  1995. 

17  M.  M.  Guin,  H.  Kato,  H.  Yamaguchi,  M.  Maeda  and  M. 

Miyanaga  "Skin  friction  reduction  by  microbubbles  and  its 
relation  with  near- wall  bubble  concentration  in  a  channel,"  J. 
Marine  Sc.  and  Tech.  1, 241  (1996). 

18  M.  M.  Guin,  H.  Kato,  H.  Yamaguchi,  M.  Miyanaga  and  M. 

Maeda  "Direct  skin  friction  measurements  and  observation  of  drag 
reduction  in  a  two-phase  air-water  channel,"  in,  ASME  Symposium 
on  Turbulence  Modification  and  Drag  Reductiop,  San  Diego,  CA, 
USA.  FED-vol  237,  p.  93  (1996). 

19  J.  L.  Mari6  “A  simple  analytical  formulation  for  microbubble  drag 
reduction,”  J.  PhysicoChem  Hydrodyn.  13, 213  (1987). 

20  Y.  Yoshida,  Y.  Takahashi,  H.  Kato,  A.  Masuko  and  O.  Watanabe 
"Simple  Lagrangian  formulation  of  bubbly  flow  in  a  turbulent 
boundary  layer  (bubbly  boundary  layer  flow)",  J.  Marine  Science 
and  Technology,  2,  1  (1997). 

21  H.  Kato,  Y.  Fujii,  H.  Yamaguchi,  and  M.  Miyanaga  “Frictional 
drag  reduction  by  injecting  high- viscosity  fluid  into  turbulent 
boundary  layer,”  J.  Fluids  Eng.  115,  p.  206  (1993). 

22  J.  O.  Hinze  “Fundamentals  of  the  hydrodynamic  mechanism  of 
splitting  in  dispersion  processes,”  AIChE  J.  1, 289  (1955). 


318 


ROLE  OF  BUBBLE  INJECTION  TECHNIQUE 
DRAG  REDUCTION 


Dr.  Robert  Latorre 
University  of  New  Orleans 
911  Engineering  Building 
New  Orleans,  LA  70148 
Tel.  (504)-280-7180 
e-mail:  rglna@uno.edu 


Professor  Viktor  V.  Babenko 

Institute  of  Fluid  Mechanics 

National  Academy  of  Sciences  8/4  Zheliabov  Str. 

Kiev,  Ukraine  252057 

e-mail:  vb@bionics.Kiev 


Abstract  -  One  approach  to  reducing  viscous  drag  is  to  introduce  air  along  the  wetted  surface.  This  paper  begins  with  a  discussion  of  the  boundary 
layer  characteristics  and  how  it  is  influenced  by  the  gas  injection.  Then  the  results  of  sets  of  experiments  are  discussed  showing  how  the  surface 
orientation  influences  the  results  of  air  injection.  Overall  the  results  indicate  a  20-30%  reduction  in  the  value  of  C/by  air  injection. 


I.  INTRODUCTION 

Viscous  resistance  denoted  by  the  coefficient  of  friction  Cf 
accounts  for  a  large  proportion  of  surface  and  submerged  craft  drag.  It 
represents  50-65%  of  the  surface  ship  seawater  drag  and  60-75% 
seawater  drag  for  submerged  craft.  It  is  possible  to  design  optimal  hull 
forms  with  computer  software.  This  makes  the  reduction  of  viscous 
resistance  an  important  problem. 

Hull  surface  air  injection  is  one  approach  to  reducing  this  viscous 
drag.  This  air  injection  can  be  accomplished  in  several  ways: 

(1)  Bubble  injection  from  electrolysis,  nozzles  or  screens,  McCormick 

[1],  Sperrou  [2],  Yoshida  [4],  Bamabel  [3],  Takahashi  [4]; 

(2)  Air  film  from  hull  slits,  Latorre  [6]; 

(3)  Air  cavity  formation.  Basin  [7]; 

This  paper  discusses  the  first  approach  -  bubble  injection  from 
electrolysis,  nozzles,  and  screens.  It  begins  with  a  discussion  of  the 
boundary  layer  characteristics  and  how  the  presence  gas  bubbles  creates 
a  favorable  influence  to  reduce  viscous  drag.  The  test  results  using 
electrolysis  to  generate  bubbles  on  a  body  of  revolution  are  presented. 
The  reduction  in  the  coefficient  of  friction  Cf  are  compared  using  the 
results  from  tests  with  bubbles  generated  by  upstream  injectors,  Yoshida 
[2]  and  upstream  screens  Bamabel  [3],  Takahashi  [4].  The  test  results 
show  the  influence  bubble  orientation  and  bubble  size  on  the  reducing 
coefficient  of  friction  Cf  These  results  are  useful  to  estimate  the  drag 
reduction  for  surface  craft  as  well  as  submerged  craft  with  bottom  and 
deck  air  injection. 

II.  Bubble  interaction  with  boundary  layer 

A  large  number  of  theoretical  and  experimental  researches  of  the 
kinematic  and  integral  characteristics  of  a  two-phase  boundary  layer 
have  been  carried  out  for  the  case  when  a  film  of  gas  bubbles  is  supplied 
into  a  fluid.  Recent  experiments  are  summarized  in  Table  L 

It  is  assumed  that  a  solid  film  forms  a  border  between  a  liquid  and 
gaseous  boundary  layer.  This  film  will  be  generated  on  a  body  surface  as 
a  result  of  gas  injection.  This  problem  is  solved  for  a  flow  over  a  plate.  It 
is  shown  in  this  case  that  the  presence  of  a  two-phase  boundary  layer  on 
a  plate  results  in  a  significant  resistance  reduction.  The  creation  and 
maintenance  of  a  gas  solid  film  requires  maintenance  of  a  steady 
interface  where  there  is  the  tendency  towards  film  break-up  into  separate 
bubbles  and  the  transition  to  a  turbulent  mode  of  motion. 

A  uniform  transition  in  the  fluid  properties  across  the  boundary  layer 
is  assumed  along  with  the  film  character  of  the  gas  flow  in  the  fluid.  The 
assumption  about  the  uniformity  of  a  gas  film  front  in  a  transverse 
direction  is  used  in  the  theoretical  treatment  along  with  a  number  of 
other  assumptions. 

The  other  approach  -  diffusion  of  bubbles  in  a  gas-water  mixture 
moving  near  a  wall  -  is  also  used  in  understanding  of  the  physics  of  this 
two-phase  flow. 

The  principle  of  the  boundary  layer  receptivity  to  various 
disturbances  is  used  as  the  basis  of  the  present  experimental  research. 
The  essence  of  this  method  consists  of  the  following:  the  exciting 
motion  passes  a  series  of  specific  formations  in  form  of  a  coherent 
vortex  structures  during  the  boundary  layer  development  Tollmien- 
Schlichting  waves  or  Klien’s  vortexes  are  examples  of  such  structures.  It 


Method 
of  Air 
Injection 

Test 

Section 

Flow 

[m/s] 

Void 

[%] 

Cf/CfD 

Ref 

Electro¬ 

lysis 

Tow  Tank 

1  m  Body 

0.33- 

2.0 

0-  75 
amps 

0.70  - 

0.95 

m 

Bottom 

Screen 

NA 

a) 4.36 

b) 8.55 

c) 10.9 

a) 0-0.3 

b) 0-0.4 

c) 0.4-0.8 

o  o  o 

[3] 

Top 

Screen 

0.1m 

0.015  m 

3  m  long 

a) 5 

b) 7 

c) 10 

a) 0-0.25 

b) 0-0.2 

c) 0-0.25 

a) 0.75-l 

b) 0.65-l 

c) 0.7-1.0 

[4] 

Injectors 

0.6x0.6  m 
Tunnel 

150  mm 
wide  slot 
20°  angle 

8.0 

a) 35  1/m 

b)  1001/m 

c) 2001/m 

a) 0.95-l 

b) 0. 8-0.9 

c) 0.2-0.5 

[5] 

Table  1.  Published  experimental  results  of  drag  reduction  by  bubble 
Injection. 

is  possible  to  use  this  method  to  effect  integrally  on  all  types  of  vortical 
structures  and  achieve  resistance  reduction.  Injection  or  suction  of  a 
boundary  layer  is  examples  of  such  a  method.  However,  it  is  possible  to 
reduce  resistance  by  this  method  through  effects  on  separate  kinds  of 
coherent  vortical  structures  (CVS).  This  method  of  receptivity  consists 
in  introducing  of  disturbances  comparable  to  the  existing  coherent 
vortex  structures  in  the  boundary  layer.  An  example  of  this  approach 
will  be  shown  below. 

III.Measurement  of  Boundary  Layer  Characteristics 

Research  of  a  boundary  layer  along  a  working  site  of  a 
hydrodynamic  bench  with  low  turbulence  e  «  0.05  %  was  carried  out 
using  the  telluric  method.  The  sensitivity  of  the  telluric  method  allows 
visualizing  the  deformation  of  velocity  profiles  U(z)  (Fig.  1)  at  s  *  0.05 
%.  Fig  1  shows  photos  of  velocity  profiles  U(z)  at  various  values  of  x. 
The  Reynolds  number  determined  experimentally  was 

Re=5.4  104. 

The  photographs  show  the  profile  U(z)  begins  to  deform  near  a 
critical  layer  at  Re=  4  - 10 4  already  (Fig.l-a).  This  is  the  premises  to 
develop  disturbances  in  a  boundary  layer  up  to  a  point  based  on  Re. 

The  distribution  of  U(z)  becomes  ordered  (Fig.  1-b)  at  increased 
Reynolds  number.  At  Re-105,  there  is  a  stable  regularity  in  the 
arrangement  of  “peaks”  and  “valleys”  at  defined  values  of  z  with 
jl  =(1.5-i-2)<£  •  The  speed  of  the  telluric  line  distribution  downstream  is 

constant  and  depends  on  the  z-location  measurement  in  each  series  of 
experiments. 

The  width  measurements  of  the  boundary  layer  show  the 
deformation  of  a  profile  U  (z)  is  observed  in  a  very  narrow  area  y/8  = 
0.2*f0.3  for  these  Reynolds  numbers.  The  deformation  appears  near  to  a 


319 


critical  layer  outside  of  which  the  flow  structures  are  plane-parallel.  For 
increased  x,  the  maximum  width  of  this  non-linear  deformation  increase 
from  0.2(y/8)  up  to  0.4(y/8).  This  is  in  agreement  with  the  measurements 
of  Klebanov  [3,7]  where  the  width  of  y  increased  downstream. 

This  investigation  in  low  turbulence  e  «  0.05  %  shows  that 
although  the  transition  phases  maintain  their  characteristic  features  and  a 
undergo  a  sequence  of  alternation,  their  development  is  significantly 
delayed  by  the  low  turbulence.  The  non-linear  effects  are  initiated  at  a 
phase  of  a  linear  plane  wave.  They  develop  in  a  narrow  conical  layer 
symmetrical  to  the  xz  plane  as  a  critical  layer  extending  as  a  cone 
downstream  (Fig.  2).  The  observed  peaks  and  valleys  are  generated 
under  influence  of  a  non-linear  deformation  of  a  plane  wave  induced  by 
a  curvature  of  a  flow  line  and  by  change  of  a  primary  vorticity.  The 
longitudinal  vortex  systems  are  not  yet  formed. 

The  development  of  the  temporal  and  spatial  disturbances  within  a 
boundary  layer  at  Re-0.7,  0.8  and  1.1-10 5  was  also  investigated  by 
telluric  method. 

The  maximum  amplitude  of  U(z)  at  Re~0.7xl05  was  observed  at  y 
=  310_3m  and  at  Re  ~  0.8  xlO5  it  was  observed  at  y  =5  10"3m. 
However  at  Re-  1.1 . 105  two  maximum  amplitudes  were  observed  at  y 
=  2- 10'3  m  and  4.10~3m.  The  presence  of  these  two  maximums 
indicates  the  more  complex  structure  of  exciting  motion.  Photos  of 
velocity  profiles  U(z)  at  Re- 0.8  •  103  are  presented  in  Fig.3.  The  results 
of  this  flow  visualization  enabled  the  development  of  a  flow  pattern 
scheme  for  the  initial  phases  of  non-linear  deformation  of  a  plane  wave 
at  large  turbulence  e  (Fig.  4).  Additional  vortex  pairs  resulted  in  the 
characteristic  small-scale  deformation  of  profile  speeds  U(z)  (Fig.3) 
being  formed  near  the  surface.  From  this  un-stationary  flow  character 
detected  in  the  experiments,  it  is  possible  to  consider  that  the  whole 
system  of  longitudinal  vortices  is  changeable.  They  are  able  to  change 
their  form,  size,  the  number  of  vortex  pairs,  as  well  as  their  ratios  and 
their  temporal  and  spatial  trajectories  of  motion.  This  is  reflected  on 
kinematic  characteristics.  Small  differences  in  the  a  and  b  system  of 
vortexes  (Fig.  4)  essentially  changes  the  resulting  velocity  profile  U(z). 

IV.  Influence  of  Surface  on  Boundary  Layer 

The  various  mechanical  devices  intended  for  formation  of  long  and 
transverse  vortexes  in  a  boundary  layer  are  developed  and  applied  in 
engineering  designs.  Examples  of  such  design  solutions  can  be  found  in 
the  scientific  articles  and  patents.  Despite  of  their  efficiency  they  have 
one  disadvantage:  the  creation  of  additional  friction  resistance.  One 
design  solution  to  this  problem  of  added  drag  is  adopting  a  ribbed 
surface.  Tests  were  made  with  five  strips  of  6  •  10~5m  x  0.003  m  x  0.23 
m  of  standard  scotch  tape  pasted  at  0.012-m  intervals  along  the  bottom 
of  the  test  section.  Site.  The  rib  effect  was  created  by  setting  lengths 
(0.2  m)  of  0. 12  ♦  10-3  m  diameter  wire  under  these  strips. 

The  operation  of  this  system  with  reduced  strip  (0.02  m  length)  was 
checked  at  Re=7-104.  The  results  in  Fig.  5 -a  show  the  velocity 
distribution  U(z)  does  not  differ  from  the  smooth  surface  velocity 
distribution.  The  visualization  of  U(z)  of  the  boundary  layer  flow  over  a 
surface  with  a  ribbed  surface  is  shown  in  Fig.  5  (b-g).  The  ribbing  of  the 
surface  begins  at  x  =  0.9  m  from  the  bottom  leading  edge  of  the  test 
section.  It  is  clearly  visible  from  these  figures  that  the  serration  of  a 
telluric  cloud  appears  near  to  a  surface  above  the  strips  in  a  range 
Re=  (0.7  -5-1.5)*  105  •  The  form  the  cloud  shed  from  a  telluric  wire  (d,  e) 

is  identical  with  the  cloud  formed  by  the  telluric  wire  moving  over  the 
strips  (f)  and  at  the  limits  (g).  The  limit  “g”  is  5  cm  downstream  of  rear 
edge  of  the  strip.  The  speed  of  disturbance  growth  defined  by  the  degree 
of  a  cloud  deformation  downstream  is  less  noticeably  in  a  case  Mf*  than 
in  a  case  “d”.  The  overtaking  part  of  the  cloud  becomes  more  plane  and 
the  magnitude  of  velocity  change  on  z  is  decreased.  This  can  be  taken  as 
the  result  of  an  optimum  interaction  of  disturbances  inserted  with  Xz  = 
0.012  m  and  natural  disturbances  at  increased  Reynolds  number. 

V. Tests  with  Electrolysis  Bubbles 

The  experiments  with  electrolysis  bubbles  were  also  completed.  Un¬ 
insulated  wires  were  pasted  to  a  plate.  They  were  energized  by  a 
constant  charge  (10  volts)  as  well  as  a  pulse  charge  (400  volts,  0.1  -5-  0.5 
s  impulse  frequency).  A  hydrogen  bubble  film  was  formed  on  a  wire 
surface  as  a  result  of  electrolysis  and  the  surface  film  moves 


downstream.  This  longitudinal  bubble  film  increases  the  intensity  of  the 
longitudinal  vortex  disturbances.  This  increases  hydrodynamic  stability 
and  delays  the  boundary  layer  transition.  Consequently,  the  drag  of  this 
two-phase  flow  is  significantly  reduced  with  longitudinal  flow  over  the 
wires 

A  Plexiglas  body  of  revolution  model  was  developed  for  measuring 
two-phase  surface  flow  influence  on  the  drag  and  boundary  layer 
characteristics.  The  0.41 5-m  x  0.04  diameter  Plexiglas  model  is  shown 
mounted  in  the  water  tunnel  in  Fig.  6.  The  metal  (brass)  nose  and  tail 
part  of  the  model  were  connected  to  a  DC  power  supply.  The  voltage 
was  set  at  10  -r  30  volts  during  the  tests.  A  film  of  bubbles  moved 
downstream  into  the  boundary  layer  from  the  rear  edge  of  the  metal 
nose.  These  tests  show  a  10-15%  reduction  in  the  model  resistance 
depending  on  the  current  and  voltage.  This  is  similar  to  McCormick’s 
towing  tank  test  results  summarized  in  Table  1  [1]. 

VI.  Bubble  Injection  from  Upstream  Screens 

Table  1  summarizes  the  results  of  systematic  tests  of  a  plate 
with  bubbles  injected  through  an  upstream  screen.  The  tests  reported  in 
the  monograph  of  Barbanel  [3]  were  completed  using  bubbles  generated 
by  a  bottom  screen  with  round  openings.  The  drag  measurements  were 
done  in  a  water  tunnel  at  test  speeds  of  4  <  V<  8  m/s.  The  bubble  and 
water  mixture  along  the  downstream  surface  is  characterized  by  <p,  the 
void  fraction  measured  by  a  laser.  The  total  force  is  measured  on  a  test 
plate  and  the  results  reduced  to  coefficient  of  friction  Cf  with  bubble 
injection  and  Cf  without  bubble  injection.  The  results  of  the  tests  are 
then  characterized  by  the  ratio  Cf  (Cf  The  test  results  are  plotted  as 
CffCf  versus  void  fraction  <p  in  Fig.7. 

Figure  7  also  shows  the  results  of  Takahashi  et  al.[4].  Takahashi 
[4]  drag  measurements  are  made  with  a  top  mounted  plate  in  the  water 
tunnel.  A  top  mounted  screen  at  the  tunnel  entrance  generates  the 
bubbles. 

It  is  clear  in  Fig.  7  that  bubble  injection  from  the  top  results  in 
some  differences  in  the  drag  reduction  when  compared  to  the  bottom 
bubble  injection.  Aside  from  differences  in  the  bubble  size  due  to 
differences  in  the  screen  size,  the  comparison  in  Fig.  7,  shows  the 
influence  of  the  bubble  buoyancy.  In  the  bottom  bubble  tests  of 
Barbanel,  the  bubble  injection  is  limited  to  an  effective  contact  region. 
Outside  of  this  region,  bubble  buoyancy  lifts  them  from  the  bottom 
surface.  With  the  top  screen,  the  bubbles  tend  to  collect  in  the  bottom 
surface  and  as  Takahashi ’s  results  in  Fig.  7  shows,  this  can  reduce  the 
plate  drag  reduction.  For  nominal  void  fraction  <p  of  0.5  to  0.1,  the 
presence  of  bubbles  results  in  a  15-20%.  drag  reduction.  Figure  7  also 
indicates  this  (frag  reduction  process  is  more  effective  for  larger  amounts 
of  bubble  injection  at  higher  flow  speeds.  At  these  higher  flow  speeds 
the  bubble  buoyancy  is  relatively  smaller  and  has  smaller  influence  on 
the  (frag  reduction  process  as  shown  in  Fig.  7. 

VII. Bubble  Injection  from  Nozzle  Injections 

Table  1  also  includes  the  results  of  Yoshida  et.  al.  [5]  tests  with 
upstream  bubbles  injected  through  nozzles  arranged  slightly  below  the 
upper  wall  of  the  0.6  x  0.6  test  section  of  the  University  of  Tokyo’s 
propeller  cavitation  tunnel.  The  bubble  diameter  from  the  injectors  was 
larger  than  the  bubble  diameter  generated  by  the  screens.  The  other 
significant  difference  was  the  orientation  of  the  nozzles  and  test  plate. 
During  these  tests,  the  bubbles  would  enter  the  flow  below  the  plate  and 
then  collect  on  the  upper  surface  as  they  moved  downstream.  The  bubble 
buoyancy  assisted  the  process  by  insuring  contact  with  the  upper  plate. 

These  tests  were  performed  for  tunnel  speeds  of  4  <  V  <  8  m/s. 
The  total  force  was  measured  on  a  test  plate  and  the  results  reduced  to 
coefficient  of  friction  Cf  with  bubble  injection  and  Cf  without  bubble 
injection. 

The  results  of  these  tests  are  plotted  as  the  ratio  of  CfiCf  the 
different  bubble-water  void  fraction  cp  for  different  injection  rates  in 
Fig.8.  The  comparison  with  the  results  reported  by  Barbanel  [3] 
indicates  the  drag  reduction  with  injectors  and  screens  is  different  This 
difference  is  due  to  three  factors: 

1.  The  larger  bubble  size  from  the  injectors 

2.  The  orientation  of  the  injection  angle  and  downstream  flow 

3.  The  injection  from  the  tunnel  top 

At  the  same  time,  the  results  support  the  earlier  conclusion  that  the 
larger  amount  of  bubble  injection  acts  to  have  a  large  reduction  in  the 
plate  drag.  The  results  independently  support  the  conclusion  that 


320 


frictional  drag  reduction  in  the  order  of  60-70%  can  be  realized  by 
bubble  injection. 

Vlll.Concluding  Remarks 

This  paper  has  presented  the  results  of  systematic  tests  on  the 
influence  from  introducing  bubbles  on  a  wetted  surface.  These  bubbles 
were  generated  by: 

a)  Electrolysis 

b)  Upstream  screen  in  the  bottom 

c)  Upstream  injectors 

Detailed  experiments  indicate  the  bubbles  favorably  interact  with  the 
boundary  layer  structure  delaying  transition  as  well  as  reducing  the 
surface  viscous  drag. 

These  results  lead  to  several  interesting  conclusions 

1.  The  presence  of  bubbles  in  the  surface  boundary  layer 
has  a  favorable  influence  on  reducing  the  energy  losses 
given  by  lower  surface  drag. 

2.  The  systematic  tests  show  that  the  ratio  of  Of  with 
bubbles  to  Of  without  bubbles  is  in  the  order  of  0.20  < 
Cf/Cf<  0.85 

3.  The  systematic  tests  show  that  the  ratio  of  CfICf  is 
sensitive  to  the  amount  of  bubble  injection  which  is 
expressed  as  the  void  fraction  <p 

4.  Comparison  of  the  drag  reduction  shows  that  at  low 
speeds  the  bubble  injection  orientation  can  have  a 
strong  influence  on  the  drag  reduction. 

The  utilization  of  bubble  injection  has  many  applications  in 
seawater  drag  reduction.  It  is  hoped  this  paper  will  encourage  designers 
to  utilize  this  approach. 


DEREFERENCES 

1.  McCormick,  M.,  Bhattacharyya,  R.,  “Drag  Reduction  of  a 
Submersible  Hull  by  Electrolysis”  Naval  Engineers  Journal, 
April  1993,  PP  11-16. 

2.  Sperrou  E.  M.,  Djonson  V.  K.,  Ekkert  R.T.  “Two-phase 
Boundary  Layer  and  Drag  Reducing  Friction  on  the  Plate”.  - 
TASME  (  1962  )  v.  29,  No.2 

3.  Barbanet  B.  A.,  Bogdevich  V.  G.,  Maltsev  L.  I.,  Malyuga  A. 
G.  Some  Practical  Applications  of  Boundary  Layer  Control 
Theory,  Malaxit,  St  Petersburg,  1994,  47pp. 

4.  Takahashi,  T.,  Kakugawa  and  Kodama,  Y.,  “Streamwise 
Distribution  of  the  Skin  Friction  Reduction  by 
Microbubbles”,  Journal  Society  of  Naval  Architects  of  Japan, 
Vol.  182,  Dec.  1997  pp.1-8 

5.  Yoshida  Y.,  Takahashi  Y.,  Kato  H.,  Masuko  A.,  Watanabe  O. 
“Simple  Lagrangian  Formulation  of  Bubbly  Flow  in  a 
Turbulent  Boundary  Layer  (bubble  boundary  layer  flow). 
Journal  of  Marine  Science  and  Technology,  SNAJ  Vol.  1, 
No.  5,  1996,  pp.  241-254. 

6.  Latorre,  R.,  “Ship  Hull  Drag  Reduction  Using  Bottom  Air 
Injection”,  Ocean  Engineering,  vol.  24,  no.2,  1997,  pp.  161- 
175. 

7.  Basin  A.  M.,  Krotkin  A.  I.,  Kozlov  L.  F.  “Control  of  Ship 
Boundary  Layer*’,  Sodostreniye,  Leningrad,  1968,  492pp. 


Fig.l  Traces  from  the  photographs  of  the  tellurium  lines  in  the  xz  plane  for  U„  =  10.5  cm/s,  y/8  '»  0.2  at  the  beginning  (a)  and  at  end  (b)  of  the  working 
section  for  (I)  -  Horizontal  and  (II)  -  Inclined  Plates; 

Key:  1  -  tellurium  wires; 

2  -  holder, 

3  -  mark  of  distance  from  the  beginning  of  the  working  section  (  cm  ); 

4  -  velocity  profile  trace; 

5  -  second  bottom. 


321 


Fig.  2  Evolution  of  non-linear  disturbances  in  low  turbulent  flow; 

Key:  1  -  plane  of  Tollmien-Schlichting  wave; 

2  -  non-linear  secondary  disturbances; 

3  -  velocity  profile  U(z); 

4  -  projection  of  velocity  profile  U(z)  onto  plan  xy  (  viewed  from  one  side  ); 

5  -  projection  onto  plane  xz  (  looking  from  above  ); 

6  -  conical  layer  of  non-linear  disturbances  development; 

7  -  plane  xz  of  critical  layer 


Fig.  3  Photos  I-VIII  of  Velocity  Profiles  U(z)  during  natural  transition  of  the  boundary  layer  U„  =  6.7  •  10"2  m/s;  distance  between  tellurium  wire  and  the 
beginning  of  the  working  section  x,  *  1.1  m;  timing  between  tellurium  clouds  *  0.5  s; 

I  -y/=3*10'3-m;  II  -  4  - 10"3  m;  III  -  5-10"3  m;IV-  6«10~3  m; 

V-  7  •  10"3  m;  VI-  8-10"3  m  ;  VII-  9  •  10~3m  ;  VIII  -  1.2'10_2m 
Key: 

1  -  tellurium  wire; 

2  -  tellurium  clouds; 

3  —  distance  scale  on  the  bottom  distance  of  tellurium  wire  from  the  bottom; 


322 


Fig.  4  Flow  structure  of  initial  stages  of  non-linear  plane  wave  deformation  for  large  turbulence « 
Top  1-8  section  cuts  showing  U  velocity  profile 

a,  b  -  Types  of  longitudinal  vortex  structures; 

Bottom  I-  II  -  III  xy  section  cuts  showing  U  velocity  variation  along  z 
Ucp=  average. 


'lilt  lr 


* '  i  ;  - 


•  'M&k  E 


:  f-  .■  z*?* 


j  ; 


Fig.  5  Traces  showing  influence  of  regular  ribbed  surface  on  boundary  layer  flow  U(z)  (  X2  =  0.012  m  ) 
a  -Re  =  7 . 104 ,  y  *  1 .0  •  10"3  m  (  0.02  m  length  of  edges); 
b  -  Re  *  5  •  10\  y  =  1.5  •  10-3  m;  (0.2  m  length  of  edges); 
c  -  Re  =  103 ,  y  =  5  ■  10^*  m,  (0.2  m  length  of  edges); 

d  -  Re  =  103,  y  =  1.5  •  10'3  m,  (0.2  m  length  of  edges); 

e  -  Re  -  103 ,  y  =  1 .0  *  10"3 ,  (0.2  m  length  of  edges); 

f-Re=  1.4103»y=  1.5-10‘3m,  (0.2  m  length  of  edges); 
g-  Re  =  1.5- 105 » y  ~  1.5  10"3m.  (0.2  m  length  of  edges) 


Fig.  6  Photo  of  Plexiglas  body  of  revolution  in  water  tunnel. 
Length  =  0.415  m,  dia  =  0.04  m. 


Key: 


Bottom  Screen  Bsrbanel  [3]  Flow  Speed  u[m/sj  A  :  u  -4.36  m/s  X :  u  -  i.SS  m/s 
Top  Screen  Takabashi  £4]  Flow  Speed  u[m/s]  O  ;  u  =•  S.O  m/s  m  ;  u  =  7.0  m/s 
at  S00  mm  downstream 


Fig .  Y  Influence  on  downstream  Screen  Air  Injection  on  Cf  =  Cf  with  air  / 
Cf  without  air  at  Flow  Velocity  u. 


324 


Nozzle  Yosfitda  [2]  Flow  Speed  u[mfs]  o,vtz-  $.00  m/s 

Injection  Rate  0(1/ min]  o  -  35  l/min  v~  100  l/min  z  -  200  i/min 

Bottom  Screen  Barbanel  [ 3 )  Flow  Speed  u[m/s]  ll  :  u  *  4.36  m/s  X :  u  *  S.SS  m/s  ®  :  u  **  10.9  m/s 

Fig.  &  Influence  on  downstream  Air  Injection  on  Cf  =  Cf  With  air  /  Ci  Without  air  at 
Velocity  u. 


325 


OPTIMIZATION  OF  THE  DISTRIBUTED  GAS  INJECTION  INTO 
A  TURBULENT  BOUNDARY  LAYER  FOR  THE  DRAG  REDUCTION 


V.G.  Bogdevich,  LI.  Mdltzev,  and.A.G.  Maluga 
Institute  of  Thermophysics, 

Siberian  Branch  of  the  Russian  Academy  of  Sciences,  RUSSIA 

Abstract  -  The  gas-bubble  saturation  of  near-wall  liquidflows  as  an.effeetive  method  for  reduction  ,  in  .  the  skin  friction  had  passed 
already  the  stage  of  laboratory  testing  and  . now  can  .be  recommended  for  practical  applications  on.sea  ships. 

The  key  question. for  engineer  accomplishment  of  this  method. for  drag  reduction,  is  the  development  of  the  optimal  method,  of 
boundary  water  layer  saturation  with  air  microbubbles.  One  of  possible  methods  is  the  air  injection. through  a  porous  coating.  The 
purpose  of  this  report  is  to  make  the  analysis  of  different  parameters  of  the  coating  and  the  recommendations  on  the  optimal  air  injection 
into  the  water  boundary  layer. 


I.  INTRODUCTION 

The  gas  bubble  saturation  of  the  near-wall  liquid  .flow  is  a 
well-known  .method. for  drag  reduction  for  water-moving  objects. 

To  the  present  time  many  works  were  performed,  in. this 
field.  The  main,  characteristics  of  he  drag-reducing  gas-liquid, 
boundary  layer  were  revealed.  It  was  demonstrated,  that  the  gas 
concentration  profile  has  a  maximum  for  applicable  variants  of  this 
technique  (a  considerable  drag  reduction  with  a  low  gas  flow  rate). 
This  maximum  of  gas  concentration  must  be  high,  and  .  the  layer  with 
a  high  gas  concentration  must  be  thin.  This  thin  layer  has  to  be  close 
to  the  solid,  wall.  Most  likely  that  the  bubble  size  in  a  given 
transversal  cross-section. of  the  boundary  layer  is  not  significant  for 
reduction  of  the  local  friction.  However,  to  provide  a  microbubble 
boundary  layer  with  drag  reduction  along  the  whole  body,  we  must 
provide  formation  of  very  small  bubbles. 

So,  the  requirements  to  near-wall  gas-liquid,  layers, 
producing  reduced  friction,  are  known.  There  are  exist  some 
methods  for  their  formation.  To  the  present  day  three  methods  for 
gas  injection. to  the  near-wall  liquid.flow  became  wide-spread: 

•  distributive  blow-in.of  gas  through  a  penetrable  coating  [1-4]; 

•  slot  injection  of  a  gas-liquidmixture  [5-6]; 

•  slot  gas  injection  under  the  near- wall  water  jet  [5]. 

First  impressive  results  on  friction  reduction  due.  to  gas 
microbubble  saturation  of  water  boundary  layer  were  obtained  ,  using 
the  first  method.  The  most  number  of  papers  in  this  field  also  imply 
the  use  of  the  penetrable  sheets.  However,  the  possibilities  of  this 
method  . are  still  not  discovered  completely  and  the  application  to  real 
objects  faces  with  some  problems.  The  matter  is  that  the  choice  of 
the  parameters  of  a  penetrable  sheet  and.  its  position  on  a  moving 
body  is  a  multi-pararaetertask.  The  structure  of  this  coating,  material 
properties,  the  porosity  distribution  over  the  gas  ejection  area  -  all 
these  features  affect  the  efficiency  of  the  gas  bubble  saturation,  for 
friction  reduction. 

AQ  these  problems,  as  well  as  some  others,  are  discussed 
in  this  report. 

II.  EXPERIMENTAL  SETUPS 

Our  experiments  were  performed  in. two  series.  We  used, 
an.  streamlined,  flat  plate  (Figure  1)  for  the  first  series,  and.  an. 
axisymmetrical  model  ~  for  another  series. 


The  plate  had  the  following  size:  910  mm  (length)  x  350 
mm  (width)  x  60  mm  (thickness).  We  installed,  a  porous  flat  sheet 
(with  the  size  of  350  mm  x  100  mm)  on  the  plate's  top  side  at  the 
distance  of  300  m  from  the  front  edge.  There  was  an  air  supply 
chamber  inside  the  body  which  was  covered  ,  with  a  porous  coating. 
It  was  sectioned  into  6  equal  parts  placed,  consequently  along  the 
stream.  The  pressure-regulated  air  flow  can  be  supplied. to  every  of 
these  sections  through  special  pipelines. 


Figure  1 .  Schematic  diagram  of  a  flat  plate 

In. our  case  a  porous  covering  was  a  stack:  of  thin,  sheets 
with  groves  on. both,  sides.  Actually,  this  penetrable  covering  was  a 
perforated  element  with  microchannels  directed  normally  to  the 
streamlined,  surface.  The  sheet  thickness  was  1.2  mm,  and.  the  slits 
between. stacked.shi.eets  were  about  30  microns. 

Downstream  (50  mm)  of  this  porous  area  we  put  an 
impenetrable  measuring  plate  with  the  size  of  55  mm  x  80  mm.  Both 
penetrable  and  measurong  plates  were  installed,  on. springy  elements 
which  allowed,  us  to  measure  the  integral  friction,  forces  for  every 
plate'  The  flat  plate  was  tested,  in  a  water  tunnel.  It  was  installed.in. 
the  horizontal  plane  of  the  working  section,  with  a  cross-section.  400 
mm  x  400  mm.  All  tests  were  performed  ,  at  the  main  flow  velocity 
Vqq  —  3  m/s. 

The  axisymmetrical  model  had. a  diameter  of  175  mm,  its 
length  was  1750  mm  with  a  long  cylindrical  part  which  was  about 


327 


75%  of  the  total  length.  Downstream  the  ogival  head  part  (length  - 
100  mm)  we  installed  4  removable  rings  made  from  penetrable  or 
impenetrable  material. 

The  penetrable  coverings  were  fabricated  ,  according  the 
technique,  mentioned  above.  The  thickness  of  stacked  sheets  was  0.8 
mm,  and  the  intersheet  clearance  was  30  microns.  The  relative  area 
of  every  section  was  8%  of  the  total  wetted  area  of  the  studied  ,  body. 
The  model  was  tugged. by  a  special  scooter  in  an  open  pool  with  the 
velocity  of  15  m/s. 

in.  EXPERIMENTAL  RESULTS 

A.  The  effect  of  the  relative  area  of  the  penetrable  coating  on  the 
efficiency  of  the  gas  bubble  saturation 

The  coefficients  of  the  integrated,  friction,  on  the 
measuring  plate  as  functions  of  the  penetrable  section  length  are 
plotted  in  Figure  2  (flat  plate). 


Figure  2.  The  integrated  skin  friction  ratio  on  the  measuring 
plate  vs.  the  length  of  porous  plate  for  Cq  =  0. 0028 


We  had  a  uniform  gas  injection  to  the  near- wall  stream 

with  a  flow  rate,  corresponding  to  the  dimensionless  coefficient 
Cq  =  0. 0028,  through  all  six  sections.  The  effect  of  the  friction 

reduction  on  the  measuring  plate  was  30%.  Here 
Cq  —  Qj where  Q  is  the  volumetric  gas  flow  rate,  S 
is  the  area  of  penetrable  coating  and  v^  is  the  main  flow  velocity. 
After  we  tuned  off  the  gas  supply  through  first  three  sections,  the 

effect  of  friction  reduction  stayed  almost  the  same  (keeping  the  ratio 
CQ  =  0. 0028)  -  see  Figure  2.  Note  that  with  the  same  CQ  the  twice 

reduction  in  area  means  the  twice  reduction  in  the  air  flow  rate. 

The  following  switching  off  the  4th  and  5th  sections  (with 
the  same  CQ  =0.0028  and  corresponding  decrease  in  the  flow  rate 

Q)  caused  the  linear  loss  in  the  initial  drag  reduction. 

The  dependency  of  the  total  drag  coefficient  on  the  gas 
flow  rate  is  depicted,  in  Figure  3  for  our  axi symmetrical  model.  It 
was  four  variants  of  the  gas  injection  into  the  stream.  Here  the  gas 
flow  rate  coefficient  is  Cq\  =  Qj  {$\  ‘^00)5  w^ere  ^  *s  the 
wetted  area  of  the  body. 


Ca  -1C" 


Figure  3.  Drag  coefficients  of  axisymmetrical  body  vs.  the 
coefficient  of  the  air  flow  rate. 

1  -  Spyj.  =  0. 08Stot;  2  -  Sp[}r=  0.16Stot;  3  -  -  0.24Stot, 

4-$^=  0.32Stot 

Curve  1  describes  the  gas  injection,  through,  the  section, 
one,  curve  2  -  through,  first  two  sections,  curve  3  -  through  first 
three  sections,  and  curve  4  -  through  all  four  sections.  One  can  see 
that  only  gas  blow-in  through  the  first  section. yielded  ,  a  considerable 
drag  reduction  with,  a  low  volumetric  air  flow  rate  (comparative  with 
other  variants). 

A  further  decrease  in. the  relative  penetrable  area  to  4% 
of  the  total  model  area  dimini  shed  the  efficiency  of  the  gas  bubble 
saturation  as  a  tool  for  drag  reduction. 

From  our  experiments  with  a  flat  plate  and  an. 
axisymmetrical  model  we  came  to  the  conclusion  that  there  exists  an 
optimal  ratio  of  the  penetrable  area  to  the  total  wetted  area,  and  this 
ratio  is  significantly  less  than  1. 

B.  The  effect  of  the  gas  injection  intensity 

Our  comprehension  of  the  mechanism  of  drag  reduction 
dictates  that  the  bubble  saturation,  of  a  turbulent  boundary  reduces 
the  transversal  impulse  flow  of  liquid.  As  a  result,  these  bubbles 
prevent  the  intensive  development  of  the  boundary  layer.  Moreover, 
the  fluid  density  near  a  solid  wall  also  decreases. 

The  upper  limit  of  gas  content  in  the  mixture  may  be  up  to 
81%  (if  bubbles  are  spheres  of  different  diameters). 

Obviously,  the  increase  in. the  gas  content  above  certain, 
level  causes  the  flow  restructuring.  Numerous  examples 
demonstrates  that  being  attained  some  minimum,  the  drag  begin,  to 
increase  with  air  flow  rate.  It  is  explained. by  merge  of  bubbles  and. 
resulting  loss  of  the  two-phase  layer  stability. 

The  second  problem  of  the  air  injection  intensity  is  the 
outlet  velocity  of  gas  from  pores. 

There  are  data  on  the  pressure  distribution  downstream 
the  porous  injection  zone  at  different  levels  of  Cq  (Figure  4). 
Obviously,  at  CQ  <  0.01  one  cannot  observe  any  significant  change 
in  the  wall  pressure.  But  at  CQ>0.01  there  exists  a  zone  of 

decreased  pressure;  this  may  be  interpreted  as  water  stream 
repulsion  from  the  wall  due  to  air  blow-irL 


328 


Figure  4.  Pressure  distribution  along  the  plate  after  the  injection, 
section.  7  -  CQ  =  0.007;  2  -  CQ  =  0.012;  3  -  C0  =  0.022 

The  air  flow  rate  Cq  =  Qj ^por  *  ^  is  a  mean- 

rate  relative  velocity  of  air  injection  through  the  porous  zone  (as  if 
air  were  supplied. uniformly  through  the  whole  zone  of  the  porous 
element).  We  already  explained,  that  the  penetrable  covering  is  a 
stack  of  thin  ,  sheets,  ant  air  is  fed.  through  the  inter  sheet  clearings. 
Their  thickness  was  1.2  mm,  ant  the  slot  size  was  0.03  mm. 
Therefore,  the  actual  velocity  of  air  injection  is  40  times  higher  than 
the  calculated  meanTrate  velocity. 

We  can.  see  from  Figure  4  that  the  flow  restructuring  in 
the  near-wall  gas-liquid. flow  and  . the  formation,  of  detachment  zone 

behind,  the  injection. zone  take  place  for  mean-rate  air  velocity  of 
CQ=0.01  (that  is,  the  actual  velocity  at  the  slot  outlet  was 

v7=  0. 4). 

In.  our  experiments  with  the  axi symmetrical  model  the 

most  significant  drag  reduction  was  achieved  for  air  blow  through 
the  only  first  section.  For  this  Spor  =  0.08x  Stot  at  CQ1  =0.00125. 

Here  the  sheets  thickness  was  0.8  mm  with,  the  clearance  size  equal 
to  Ah  =  0.03  mm.  The  best  result  on  drag  reduction  was  obtained  ,  for 
CQ  =0.0156  (”=0.42). 

From  all  things  concerned,  we  can.  conclude  that  in. 
making  the  bubble-saturated. layer  for  drag  reduction,  (with  a  porous 
coat-ing)  we  have  to  obtain  . a  uniform  (in  mathematical  sense)  air  in¬ 
jection,  with  the  out-of-pores  velocity  not  higher  than  40%  of  the 
main  stream.  Velocity  above  this  level  may  cause  intensive  mix-ing 
in  the  boundary  layer;  this  would  ,  spoil  the  gas  concentration  profile 
and.  increase  the  pressure  and.  velocity  pulsation,  in  the  boundary 
layer. 

C.  The  effect  of  air  injection  distribution  along  the  stream  on  the 
efficiency  of  the  air  saturation 

Experiments  with  axisymmetrical  model  demonstrated, 
that  the  law  of  the  flow  rate  of  injected  air  along  the  stream  must  be 
decreasing.  Experiment  with  sectioning  of  the  injection,  zone  and. 
different  variant  of  active  sections  combinations  persuaded  us  that 
the  best  results  were  obtained  . if  the  air  flow  rate  decreases  from  the 
first  section,  to  the  next  one  (counting  downstream).  There  was 
always  a  negative  pressure  gradient  on  the  head.part  of  real  objects. 
Looking  from  the  practical  point  of  view,  it  will  be  easy  to  provide  a 
desired  ,  air  flow  rate  distribution,  along  the  body  using  a  single  air- 
supply  chamber  with,  a  uniform  porous  covering. 


D.  The  wetting  effect  of  the  porous  coating  on  the  character¬ 
istics  of  a  gas-liquid  flow 

There  are  three  media  which,  participate  in  formation  of  a 
gas-liquidflow:  gas,  liquid,  and  solid. porous  coating.  All  the  results 
mentioned  above  were  obtained  for  models  fabricated  from 
aluminum  alloys  (and.  porous  coating  as  well).  That  is,  they  had. 
hydrophilic  surfaces. 

But  our  experiments  with  the  flat  model  discovered,  that 
the  treating  of  the  porous  coating  by  a  special  hydrophobic  substance 
change  situation  dramatically.  If  the  porous  material  was  hydro- 
phobic,  we  have  gaseous  torches  at  the  pores  outlets.  Their  inter¬ 
action  with  water  stream  makes  an  unstable  loose  gas-liquid  flow. 

Figure  5  demonstrates  the  difference  in  the  integral  gas- 
saturation  effect  between,  hydrophilic  and.  hydrophobic  porous 
coatings. 


CvIO1 


Figure  5.  Integrated,  skin  friction,  on.  the  porous  plate  (curves  7,  2) 
and  on  the  measuring  plate  (curves  3 ,  4)  as  the  functions  of  the  air 
flow  r$te  coefficient  1,2-  hydrophobic  porous  coating;  3,  4  - 
hydrophilic  porous  coating 

The  gas  inflation  through  the  hydrophobic  porous  coating 
did  not  yield  any  friction. reduction  on.  the  coating  (curve  7),  and 
made  only  slight  decrease  of  that  on  the  measuring  plate  downstream 
the  porous  zone  (curve  2). 

Under  the  other  equal  conditions,  the  air  inflation  through 
a  hydrophilic  coating  allowed  us  to  decrease  friction,  considerably 
both  on  the  coating  (curve  3),  and  on  the  measuring  plate  down¬ 
stream  it  (curve  4). 

IV.  CONCLUSION 

We  made  experiments  with,  a  streamlined,  plate  and 
axisym-metrical  model  aimed  to  find,  out  the  effect  of  different 
parame-ters  of  porous  coatings  on  the  efficiency  of  the  gas-bubble- 
satura-tion  method  on  the  friction  reduction. 

It  was  discovered  that  the  percentage  of  the  porous  zone 
on  an.  oblong  body  must  be  about  8-10%  of  the  total  wetted  area. 
This  penetrable  coating  have  to  be  positioned  .at  the  head  part  of  the 
body,  where  exists  a  negative  pressure  gradient.  An  efficient  variant 
may  be  obtained. if  the  air  injection  rate  decreases  along  the  body. 
The  material  of  the  porous  coating  must  be  hydrophilic. 

Naturally,  these  are  only  recommendations.  The  precise 
knowledge  of  an. injection. distribution. and.  parameters  depends  on. 
the  shape  and. size  of  the  body,  etc. 

V.  ACKNOWLEDGMENT 

The  research,  described  in  this  report  was  partially  supported  by 
INTAS,  grant  number  INTAS-94-3737. 


329 


VI.  NOMENCLATURE 

Cf  integrated  skin  friction  with,  gas  bubbles; 

C  f0  integrated  skin  friction  without  gas  bubbles; 

Cf  dimensionless  integrated  skin  friction,  (Cf  =Cf  jCfQ); 

Cq  dimensionless  air  flow  rate,  ( Cq  =  Ql ))? 

CQ1  dimensionless  air  flowrate,  (Cq\  o^tot))i 

main-flow  velocity,  (m/s); 

Spyj.  area  of  the  porous  coating,  (m2); 

£^ot  area  of  the  wetted  surface  of  a  body,  (m2); 
v,  air  velocity  through  pores,  (m/s); 

Q  volume  air  flow  rate,  (m3/s); 

D  hydrodynamic  drag  of  axi symmetrical  body  with  gas 

saturation,  (kg); 

D0  hydrodynamic  drag  of  axi  symmetrical  body  without 

gas  microbubbles,  (kg); 

U"D  =D/D0. 


VII.  REFERENCES 

1.  G.S.  Migirenko  andA.R.  Evseev,  "Turbulent  boundary  layer  with 
gas  saturation".  In:  Problems  in  thermal  physics  and  physi-cal 
hydrodynamics,  Novosibirsk:  Nauka  Publ.  House,  1974.  (In  Russian). 

2.  V.G.  BogdevichandA.G.  Malyuga,  "Distribution. of  skin.fric-tion 
in  . turbulent  boundary  layer  of  water  behind  the  gas  injection  point". 
In:  Study  on  the  boundary  layer  control.  Novosibirsk,  1976.  (In 
Russian). 

3.  V.G.  Bogdevich  and  A.R.  Evseev,  "Effect  of  gas  saturation  on 
wall  turbulence".  In:  C.C.Kutateladze  and  G.S.  Migirenko  (ed.), 
Investigation  of  Boundary  Layer  Control.  Novosibirsk:  Thermo - 
physics  Institute  Publishing,  1976.  (In Russian). 

4.  G.L.  Merkle  and.S.  Deutsch,  "Microbubbles  Drag  Reduction".  In; 
Bushnell  and  Hefner  (eds.)  Viscous  Drag  Reduction  in  Boundary 
Layers.  (Progress  in  astronautics  and  aeronautics',  vol.  123),  1993. 

5.  L.I.Maltzev,  "Jet  Methods  of  Gas  Injection  into  Fluid  Bound-ary 
Layer  for  Drag  Redution",  Appl.  Sci.  Res.  v:  54,  1995. 

6.  H.  Kato,  M.  Miyanaga,  and  M.M.  Guin,  "Frictional  Drag  Re¬ 
duction  by  Injecting  Bubble  Water  into  Turbulent  Boundary  Layer”. 
FEDv:  190,  Cavitation  and  Gas-Liquid  Flow  in  Fluid  Machinery  and 
Devices .  ASME,  1994. 


330 


EFFECT  OF  MICROBUBBLE  DISTRIBUTION  ON  SKIN  FRICTION  REDUCTION 


Yoshiaki  Kodama 
Ship  Research  Institute 
6-38-1,  Shinkawa,  Mitaka 
Tokyo  181-0004,  Japan 
kodama@srimotgo.jp 

Abstract  -  Microbubble  experiments  were  carried  out  using  a  small  circulating  water  tunnel.  The  skin  friction  reduction  up  to 
40%  was  obtained.  The  local  void  ratio  was  measured  using  two  methods,  one  by  inserting  a  suction  tube  in  the  test  section,  and 
the  other  by  counting  the  bubbles  from  photog*aphs.  The  results  suggest  that  the  local  void  ratio  near  the  wall  is  a  dominant 
factor  for  die  skin  friction  reduction. 


L  INTRODUCTION 

It  is  well  known  that  small  bubbles  called  microbubbles  injected  into 
the  boundary  layer  on  a  solid  wall  reduce  the  skin  friction 
signiflcantly[l].  But  the  energy  needed  for  injection  is  not  nominal,  and 
the  net  drag  reduction  is  difficult  to  obtain  when  it  is  applied  to  full-scale 
ships.  Therefore,  it  is  necessary  to  reduce  the  amount  of  air  and/or 
increase  the  drag  reduction  by  studying  the  drag  reduction  mechanism. 
Recently,  studies  on  microbubbles  have  been  carried  out  in  Japan 
experimentally [2]  and  numerically[3].  The  author's  goup  are  studying 
the  mechanism  and  the  scale  effect  of  microbubbles[4],  in  order  to  apply 
the  technique  to  full-scale  ships.  In  this  paper,  some  recent  experimental 
results  will  be  shown. 

n.  EXPERIMENTS 
n.l  Test  facility 


A  small  circulating  water  tunnel  specially  designed  for  microbubble 
study  was  constructed  (Fig.  1).  The  air  is  injected  in  the  test  section  to 
generate  microbubbles.  At  downstream  of  the  test  section  there  is  a 


dump  tank,  in  which  the  injected  bubbles  are  removed  by  buoyancy,  thus 
making  continuous  tests  possible. 


Ai  r 


Fig.l  A  small  circulating  water  tunnel  for  testing  microbubbles 
Fig.2  Bubble  generation  using  a  porous  plate 

The  tunnel  has  a  test  section  of  100mm  times  15mm  times  3000mm  in 
size.  The  bubbles  are  generated  by  injecting  air  through  a  porous  plate 
made  of  metal  with  nominal  pore  radius  of  lOmum  (Fig.2).  The  plate  is 
located  at  1038mm  downstream  from  the  upstream  end  of  the  test  section. 


where  the  flow  is  fully  developed.  This  location  will  be  called  Position  1. 
At  three  consecutive  locations,  500mm  apart  from  each  other,  various 
measurements  are  possible.  These  locations  will  be  called  Positions  2,  3, 
and  4  in  the  downstream  order. 

The  amount  of  injected  air  is  represented  by  the  average  void  ratio  Oa 
defined  as 

where 

Qa  :  air  flow  rate 
Qw :  water  flow  rate 

II.2  Bubble  photographs 

Photographs  of  the  microbubbles  were  taken  using  a  high-definition 
CCD  camera  (Fig.3)[5j.  A  YAG  laser  was  used  as  a  light  source,  taking 
advantage  of  its  short  duration.  The  light  sheet  was  placed  30mm  from 


the  plane  of  symmetry  toward  the  camera,  in  order  to  get  a  better  image. 
Fig.4  shows  the  photos  at  Ota=0.05  in  Positions  2  and  3.  The  flow  is  from 


right  to  left.  The  top  end  of  each  photo  corresponds  to  the  upper  wall  of 
the  test  section.  The  vertical  length  of  the  photo  corresponds  to  10mm. 
The  bubbles  are  clustered  near  the  top  end,  where  the  bubbles  were 
generated.  The  size  of  the  bubbles  are  mostly  less  than  1mm  in  diameter, 
although  it  depends  on  the  flow  speed. 

Fig. 3  Camera  and  light  source  layout[5] 


(a)  U=7m/sec,  Position  2 


737  =  ^ 

0_  Q*  +  Q* 


(1) 


331 


of  the  test  section. 


(c)  U=7m/sec,  Position  3 


(d)  U=10m/sec,  Position  3 
Fig.4  Photogaphs  of  microbubbles  at  Ota  =0.05  3 [5] 


Fig.5  Skin  friction  sensor 

In  Fig.6,  the  measured  Cf  values  are  shown  as  the  ratio  to  Cfl),  the  Cf 


aa-0.  026 


1.00 

- T 

1  t 

- 

0.  90 

2 

J=10.  Om/s 

U=7.  Om/s 

. .  . a 

. -a . 

- 

0.  80 

-U=5.  Om/s  -D-- 

- 

0.  70 

n  cn 

- 

i  i 

- 

12  3  4 

position 

value  in  the  non-bubble  condition.  When  the  air  is  injected,  the  flow 
speed  increases,  and  therefore,  in  the  bubble  condition,  the  Cfi)  value  was 

aa=0.  053 


aa=0.  081 


(b)  Ota  =0.053 


113  Skin  friction 

A  skin  friction  sensor  is  useful  in  measuring  skin  friction  directly [6].  A 
sensor  of  2  gams  full  scale  was  used  for  measuring  skin  friction  with  or 
without  bubbles  (Fig.5).  The  sensor  was  placed  on  the  plane  of  symmetry 


C*W.)  =  C/„(  0)^  (2) 


r(/)  =  0.03325pz/1/4/7/V1/4  (3) 


(c)  Ota  =0.081 


(d)aa-O.ll 

Fig.6  Skin  friction  reduction. 

The  skin  friction  was  measured  at  three  speeds  in  three  downstream 
locations,  changing  the  rate  of  bubble  injection.  At  U=10m/sec,  the  skin 
friction  reduction  increases  as  CXa  increases,  saturating  at  (Xa  =0.081  and 
0.11  and  reducing  rapidly  in  the  downstream  direction.  At  U=7m/sec,  the 
overall  tendency  is  similar  to  that  at  U=10m/sec,  except  that  the  reduction 
persists  longer  in  the  downstream  direction.  At  U=5m/sec,  the  tendency 
is  different  from  the  other  two,  i.e.,  the  reduction  saturates  at  small  Cta 
values  and  appears  to  increase  in  the  downstream  direction.  In  total,  the 
microbubbles  are  the  most  effective  at  U=7m/sec. 

What  is  difficult  to  understand  is  that,  at  Cta  =0.026  and  0.053,  the  skin 
friction  reduction  is  consistently  r  at  smaller  U.  Generally  the  bubble  size 
is  greater  at  lower  speeds  due  to  the  smaller  shear  stress  acting  on  the 
porous  plate  where  the  bubbles  are  generated,  and,  if  it  is  true  that 


In  order  to  clarify  that  point,  it  is  necessary  to  measure  local 
properties.  Thus  the  local  void  ratio  CXa  was  measured  using  a  suction 
tube  system  (Fig.7)  similar  to  the  one  used  in  ref.6.  A  small  tube  with  a 
flat  opening  was  placed  in  the  test  section.  The  tube  was  connected  to  a 
vacuum  pump  for  suction  through  two  chambers  to  measure  air  volume 
and  water  volume  separately. 

Fig.  7  Suction  tube  for  measuring  local  void  ratio 


(a)  U=7m/sec 


(b)  U=10m/sec 

Fig.8  Local  void  ratio  Cta  at  CXa  =0.053. 

The  measurements  were  made  at  two  speeds  in  two  locations  at  Cta 
=0.053  (Fig.8).  At  U=7m/sec,  Cta  closest  to  the  wall  is  g-eater  in  Position 
2  than  in  Position  3,  which,  together  with  the  results  shown  in  Fig.6(b), 
suggests  that  the  local  void  ratio  near  the  wall  is  the  dominant  factor  for 
skin  friction  reduction.  The  Cta  values  closest  to  the  wall  at  U=7  and 
lOm/sec  and  in  Positions  2  and  3  correlate  well  with  the  Cf  /  Cfl)  values  in 
those  conditions.  But  the  integrated  Cta  at  U=10m/sec  is  clearly  smaller 
than  that  at  U=7m/sec.  They  should  be  about  the  same  because  Cta  was 
kept  the  same.  The  reason  for  this  is  perhaps  that  the  suction  pressure 
was  not  appropriately  controlled,  as  described  in  ref.6. 

n.5  Measurements  using  photographs 
The  distribution  of  the  bubbles  was  measured  at  CXa  =0.053  from  the 
photographs  as  shown  inFig.4.  The  measurement  volume  was  18.75mm 
times  10mm  times  1mm,  the  size  of  the  photo  and  the  thickness  of  the 
laser  sheet.  At  each  condition  the  number  and  size  of  the  bubbles  were 
obtained  by  counting  in  eight  photos  and  averaging.  The  average  number 
of  counted  bubbles  was  111.9  at  U=7m/sec  and  144.1  at  U=10m/sec. 

Fig.9  shows  the  bubble  radius  distribution  and  Table  1  shows  the  mean 
bubble  radius.  The  bubble  radius  is  distributed  between  zero  and  0.8mm. 
There  is  no  significant  difference  in  Positions  2  and  3.  The  bubble  size  is 
slightly  smaller  at  the  higher  speed. 


tS 


the  opposite. 


0.50 

0.40 

0.30 

0.20 

0.10 

0.00 

0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15 
distance  from  the  wall 


position  2  •  - 

•  • 

position  3  O 

o  o  # 

_ 

o  * 

°o 

°o0 

II.4  Local  void  ratio 
6.50 


0.40 


0.30 

* 

0.20 

0.10 


0.00 

0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15 
distance  from  the  wall 


— i — ] — i — i — i — i — i — i — r 

t  i  i  i  i 

position  2  #  ■ 

position  3  O 

- 

-O  • 

. 

°S*«000 
_ ■  ■  *  ‘ _ i _ i  ■■■; . i — l 

_ i — i _ i — i _ i — 

(a)U=7m/sec. 


(b)  U=10m/sec. 

Fig.9  Bubble  radius  distribution.  CXa  =0.053. 


333 


Fig.  10  shows  the  local  void  ratio.  Oscillations  in  the  distribution  suggest 
that  the  number  of  photographs  used  in  each  condition  (i.e.  8)  was  not 
enough.  At  U=7m/sec,  the  distributions  in  Positions  2  and  3  are  similar, 


>n  2 

3 

7  m/sec 

0.  38 

0.  34 

10  m/sec 

0.  31 

0.  33 

and  they  are  comparable  to  those  in  Fig.8(a).  At  U=10m/sec,  Position  3 


D.6 


m 

<3  0.4 


cr 


,  *  o 

1  0.2|.fio  * 


•  Position  2 
o  Position  3 

U=  7 m/s 


6  *  • 

°  0  ^  •  %  A  ft 

_ i _ i _ i  q.-lQ _ i _ &j 


%  2  4  6  8 

Distance  from  Wall,  mm 


10 


seems  to  have  higher  void  ratio  near  the  wall,  which  is  in  contradiction  to 
that  shown  in  Fig.8(b). 

0.6r 


<c 

3  0.4 

o' 

ts 

( X 

|  0.2 


•  Position  2 
°  Position  3 

U=  ID  m/s 


A  O  0 

8.  .  2  °  •  #  * 


°  O  o 


2  4  6  8 

Distance  from  Wall,  mm 


•  *  ° 

■  °  .o  <?  *i 


10 


Table  1  Mean  bubble  radius  (mm) 


^ 

>n  2 

3 

7  m/sec 

0.  118 

0.  094 

10  m/sec 

0.  Ill 

0.  093 

(a)  U=7m/sec. 


summing  all  the  bubble  volume  and  dividing  by  the  measurement  volume. 
The  corresponding  average  void  ratio  termed  as  CXa  H/2  is  obtained  using 
eq.(l)  where  Qw  this  time  is  the  flow  rate  in  the  upper  half  of  the  test 
section.  Thus  Cta  =0.053  corresponds  to  (Xa  H/2=0.10.  The  integrated 
void  ratios  are  in  good  agreement  with  Cta  H/2,  suggesting  the  reliability  of 
this  method  based  on  photographs. 

This  result  suggests  that  the  suction  tube  method  whose  results  are 
shown  in  Fig.8  has  a  problem,  especially  at  U=10m/sec.  Further  study  is 
needed  in  this  point. 

in.  CONCLUSIONS 

The  skin  friction  was  measured  in  a  circulating  water  tunnel  at  various 
flow  conditions  with  or  without  bubbles.  The  local  void  ratio  was 
measured  using  two  methods.  They  suggest  that  the  local  void  ratio  close 
to  the  wall  is  a  dominant  factor  for  skin  friction  reduction  due  to 
microbubbles.  Further  studies  are  needed  for  clarifying  the  mechanism 
for  skin  friction  reduction  by  microbubbles,  and  for  reducing  the  amount 
of  bubbles  needed,  in  order  to  put  the  method  into  practical  use. 


PREFERENCES 

TBushnell,  D.M.  and  Hefner,  J.N.(ed.):Viscous  Drag  Reduction  in 
Boundary  Layers",  Prog-ess  in  Astronautics  and  Aeronautics  vol.123, 
AIAA,  1990. 


2.Kato,  H.  et  al.: "Frictional  Drag  Reduction  by  Injecting  Bubbly  Water 


into  Turbulent  Boundary  Layer",'  Cavitation  and  Gas  Liquid  Flow  in  Fluid 
Machinery  and  Devices,  FED-vol.l90,ASME,  1994,  pp  18 5- 194. 

3. Kanai,A.  et  al.: "Direct  numerical  simulation  of  multiple  bubbles  in  a 
boundary  layer",  Proceedings  of  the  11th  Computational  Fluid  Dynamics 
Symposium,  pp.221-222,  December  1997,  Tokyo,  Japan. 

4. Takahashi,T.  et  al.: "Stream wise  Distribution  of  the  Skin  Friction 
Reduction  by  Microbubbles",  J.  of  the  Society  of  Naval  Architects  of 
Japan,  vol.  182,  November  1997. 

5. Kakugawa,A.  et  al.:"The  Effect  of  Microbubble  Distributions  on  Drag 
Reduction",  70th  General  Meeting  of  Ship  Research  Institute,  December 
1997. 

6. Guin,  M.M.  et  al.: "Direct  Skin  Friction  Measurements  and  Observation 
of  Drag  Reduction  in  a  Two-Phase  Air-Water  Channel,"  ASME 
Symposium,  San  Diego,  1996. 

7. Schlichting,H.:  "Boundary-Layer  Theory",  6th  edition,  McGrawhill, 
1968. 


(b)  U=10m/sec. 

Fig.  10 Local  void  ratio  distribution  in  depthwise  direction. 

Table  2  Void  ratio  integ-ated  in  half  depth.  (Xa  =0.053  &  CXaH/2=0.10ms 


334 


COMBINED  POLYMER  AND  MICROBUBBLE  DRAG  REDUCTION 


R.B.  Philips,  J.M.  Castano  and  J.  Stace 

Naval  Undersea  Warfare  Center 
Division  Newport 
Newport,  Rhode  Island  02841 

philip  s@c  80  .np  tnuwc  .navy  anil 
castanojm@code80npw.nuwc.navy.  rail 

Abstract  -  Two  well  known,  skin,  friction  reducing  techniques  were  combined  to  examine  the  possibility  of  realizing  synergistic  drag 
reductions,  i.e.,  a  reduction  in. drag  greater  than  the  sum  of  each,  reducing  technique  individually.  Polymer  (polyethylene  Oxide)  additive  and. 
gas  (  compressed  air  in.  the  form  of  a  microbubble  sheet)  injection,  into  fully  developed,  turbulent  boundary  layers  have  separately 
demonstrated  substantial  and  consistent  drag  reducing  capabilities.  These  two  robust  drag  reducing  techniques  were  combined,  in  a  flat  plate, 
saltwater,  tandem  injection,  experiment  employing  a  set  of  floating  element  drag  balances  immediately  behind,  the  injection,  locations  to 
measure  integrated. skin  friction.  Individually  each,  additive  showed  expected  levels  of  drag  reduction.  Combining  the  two  techniques  showed  , 
drag  reduction  levels  exceeding  the  individual  sum  of  drag  reduction  up  to  10%.  The  order  of  injection  ,  was  an.  important  factor  in  .  obtaining 
synergy: 


I.  INTRODUCTION 

A  number  of  investigators  have  noted,  the  similarities  between 
polymer  and. microbubble  drag  reduction.[l]  [2]  [3].  The  injection. of 
polymers  or  microbubbles  into  the  boundary  layer  has  been  shown  [4] 
[5]  [6] [7]  to  remove  turbulent  flow  energy  and.  change  momentum 
transport  near  the  wall  in  a  turbulent  boundary  layer  thereby  reducing 
skin  friction.  For  microbubble  drag  reduction.  Pal  et  al.  [6]  and,  more 
recently,  Guin.et  al.[8]  have  demonstrated,  that  bubble  concentrations 
must  be  maximized  between  the  wall  and  a  y+  of  150  for  effective 
drag  reduction  (y+  =  y  u*/v  where,  y-is  normal  distance  from  the  wall, 
u*  is  the  friction  velocity  and.  v  is  the  kinematic  viscosity).  Walker  et 
al.  [9]  determined. the  optimal  polymer  injection. rate  for  polymer  drag 
reduction  in  a  channel  to  be  .5.1  times  the  volumetric  flow  rate  of  the 
viscous  sublayer,  demonstrating  the  importance  of  maximizing  the 
polymer  concentration  in.  or  near  the  buffer  layer.  This  observed 
similarity  in  the  drag  reducing  mechanism  of  each  method  ,  suggests  the 
possibility  of  mutually  enhancing  their  respective  mechanisms  by 
simultaneously  injecting  polymers  and.  microbubbles  into  a  turbulent 
boundary  layer.  The  ability  to  increase  skin. friction. reduction,  beyond, 
the  sum  of  the  individual  components,  thereby  creating  a  synergistic 
effect,  implies  that  bubbles  may  promote  the  elongation  of  polymer 
molecules  and/or  that  polymers  enhance  the  concentration  of  small 
bubbles  near  the  wall.  In  either  case,  the  size  of  the  smallest  turbulent 
fluctuations  would  he  increased,  resulting  in  a  thickening  of  the  buffer 
layer  and  anupward.shift  in  the  log-region  velocity  profile. 

Indeed,  a  study  performed  by  Malyuga  et.  al.  [10]  in  the  former 
Soviet  Union,  suggests  synergistic  drag  reduction,  takes  place  when, 
microbubble  and  polymer  injection  takes  place  simultaneously: 
Malyuga,  who  performed  microbubble  drag  reduction  experiments  in. 
the  late  1970 ’s,  injected  aerated  polyethylene  oxide  solution  into  a 
turbulent  boundary  layer  and.  measured,  skin  friction,  on.  three  2 3 -mm 
diameter  flush,  mounted,  disks  downstream  of  the  injection,  point. 
Malyuga’s  team  concluded. that  there  was  a  "...  mutual  intensification 
of  two  methods  for  drag  reduction."  They  attribute  this  effect  mostly  to 
the  greater  concentration,  of  small  diameter  bubbles  which  they 
observed  . when  the  polymer  solution  was  aerated  just  prior  to  injection. 
Few  physical  dimensions  of  the  polymer  aeration  process  were 
provided  from  which  to  discern,  the  possible  bubble  size  distribution. 
The  aerated,  polymer  solution  was  irgected.  through  an  8-degree,  1.8 
mm  wide  slot.  The  Russian,  authors  suggested  their  polymer 
(polyethylene  oxide  -  PEO)  reduced,  bubble  surface  tension,  thereby 
generating  smaller  bubbles  than. expected-  They  measured  local  skin 
friction  reductions  up  to  80%  at  the  floating  element  closest  to  the 
injection,  slot,  with  reductions  tapering  off  further  downstream. 
Malyuga  noted  that  the  drag  reduction,  levels  attained  by  aerating  the 
polymer  solution,  would  exceed,  reduced,  drag  levels  measured,  with 
only  air  or  only  polymer  injection  into  the  boundary  layer. 

The  possibility  of  enhancing  the  intrinsic  ability  of  each  polymer 
molecule,  and/or  gas  microbubble,  to  reduce  skin  friction,  once 
introduced  into  a  turbulent  boundary  has  significant  ramifications.  In. 
many  applications,  both  techniques  are  limited,  in.  practice  by  their 
friction. reducing  density,  i.e.,  the  amount  of  drag  reduction,  per  unit 
volume  of  polymer  solution  or  gas  injected  into  the  boundary  layer. 
Microbubble  drag  reduction. on  submerged,  vehicles  requires  a  greater 
mass  of  gas  to  maintain  reduced  drag  as  speed  and  ambient  pressure 


increase.  Efficient  polymer  drag  reduction  techniques  require  either 
highly  concentrated .  polymer  slurries  be  carried,  by  the  vehicle  then, 
hydrated',  to  lower  concentrations  prior  to  injection,  or  the  onboard, 
processing  of  the  bulk  material  into  a  drag  reduction,  solution.  If  the 
combination  of  polymer  and  microbubbles  can  reduce  the  volume  of 
gas  and/or  polymer  solution  required. to  maintain  desired  . levels  of  drag, 
these  two  robust  and.  well  known,  techniques  become  much  more 
attractive  for  undersea  applications. 

In.this  study,  a  flat  plate  test  geometry  with  two  ejectors  placed  in 
tandem  was  employed. to  determine  if  synergistic  drag  reducing  effects 
were  possible  with  simultaneous,  but  separate,  polymer  and. 
microbubble  injection-  Two  separate  ejectors  were  employed  for  the 
additives  to  eliminate  uncertain,  plenum  mixing  attributes  from  the  test 
variables.  The  parameter  space  for  this  investigation  included, 
streamwise  injection  order  (i.e.,  polymer  upstream  of  microbubbles  and 
vice  versa),  volumetric  flow  rates  for  both,  additives.  The  measured, 
quantities  were  integrated,  shear  stress  at  multiple  downstream 
locations,  and. other  ambient  pressure,  temperature  and  velocity  values. 
Laser  aneraometry  was  employed  to  confirm  the  baseline  boundary 
layer  parameters,  in  addition  to  the  integrated,  shear  stress 
measurements.  Salt  water  was  used  as  the  base  fluid  since  bubbles 
produced  in  salt  water  are  roughly  an  order  of  magnitude  smaller  than, 
those  produced  similarly  in  .fresh  water  (Cary  et.  al.  [11],  Hrubes  et.  al. 
[12]  and. Monahan  et.  al  [13]),  and  bubble  size  may  be  a  factor  in. 
microbubble  drag  reduction  and  in  combination  with  polymers.  In  a 
previous  bubble  size  study,  Kuklinski  [14]  showed,  that  the  salt  water 
had.  a  very  significant  effect  upon,  bubble  size  versus  fresh,  water. 
However  the  combination. of  polymer  with  salt  water  produced,  little 
additional  effect  upon  the  bubble  size  distribution. 

II.  FACILITIES  AND  PROCEDURE 

The  experiments  were  conducted  in.  the  closed  loop 
Hydrodynamics  Research  Water  Tunnel  at  NUWC.  It  operates  with 
both  man-made  salt  water  and  fresh  water  for  investigations  where  the 
fluid  medium  is  a  critical  parameter  and  has  a  fully  integrated  water 
treatment  system.  This  facility  includes  an  on-line  air  removal  or 
deaeration. system.  The  maximum  operating  velocity  in.  the  test  section, 
is  7.6  m/s  (25  ft/s),  which  is  driven  by  a  30  hp  motor.  The  motor  drives 
an  axial  flow  pump,  whichhas  four  blades  with  twist  designed  to  give 
uniform  radial  velocity  profiles.  A  stainless  steel  honeycomb  with  0.25- 
inch  cells,  six  inches  thick:  (for  an.  aspect  ratio  of  24)  is  located 
upstream  of  the  nozzle  to  straighten,  the  flow  and.  control  of 
background  turbulence.  Finally,  the  tunnel  is  equipped,  with  an 
automated. static  pressure  control  system,  which. maintains  the  pressure 
in  .the  test  section  within ±  1  psi. 

The  facility  has  a  3.05  m  (10-ft)  long  test  section,  with  a  .305m 
(1-ft)  square  cross  section,  which  allows  for  large  arclength  Reynolds 
number  investigations.  The  test  section  has  16  access  panels  or 
windows  25.4  cm  (10-in)  by  61  cm  (24-in),  which  allow  for  up  to  65% 
of  the  test  section. to  be  optically  accessible.  Pressure  taps  along  the 
test  section,  and  in  the  window  panels,  allow  for  streamwise  pressure 
gradient  measurements,  which  are  made  with  a  rotating  tap  selection, 
valve  and  pressure  sensor. 

The  flat  plate  testbed,  has  an  elliptical  leading  edge  and  can  be 
positioned  in  the  test  section,  so  as  to  produce  a  variety  of  streamwise 


335 


pressure  gradients.  A  trailing  edge  flap  is  used,  to  make  small  pressure 
gradient  corrections  to  be  made  while  running.  The  plate  has  three 
identical  0.508  m  long  by  0.178  m  wide  inserts  which  can  be  removed. 


Po^mer/  Microbubbfe  Ejection  Plate  &  Balances 


Flat  Plate 
Bottom  View 


r — n 

r 

JU1- 

ill 

r_j 

— j 

,1 

[30.5 

\ 


Lead  ng 
age 


Tiling  Edge 
Rap 


jm 


MM. 


li 

*•30.5 

J< 


Flat  Plate  h  Water  TUnn el 
Side  View 


Fig.  1 .  Schematic  of  overall  flat  plate  (dimensions  in.'cmf 


instrumented  and. re-inserted  at  any  of  three  streamwise  locations.  Side 
and  top  views  of  the  plate  configuration  are  provided  . in  .  figure  1.  The 
orientation  of  the  plate  was  such  that  the  injection  and  drag  balances 
were  on  the  bottom  surface  of  the  flat  plate.  This  made  the  fabrication, 
of  the  drag  balances  easier. 

For  this  test  the  first  insert  was  designed  ,  to  carry  a  polymer 
injection  module,  a  microbubble  injection  module,  and  three  floating 
element  skin  friction,  balance  modules.  Each  module  was 
interchangeable  so  that  their  relative  streamwise  positions  could  be 
varied  as  desired.  A  schematic  of  this  instrumented  injection  insert  is 
given  in  figure  2. 


Fig.  2.  Schematic  of  injectors  and  drag  balances  -  upstream  polymer, 
downstream  microbubble  shown  (dimensions  in  cm) 


In  the  design  of  this  experiment,  flexible  injection,  geometries 
were  considered  an  important  feature  since  this  would  allow  for 
injection  position  and  mixing  parameters  to  be  analyzed-  The  five 
modules  shown  in. figure  2  can.be  positioned  in  any  order  desired, 
however,  the  only  configurations  tested  to  date  consisted,  of  three 
balance  modules  downstream  of  two  injection  modules.  The  three 
floating  element  balances  were  designed  to  be  very  stiff  yet  sensitive  to 
±3.0  grams  over  a  range  of  100  grams  (±3%  error  under  static, 
calibration ioad  conditions).  A  sample  calibration. curve  is  provided  in. 
Figure  3.  Error  bars  indicating  ±2  standard  deviation  levels  are  shown 
Drag  was  measured  via  a  shear  web  member  made  of  0.002-inch  thick 
brass  shims  for  each  element.  Four  bending  members  which  only  allow 
motion  in  the  streamwise  component  support  each  element  and. 
eliminate  the  possibility  of  buckling  the  paper-thin  brass  shear  webs.  To 
further  inhibit  buckling  and  promote  high  bubble  concentrations  near 
the  wall  at  lower  speeds,  the  plate-on-top  test  geometry  configuration 
was  used.  This  required  that  all  the  injection  and. balance  test  modules 
face  downward,  with  additives  injected,  beneath  the  plate  in  the  test 
section’s  free  stream  flow.  The  center  of  drag  balances  1  and. 2  were 
located.  0.679m  and  0.766m  from  the  leading  edge  of  the  plate 
respectively. 


Grams  Input 


Fig.  3.  Plot  of  drag  balance  calibration. 


Both  injection. modules  (see  figure  4)  consisted  of  a  small  plenum 
with,  a  row  of  twelve  1.6  mm  (l/16th-in)  diameter  holes  spaced  .  9. 5  mm 
(3/8-in)  apart,  through  which,  the  additives  were  introduced.  The 
polymer  injection  plenum  contained  a  small  amount  of  open-cell  foam, 
and' had'  an  17.8  cm  (7-in)  wide  by  1.6  mm  (l/16th-m)  slot  angled  at  15- 
degrees  to  the  wall.  The  slot  injection  angle  was  designed  to  minimize 
boundary  layer  perturbations  during  injection.  Previous  experience 
with  polymer  injection  hardware  has  shown  that  a  shallow  angle 
produces  a  smaller  disturbance.  This  was  also  the  shallowest  angle  that 
could  be  machined  while  retaining  the  desired  tolerances  across  the 
slot.  The  downstream  edge  of  the  slot  was  fared  (rounded)  so  that  the 
ejected  polymer  would  enter  the  boundary  layer  without  having  to  flow 
over  a  sharp  edge.  This  provided  uniform  spanwise  distribution. of  the 
polymer  which  was  visually  confirmed  by  adding  red  dye  to  several 
preliminary  runs  of  polymer  injection 


Polymer 

Side  View  Ejection 

Slot 


Ejector  ^ 

J  6.35  mm 


Manifold 


Gas  Inlet 


5  Micron  Filter  Material 
Porous  Material  Sealed  Along  Edges 


Fig.  4.  Schematic  of  polymer  and  microbubble  ejectors 


The  air  injection  .module  had  a  16.5  cm  (6.5-in)  wide  by  6.35  mm 
(0.25 -in)  slot  into  which  a  5- pm  absolute  sintered  plastic  filter  material 
was  fitted.  This  provided  a  flush,  smooth,  wetted  surface  through  which 
a  fairly  uniform  sheet  of  microbubbles  was  injected  normal  to  the 
streamwise  flow.  There  were  no  quantitative  measurements  of  bubble 
concentration  profiles.  Visual  observation  served,  to  check  on.  the 
uniformity  of  the  microbubble  sheet. 

The  polymer  injection  procedure  consisted  ,  of  mixing  18.8  grams 
of  PEO  Water  Soluble  Resin  (WSR-301)  powder  info  18.9  liters  of 


336 


fresh,  tap  water  and  allowing  the  1000  wppm  solution  hydrate  several 
hours.  Once  the  0.1%  PEO  concentrated,  solution  was  sufficiently 
hydrated,  a  flexible  neoprene  tube  running  through  a  peristaltic 
Masterflex  L/S  pump  head  was  used,  to  pump  the  polymer  solution, 
through  the  plenum  and  into  the  flat  plate  boundary  layer.  The 
Masterflex  pump  system  included,  a  calibrated  flow  rate  readout 
correlated. to  theRPM  of  the  three  rollers  in  the  pump  head .  providing 
600ml/min±3ml/min  at  ambient  pressure.  In-situ  calibrations  of  the 
polymer  pumping  system  were  performed,  (with  the  help  of  graduated 
cylinders)  which,  provided  ,  a  correction,  for  test  section,  static  pressure 
conditions.  These  calibrations  demonstrated,  the  polymer  flow  rate 
measurements  were  accurate  to  within.±5%.  The  polymer  injection 
flowrate  coefficient  is  defined  as, 

n  -  f  concentration)  x  (  polymer  solution  flow  rate)  /n 

CQpoly  1  ' 

(baseline  boundary  layer  flow  rate) 

n 

and. values  ranged. from  CQp0jy  =  2  to  20  (xlO" '). 

The  computer  controlled  air  injection  system  used,  a  100  psi 
proportional  in-line  regulator  designed  to  maintain,  a  target  pressure 
within ±  2  psi.  A  simple  floating  ball  flow  meter  calibrated  ,  to  a  range 
of  100  ±  20  standard  cubic  feet  of  air  per  hour  (SCFH)  was  positioned, 
just  outside  the  test  section.  Air  flow  and. temperature  (via  a  J-thermo- 
couple)  were  measured  . and. recorded  at  the  entry  point  of  the  air  flow 
meter  to  provide  the  necessary  gas  volumetric  flow  rate  correction.  A 
ball  valve  at  the  test  section  air  inlet  point  was  used,  to  activate  and. 
shut-off  the  air  injection  sequence.  The  gas  injection  flow  rate 
coefficient  is  defined. as, 

r  =  _ (gas  yolume  flow  ratfe] _  (2) 

CQgas 

{  gas  vol  flow  rate  )  +  (boundary  vol  layer  flow  rate) 
and  values  ranged. from  CQgag  =  75  to  300  (xlO-3). 

The  test  variables  and  all  the  tunnel  operational  parameters  were 
continuously  monitored,  and.  recorded,  by  Lab  View  data  acquisition. 
Software.  The  sampling  rate  for  the  tunnel  operating  parameters  was 
set  at  40  Hz  and  .  included  ,  the  bulk  velocity,  motor  RPM,  tunnel  static 
and  bypass  system  tank :  pressures,  bulk .  temperature,  and.  auxiliary 
system  parameters.  Data  acquisition  is  performed,  via  a  National 
Instruments  SCX3-1000  signal  conditioning  system  and  an.  AT.-MIO- 
16X  high-performance  multifunction  analog,  digital  and  timing  I/O 
board  inn  166  MHz  Pentium  Computer.  All  the  strain,  gauge  data  was 
low  pass  filtered. at  100  Hz,  and  the  sampling  rate  for  all  cases  was  1 
kHz.  Drag  balances  1  and  .  2  provided  consistent  data  for  most  of  the 
runs.  Balance  3  failed,  early  on. in  the  experimental  program  and.no 
results  from  it  will  be  shown. 

The  general  procedure  for  the  synergy  runs  consisted  of 
establishing  the  desired. test  section. velocity  (  4.27  or  6.10  m/sec)  and 
static  pressure  (  5  to  8  psig)  conditions  for  the  run,  and  then,  initiating 
injection,  sequences  while  recording  time  histories  for  all  the  test 
variables.  A  typical  run.  would,  include:  (1)  initiating  the  data 
acquisition  system  to  provide  a  time-history  of  the  event;  (2)  beginning 
a  velocity  3-step  increase  up  to  test  velocity  giving  drag  data  at 
different  velocities  for  in-situ  balance  verification;  (3)  after  reaching 
steady  state  at  the  desired,  test  velocity,  a  baseline  microbubble-only 
drag  reduction. injection. sequence;  (4)  after  a  few  minutes  to  purge  gas 
from  the  tunnel,  a  polymer-only  injection  ,  sequence  was  begun,  during 
which,_  after  several  seconds  of  polymer  injection,  the  same 
microbubble  flow  rate  previously  used,  was  also  injected;  (5)  the 
polymer  and  .microbubble  injection  was  secured;  (6)  after  purging  the 
tunnel  of  air,  the  previous  step  was  repeated,  at  different  polymer 
injection. rates;  (7)  upon  completing  several  dual  injection  sequences, 
the  flow  was  reduced',  to  zero  velocity  in.  steps  to  recalibrate  the 
balance  drag  vs.  velocity  response.  An. example  of  the  time  history  of 
a  data  runis  shown  in  figure  5.  Post  processing  of  the  data  consisted. of 
removing  observed  linear  trends  (strain. gages  were  not  temperature  or 
pressure  compensated).  Relative  drag  reduction  results  were  obtained  . 


by  normalizing  drag  measurements  by  the  drag  with  no  injection. 


Fig-  5.  Time  history  for  drag  reduction  measurements  at  6.1 
m/sec,  upstream  microbubbles,  downstream  polymer  (PEO).  A  - 
baseline  condition;  B  -  microbubble  ejection. Cq=0. 09 8,  %Cp87.9%;  C 
-  polymer  ejection.  Cq=2.7E-07,  %C,-93.3%;  D  -  polymer  + 
microbubbles  %Ci-75.2%  microbubble  Cq  same  as  B  Polymer  Cq  same 
as  C;  E  -  polymer  ejection.  Cq=5.4E-07,  %Cr85.5%;  F  -  polymer  + 
microbubbles  %Cr=64.0%  microbubble  Cq  same  as  B  Polymer  Cq  same 
as  E;  G  -  polymer  ejection.  Cq=6.7E-07,  %Cr=82.9%;  H  -  polymer  + 
microbubbles  %Cr=61.7%  microbubble  Cq  same  as  B  Polymer  Cq  same 
as  G;  I  -  polymer  ejection  Cq=1.0E-0 6,  %Cr=93.3%;  J  -  polymer  + 
microbubbles  %Cp=57.8%  microbubble  Cq  same  as  B  Polymer  Cq  same 
as  I. 


The  baseline  boundary  layer  parameters  at  the  gas  and  polymer 
injection,  location  were  determined  from  measurements  of  velocity 
profiles  by  a  one-component  laser  Doppler  velocimeter.  The  profile 
data  were  then,  integrated,  and.  curve-fitted,  to  the  Law-of-the-Wall  to 
deduce  the  friction  velocity  at  the  surface.  Profile  sweeps  were  made 
as  close  as  possible  to  the  trailing  edge  of  each,  floating  element  and  .  at 
several  downstream  locations.  Several  profiles  and  their  corresponding 
arclength  positions  are  shown. in. Fig  6  for  the  4.27  m/sec  (14  ft/sec) 
case.  The  profiles  are  normalized  by  the  displacement  thickness  and 
free  stream  velocity:  The  fully  developed,  nature  of  the  turbulent 
boundary  layer,  corresponding  to  arclength  Reynolds  numbers  of 
between  3  and.  4  million,  is  evidenced  ,  by  the  collapsing  profile  data. 
Hot  film  data  from  probe  position.l  (0.4  m  from  leading  edge  of  plate) 
indicated  turbulent  flow  at  4.27  m/sec. 


o 

n 

T3 

I 

o> 

£ 


O 


10 

9 

8 

7 

6 

5 

4 


I  I 

Arclength  Profile 
Positions 

_  4  x-  74.44  cm  _ 

■  x=  74.44  cm 
A  x=  83.34  cm 
*x=  92.23  cm 

-  31  x=  96.04  cm  — 

•  x=  98.56  cm 
4x=  103.7  cm 


t 


0.2  0.4  0.6  0.8  1 

Normalized  Velocity  Profile  U(y)/Ue 


1.2 


Fig. 


Normalized 


velocity 


profile. 


337 


II.  RESULTS  AND  DISCUSSION 

For  this  study,  synergistic  drag  reduction  is  defined  as  reductions 
in. drag  which,  are  greater  than  the  sum  of  the  drag  reductions  observed 
during  individual  injection. (of  either  gas  or  polymer).  The  focus  of 
this  effort  was  to  explore  the  possibility  of  generating  such,  synergistic 
drag  reduction  by  employing  these  two  additives  in.  a  combined 
injection  into  the  boundary  layer  and  of  mapping  regions  containing 
synergy. 

During  each  data  run,  typified  by  fig.  5,  the  response  of  the  drag 
balances  to  several  flow  speeds  was  examined  prior  to  the  start  of  the 
drag  reduction  portion  of  the  run.  This  provided  an .  in- situ  calibration 
check  ,  on.  all  the  strain  gauges.  Also,  each  additive  was  injected 
independently,  to  provide  a  gas-only  and. polymer-only  drag  reduction, 
response  as  a  ftmction.  of  injected  flow  rate.  The  percent  drag 
reduction,  defined  ,  as 

DR%  =  (Cfo-Cf)  x  lOO/Cfo  (3) 


Microbubble  CQ 

Fig.  8.  Plot  of  typical  microbubble  drag  reduction. 


where  is  the  baseline  or  no-injection  skin  friction  coefficient. 

Sample  independent  injection  data  are  plotted  in  .Figures  7  and  8.  Both 
additives  generated  the  expected,  increase  in  drag  reduction  with 
increased  additive  inj  ection  rate. 

The  first  series  of  combined  injection  tests  were  performed  ,  with 
the  polymer  injection  slot  located. 6. 60  cm  upstream  of  the  gas  injection 
slot  Figure  9  shows  these  results.  This  configuration  demonstrated 
only  slight  synergistic  reductions  in.  drag  at  best,  and  more  generally, 
decreased  drag  reducing  capability.  In  the  following  figures  the 
experimental  combined  level  is  plotted  versus  the  %  drag  reduction  of 
the  two  techniques  assuming  they  are  only  additive.  Plotting  in  this 
manner  clearly  shows  regions  of  synergy;  The  additive  drag  reduction 
levels  are  on. the  abscissa  and  the  measured  levels  on. the  ordinate.  The 
line  indicates  the  reductions  are  strictly  additive.  Those  values  below 
the  line  indicate  no  synergy  was  present.  Results  above  the  line 
indicate  synergy. 

25.0% 


20.0% 

c 

o 

=  15.0% 

QL 

2  10.0% 

o 

5? 

5.0% 


0.0% 

0.Q0E+00  5.00E-07  1.00E-06  1.50E-06 

Polymer  CQ 

Fig.  7.  Plot  of  typical  polymer  drag  reduction 


O  60.0% 

15 

§ 

e  40.0% 

s 

a 

ui 

s?  20.0% 


%  Additive  DR 

Fig.  9.  Plot  of  experimentally  measured  combined  ,  and.  additive  drag 
reduction. (up stream  polymer). 

The  tandem  injection  ports  were  then  switched  so  as  to  place  the 
polymer  injection  slot  10.7  cm  behind  the  microbubble  injection 
location*  No  other  changes  were  made  to  the  balance  hardware  or 
instrumentation*  Now  the  polymer  solution  is  being  injected  between  a 
sheet  of  microbubbles  and  . the  flat  plate’s  surface.  The  results  at  4.27 
m/sec  show  (figure  10)  the  existence  of  synergy  on. drag  balances  1 
and. 2.  Figure  11  presents  the  results  on  both  drag  balances  for  6.10 
m/sec.  Both  balances  clearly  show  the  presence  of  synergy.  Synergy 
was  found  for  the  many  cases  were  microbubble  injection. 

4.27  m/sec 

Upstream  Microbubbles 


0.0%  20.0%  40.0%  60.0%  80.0% 

%  Additive  DR 

Fig.  10.  Plot  of  experimentally  measured  combined  and  additive  drag 
reduction  (up stream  microbubbles). 


338 


was  upstream  and  polymer  downstream. 


6.1  m/sec 

Upstream  Microbubbles 


+  Drag  Bal  1 
□  Drag  Bal  2 
- Additive  Line 


Fig.  11.  Plot  of  experimentally  measured  combined  and  additive  drag 
reduction.(upstream  microbubbles). 


Figures  10  and  11  show  the  existence  of  synergy  however  they  do  not 
indicate  the  relative  levels  of  drag  reduction,  between  polymer  and. 
microbubble  drag  reduction  to  achieve  this  result.  The  following  figure 
attempts  to  show  the  individual  magnitude  of  drag  reduction,  (either 
polymer  or  microbubble)  required.  for  synergy. 


4.27  m/sec 


•  Microbubbles  DB  1 
□  Microbubbles  DB  2 


Fig.  12.  Effect  of  %  microbubble  drag  reduction  level  upon.%  synergy 

Figure  12  is  a  plot  of  the  individual  independent  microbubble  drag 
reduction,  level  for  both  drag  balances  versus  the  percent  synergy 
achieved  . when  combined  with  polymer.  From  this  figure  it  is  clear  that 
microbubble  gas  ejection  levels  exceeding  30%  drag  reduction  do  not 
produce  synergy,  in.  this  configuration,  at  this  tunnel  speed.  At  higher 
speed  the  trend  is  the  same  but  higher  gas  flow  rates  are  required  ,  to 
definitize  the  result.  The  effect  with  polymer  shows  a  trend,  toward, 
lower  synergy  with  increasing  drag  reduction^  however  this  trend  is  not 
as  pronounced  as  in.  the  microbubble  case.  Figure  13  shows  the 
relationship  between  microbubble  and  polymer  injection  .  Cq  versus  the 
amount  of  synergy  achieved.  This  case  is  for  drag  balance  1  at  6.10 
m/sec  with  upstream  microbubble,  downstream  polymer  injection. 
Note  the  best  levels  of  synergy  are  achieved,  for  low  microbubble 
injectionfor  nearly  all  polymer  injection  .rates. 


Fig.  13.  Contour  Plot  of  synergy  vs  microbubble  and  polymer  Cq. 

IV.  DISCUSSION 

Synergy  was  found. for  the  combined. injection  of  polymers  and. 
microbubbles.  When  . the  order  of  injection  was  microbubbles  upstream 
and.  polymer  downstream  there  were  clear  cases  of  synergy:  The 
reverse  order  did',  not  demonstrate  synergy.  The  observed,  synergy 
implies  that  the  effectiveness  of  individual  additives  is  enhanced  -  when, 
used  in  .combination.  Turbulent  mixing  at  very  small  scales  is  assumed  , 
to  be  locally  isotropic,  making  the  order  of  microbubble  and  polymer 
mixing  irrelevant  to  their  near  wall  effect  on.  the  flow.  The  lack,  of 
synergistic  reductions  when  polymer  is  introduced,  upstream  of  a 
microbubble  injection  slot  implies  that  intrinsic  interaction,  or  near  wall 
mixing  of  the  two  additives  does  not  have  a  strong  influence  on.  the 
resulting  TBL.  In  this  configuration  (polymer  upstream  ,  microbubbles 
downstream)  the  polymer  layer  introduced  into  the  boundary  layer 
appears  to  experience  more  mixing  as  it  encounters  the  microbubble 
ejector.  As  microbubble  injection,  increases,  more  mixing  occurs, 
reducing  the  overall  level  of  polymer  drag  reduction  as  the  polymer 
diffuses  more  rapidly  out  of  the  buffer  layer  where  it  is  effective.  The 
observed,  synergistic  reductions  obtained  with  microbubble  injection 
upstream  of  a  polymer  slot  demonstrate  that  when  a  bubble  sheet  rides 
over  a  confined,  polymer  solution,  larger  reductions  are  possible. 
Since  intrinsic  interactions  are  not  important,  preferential  enhancement 
of  one  of  the  additives’  drag  reducing  mechanisms  must  be  taking 
place.  Knowing  that  both  additives  work  best  when  present  in.  the  near 
wall  region,  we  suggested  ,  that  the  microbubble  sheet  is  inhibiting 
polymer  transport  or  diffusion  away  from  the  wall  thereby  locally 
increasing  the  relative  polymer  concentration.at  the  buffer  layer. 

Testing  aerated  polymer  injection  from  the  same  slot  would, 
solidify  this  hypothesis.  If  our  hypothesis  is  accurate,  then,  no 
significant  synergistic  reductions  will  be  observed,  since  the  aerated 
polymer  mixture  will  not  effectively  prevent  polymer  diffusion.  If 
synergistic  reductions  are  observed,  then,  alternate  hypotheses  of 
polymers  enhancing  the  surfactant  chemistry  of  microbubbles  should, 
be  considered. 

One  feature  of  this  test  it  is  important  to  bear  in  .mind.  All  testing 
was  performed  in  salt  water.  From  the  results  of  Kuklinski  the  bubble 
size  does  not  change  with  the  addition  of  the  polymer  solution.  Similar 
experiments  conducted  in  fresh  water  may  show  differences  in.bubble 
size  with,  the  addition  of  polymer.  This  could  ,  change  the  character  of 
synergy. 

V.  ACKNOWLEDGMENTS 

R.  Philips  would  like  to  acknowledge  many  useful  discussions  on. 
experimental  procedures  with  Dr.  C.  Henoch.  Drs.  P.  Bandyopadhyay 
and  P.  Hendricks  provided,  helpful  critique  of  the  this  work.  Dr.  R 
Kuklinski  supplied  the  microbubble  sizing  information,  for  polymer 
solutions  in  salt  water.  This  work  was  supported  under  in-house  Bid 
and  Proposal  funding. 

VI.  REFERENCES 

1.  J.  L.  Lumley,  1977:  "‘Drag  reduction,  in  two-phase  and.  polymer 
flows”,  Physics  of  Fluids,  20,(10):S65-S71,  Part  II . 


339 


2.  S.  Deutsch  and  J.  Castano  1986:  Microbubble  skin  friction. reduction, 
on  an  axi  symmetric  body.  Physics  of  Fluids,  29,  3590-3597. 

3.  A.  Fontaine  and  S.  Deutsch  1992:  The  influence  of  the  type  of  gas 
on  the  reduction  of  skin  friction,  drag  by  microbubble  injection. 
Experiments  in  Fluids ,  13,  128-136. 

4.  Hoyt  1991,  in  Viscous  Drag  Reduction,  edited  by  D.  M.  Bushnell, 
Progress  in  Astronautics  and  Aeronautics,  vol.  23,  413-432 

5.  N.  Madavan,  S.  Deutsch,  and  C.  Merkle  1985:  Measurements  of 
local  skin  .friction  in  a  microbubble  modified .  turbulent  boundary  layer. 
J.  Fluid  Meek,  156,  237-256. 

6.  S.  Pal,  S.  Deutsch,  and  C.  Merkle  1989:  A  comparison  of  shear 
stress  fluctuation  statistics  between  microbubble  modified  and. polymer 
modified  turbulent  boundary  layers.  Physics  of  Fluids  A1 ,  1360-1362. 

7.  J.  E  Koskie  and  W.G.  Tiederman  1991,  “Polymer  Drag  Reduction  of 
a  Zero  Pressure  Gradient  Boundary  Layer,1 ”  Purdue  University  Report 
PME-FM-91-1 

8.  M.M.  Guin,  K.  Hiroharu,  H.  Yamaguchi,  M.  Maeda  and.  M. 
Miyanaga,  in  publication:  ’'Reduction  of  skin  friction. by  microbubbles 
and  its  relation  with  near-wall  bubble  concentration  in  a  channel,”  .  J. 
of  Marine  Science  and  Technology. 

9.  D.  Walker  and  G.  Tiederman.  1989:  ’’The  concentration  field  in  a 
turbulent  channel  flow  with  polymer  injection  at  the  wall,”  . 
Experiments  in  Fluids  8,  86-94. 

10.  A.  Malyuga,  V.  Mikuta,  and  A.  Nenashev  1989:  Local  drag 
reduction,  at  flow  of  polymer  solutions  aerated  by  air  bubbles. 
Proceedings  of  the  18th  Scientific  &  Methodological  Seminar  on  Ship 
Hydrodynamics  ,  Vama  Bulgaria  Sept.  25-30  1989,  pp.  74-1  -  74-6. 
Kuklinski,  1997  Personal  Communication 

11.  W.  M.  Carey,  J.  W.  Fitzgerald,  E.  C.  Monahan  and  Q. Wang  1993: 
"Measurement  of  Sound  Produced  by  Tipping  Trough  with  Fresh,  and 
Salt  Water,”  JASA  93,  No.  6. 

12.  J.  D.  Hrubes  ,  C.  W.  Henoch,  G.  C.  Pacifico,  and.W.  G.  Fennell 

1994:  "Development  of  a  Gas/Liquid  Hydro  cyclone  Separator  for 

a  High  Energy  Aqueous  Battery,"  NUWC  Division,  Newport, 
Technical  Report  10,346. 

13.  E.  C.  Monahan,  Q.  Wang,  X.  Wang  ,  and  M.  B.  Martin,  1994:  "Air 
Entrainment  by  Breaking  Waves:  A  Laboratory  Assessment,"  FED- 
Vol.  187,  Aeration  Technology,  ASME. 

14.  R.  Kuklinski,  1997,  personal  communication- 


340 


MICROBUBBLE  FORMATION  AND  SPLITTING  IN  A 
TURBULENT  BOUNDARY  LAYER  FOR  TURBULENCE  REDUCTION 

James  C.  S.  Meng  and  James  S.  Uhlman,  Jr. 

Naval  Undersea  Warfare  Center 
Newport,  Rhode  Island  02841-1708 

Abstract  -  Bubble  formation  traditionally  has  been  addressed  by  chemical  engineers  for  bubbles  generated  in  a  stationary  liquid.  Here  the 
emphasis  is  on  obtaining  quantitative  relationships  of  bubble  formation  in  a  high-speed  turbulent  boundary  layer  (TBL)  and  on  determining 
whether  bubble  splitting  is  a  possible  mechanism  for  absorbing  turbulence  energy  and,  therefore,  turbulence  reduction.  This  study  is  conducted 
to  address  the  mechanisms  that  dominate  during  a  bubble  formation  in  a  TBL,  and  how  to  establish  quantitatively  the  relationship  among  Qporc, 
dpore  and  U0.  This  study  offers  some  insight  into  bubble  size  regimes,  bubble  size  spectrum,  bubble  splitting,  and  bubble  transport  in  a  TBL. 
Based  on  the  results,  a  concept  of  the  possible  mechanism  for  microbubble  drag  reduction  based  on  bubble  splitting  energetics  is  presented.  An 
estimation  is  made  of  the  total  amount  of  turbulent  kinetic  energy  needed  to  split  bubbles  in  a  TBL  and  is  compared  with  the  total  energy 
available  in  a  TBL.  It  is  suggested  that  bubble  splitting  is  a  plausible  basic  mechanism  for  reducing  turbulence  in  a  microbubble-laden  TBL. 


1.  BUBBLE  FORMATION  DYNAMICS 

1.1  Hydrodynamics  of  Bubble  Formation.  The  physics  governing  the 
formation  or  “breakaway”  of  a  microbubble  at  a  pore  in  a  wall  beneath  a 
moving  liquid  are  complex.  In  order  to  model  the  physics  properly,  one 
must  consider  effects  of  low  Reynolds  number  viscous  and  inertial  forces, 
wall  effects,  buoyancy,  surface  tension,  and  free-surface  phenomena, 
including  surface  chemistry,  all  varying  with  time.  To  model  such  a 
problem  analytically  would  require  an  immense  effort.  The  goals  here  are 
much  more  modest.  By  identifying  various  hydrodynamic  forces  and 
performing  approximate  force  balances,  both  parallel  and  perpendicular  to 
the  wall,  one  can  obtain  equations  that  yield  order-of-magnitude  estimates 
of  the  bubble  breakaway  size  under  various  assumptions.  Therefore,  the 
first  step  is  to  identify  and  quantify  the  various  forces,  both  tangential  and 
normal  to  the  wall.  We  will  start  with  the  tangential  forces. 

When  a  bubble  is  exuded  from  a  pore  in  a  wall  into  a  liquid  flow 
parallel  to  the  wall,  the  flow  exerts  a  drag  force  on  the  bubble.  As  a  result 
of  the  drag  force  the  bubble  shape  is  altered,  becoming  skewed.  The 
skewed  bubble  shape  introduces  a  component  of  surface  tension  force 
parallel  to  the  wall,  which  balances  the  drag  force.  The  bubble  detaches 
from  the  wall  when  some  critical  skew  angle  is  reached  or  when  either  a 
lift  force  or  the  buoyancy  overcomes  the  vertical  component  of  surface 
tension,  whichever  occurs  first. 

The  horizontal  component  of  surface  tension  force  was  obtained  by 
Al-Hayes  and  Winterton  [1,2];  they  calculated  the  horizontal  component 
of  surface  tension  force  from  the  following  equation: 

F^  =  58  -  +  0.14 1  x  —  7tRtfsin0o  x  (cos0r  -  cos0a) ,  where  a  is  the 

[0o+5  J  2 

surface  tension  between  air  and  water  and  0O  is  the  equilibrium  contact 
angle  between  the  bubble  and  the  wall,  i.e.,  sin  0O  =  r/R,  and  0rand  0a  are 
the  receding  and  advancing  contact  angles  (figure  1),  respectively,  when 
the  bubble  is  in  a  cross  flow.  Values  for  the  various  angles  involved  were 
determined  experimentally,  and  the  quantity  in  brackets  is  a  correction 
factor  that  Al-Hayes  and  Winterton  applied  to  their  equation  to  improve 
the  comparison  between  theory  and  experiment.  Following  Al-Hayes  and 
Winterton,  we  can  assume  that  the  angles  are 

0O  *  40°, 0r  *  30°,  and0a  «  50°,  then  Fst  =  -O.167iRasin0o.  (1) 

If  we  now  assume  that  the  drag  force  balancing  the  surface  tension  is  FD  = 
V2  p  CD  U02  tcR2,  substituting  CD  =  1 .22  and  0O,  0a,  and  0r  values  we  obtain 
the  following  drag-surface  tension  force  balance  equation:  p  ((U2R)/o)  = 
0.17. 

An  alternative  formulation  of  the  balance  between  the  drag  force  on  the 
bubble  and  the  horizontal  component  of  surface  tension  force  can  be 
derived  by  assuming  that  the  contact  angle  of  the  bubble  has  a  simple 
sinusoidal  dependence.  With  this  assumption  0  =  0O  +  80cos<|> ,  where  <j) 
is  the  angle  about  the  base  of  the  bubble  clockwise  from  upstream  (figure 
1).  Hence,  0a  -  0O  +  50  and  0r  =  0O  -  60.  The  horizontal  component  of  the 

surface  tension  force  is  then  Fst  -  rcrj^  cos[0o  +  60  cos<t>]  cos 4>  d<j)  =  - 
2nro  sin0o  1,(50),  where  is  the  Bessel  function  of  order  1  (Gradshteyn 


and  Ryzhik  [3]).  However,  J1(50)wl/260  for  60  «  1,  thus  we  find 
Fst  =  -7ircr  sin0o  60.  (2) 

According  to  the  data  of  Al-Hayes  and  Winterton  [1,2]  the 
quantities  |0O  -  0a  |  and  |0O  -  0r  |  appear  to  be  fairly  constant,  with  a 

value  of  approximately  10°.  Thus  80  =  0.17,  so  (1)  differs  from  (2)  by 
r/R.  If  the  drag  force  is  now  assumed  to  follow  Hadamard’s  law  because 
the  bubble  Reynolds  number  is  very  low,  then  the  drag  force  to  surface 
tension  force  balance  becomes  47rjiRU0  =  na  (r2/R)50. 


Proceeding  to  the  normal  force  balance  case,  the  normal  component  of 
surface  tension  force  can  be  calculated  similarly  to  the  tangential  case,  and 
we  have  Fsn  =  2n  r  o  sin0o  J0  (50)  =  2;ta  r2/R.  Another  normal  force  to 
consider  is  the  low  Reynolds  number  “Saffman”  lift  force  (see  Saffman  [4, 
5]).  Its  effect  is  to  lift  the  bubble  away  from  the  wall.  Strictly  speaking, 
the  Saffman  lift  result  applies  only  to  a  particle  in  an  unbounded  fluid. 
However,  it  is  applied  here  to  a  bubble  near  a  wall  for  the  purpose  of  an 
engineering  order-of-magnitude  estimate.  Voloshko  et  al.  [6]  identified 

other  normal  forces  to  be  the  added  mass  term  sm  71  pr  ,  the  gravity  or 

12R 

buoyancy  term  (4/3)  ;rR3(p  -  p')g,  and  the  gas  injection  flux  term  p'vo^r2, 
where  em  is  the  added  mass  coefficient,  p'  is  the  gas  density,  and  v0  is  the 
velocity  of  the  gas  as  it  exits  a  pore.  If  in  addition  the  Saffman  lift  term 
CL  7ipR2U0(vk)1/2  and  surface  tension  terms  are  also  included,  following 
Voloshko  et  al.  [6]  a  modified  Voloshko  equation  governing  bubble 
normal  force  balance  becomes 

+  2it  =  ijtR3(p  -  p')g  +  CLJtpR2U0(  vk)1'2  +  p' v^r2 ,  (3) 

12  R  K  j 

where  U0  is  the  flow  past  the  wall  at  the  bubble  centerline,  u  is  the 
kinematic  viscosity  of  the  liquid,  and  k  is  the  effective  shear  in  the  liquid 
at  the  bubble  centerline. 


1.2  Bubble  Size  Regimes.  In  contrast  to  the  commonly  referred  to 
bubble  geometry,  depicted  in  figure  1,  as  much  as  four  bubble  regimes  can 
be  identified  (figure  2).  To  analyze  the  bubble  size  spectrum,  which  may 
be  a  natural  consequence  of  generating  bubbles  in  a  TBL,  the  basic  bubble 
hydrodynamics  are  extended  to  include  analysis  of  bubble  geometries 
other  than  a  semisphere.  The  sheared  spherical  cap  case  was  attributed 
to  MacIntyre  [7],  while  the  other  three  cases  were  identified  by  Silberman 
[8].  These  four  regimes  can  be  delimited  by  comparison  of  the  ratio  of  the 
gas  pore-exit  velocity  with  the  liquid  velocity. 


For  the  sheared  spherical  cap  case  (figure  2(a)),  height  h  =  R  -  (R2  - 
i^pore)172.  where  R  is  the  radius  of  curvature  of  the  cap,  and  the  cap  volume 
7t/ 6  h(h2  +  3r2porc)  is  assumed  to  be  the  bubble  volume  after  it  is  sheared 
off  the  pore.  Since  the  spherical  cap  cannot  be  sheared  off  the  pore  faster 


jt  h(h2  +  3r2 


:)  ^  *pore 


than  the  fluid  flows  over  the  pore,  we  find  that  — 

6  Q  U0 

where  Q  is  the  volumetric  gas  flow  rate.  Replacing  h  in  terms  of  R  and 
rpore  and  taking  the  limit  of  small  rporc/R,  the  above  equation  becomes: 


341 


4Q 


1  + 


1  [  *porc 


R 

>  — ,  or 

Un 


— 9 —  <  _L  .  Judging  from  the 

™poreU0  4  R 


figure,  rporc/R  <  0.2,  and  replacing  Q  with  nr2^ 


,  we  obtain  vpore/U0  < 


0.05. 

In  the  single  bubble  regime,  figure  2(b),  the  bubble  formation  time  is 
longer  than  the  time  it  takes  for  the  fluid  to  flow  over  the  pore.  Since  the 
bubble  in  this  case  has  the  time  to  grow  to  a  nearly  spherical  shape,  the 
bubble  volume  is  4/3  tuR3.  The  time  scale  for  the  bubble  growth  is  then 

,  „  4  7lR3  Iporc 

4/3  7tR3/Q,  which  is  greater  than  the  flow  time,  i.e.,  — — —  >  ,  or 


3  Q 


U0 


‘pore  '-'0 


/  \3 
3  V  ^porc  / 


Replacing  Q  with  jrr2^  and  using  the  minimum 


value  for  the  right-hand  side,  we  find  that  for  the  single  bubble  regime 
Vpon/Uo  <  1  should  apply. 


In  the  jet  disintegration  regime  (figure  2(d)),  as  a  result  of  high  gas- 
injection  rate,  the  jet  formation  time  is  shorter  than  the  flow  time;  it  is  the 
instability  of  the  gas  jet  that  determines  the  final  bubble  size.  Rayleigh  [9] 
studied  this  problem  and  found  that  the  wavelength  of  the  maximum 
amplification  of  instability  is  6.48  times  the  mean  jet  diameter  J. 


6.48  J 


TtJ2 


Therefore,  the  jet  formation  time  is  - — ,  and  it  should  be  shorter 

Q 

,  3 


than  the  flow  time  rporc/U0.  In  other  words, 


*rPorcU0 


-  >  12.96; 


.96  - 


J 


Id 


pore  / 


Replacing  Q  with  ftr2^  vporc  and  using  the  maximum  value  for  the  right- 
hand  side,  we  find  vporc/U0  >  10  for  the  jet  regime. 


The  intermediate  regime  (figure  2(c))  corresponds  to  a  bent  jet,  and 
the  bubble  breakaway  mechanism  is  due  more  to  the  liquid  dynamics  than 
the  dynamics  of  the  jet  itself.  In  this  regime,  the  formation  time  analysis 
gives  vpore/U0  >  5.  We  have  thus  completed  a  description  of  different 
bubble  regimes.  Naturally,  different  hydrodynamic  mechanisms  control 
the  bubble  formation  in  different  regimes  and  different  dependencies  of 
the  bubble  size  on  vpore/U0,  and  the  surface  tension  results.  It  is  important 
to  note  that  one  single  parameter  vporc/U0  emerges  from  this  analysis  as  the 
key  parameter  demarcating  the  different  regimes.  In  figure  3  are  the 
approximate  values  of  bubble  diameter  criteria.  The  ordinate  is  the  ratio 
dbubbicAW  and  the  abscissa  is  the  “injection  coefficient,”  or  more 
precisely  the  ratio  vporc/U0  that  was  identified  to  be  the  key  parameter  in 
the  bubble  formation  time  analysis.  As  noted  in  figure  3,  two  distinct 
regions  are  identified:  the  liquid  at  rest,  which  corresponds  to  the  vporc/U0 
— >co  limit;  and  the  flowing  liquid  case. 


In  the  liquid  at  rest  case,  the  bubble  sizes  are  determined  by  two 
possible  normal  force  balances  (assuming  the  wall  to  be  normal  to  the 
gravity  force  vector).  Notice  that  in  this  case,  the  tangential  force  balance 
is  not  operative.  First,  at  low  gas-injection  rate,  the  bubble  buoyancy  is  in 
equilibrium  with  the  surface  tension  between  the  gas  bubble  and  the  wall, 


4  ( c 

—  7C  - 

3  l 


,Y 


2  ) 


P liquid  g  =  ^dporc^.  » 


r 


6cr 


VP£dp< 


Second, 


at  a  higher  gas-injection  rate,  Silberman  [8]  applied  three  assumptions  to 

.  \i/5 


obtain  the  following  relationship:  bubble  =  1.41 

dpore 


§dpore  / 


The  three 


assumptions  are:  the  unstable  wavelength  obtained  by  Rayleigh  in  a 
stationary  environment  is  valid  in  a  shearing  flow,  Bernoulli’s  equation 
can  relate  the  jet  velocity  and  jet  height  against  gravity,  and  the  diameter 
of  the  bubble  is  related  to  the  liquid  velocity  U0  the  same  way  as  the  gas 
jet  velocity.  The  last  assumption  is  probably  the  weakest. 


In  the  flowing  liquid  case,  the  physics  governing  bubble  size  can  be 
divided  into  at  least  three  regimes,  which  in  turn  can  be  further  divided 


into  smaller  groups.  At  the  high  injection  limit,  i.e.,  v^e/Uo  >  10,  the  gas 
jet  instability  perpendicular  to  water  flow  was  obtained  by  Silberman  [8]: 

/  y/2 

d  bubble  _24  — ^ —  Notice  the  dependence  of  bubble  diameter  on 

dporc  V^OdporeJ 

the  flow  rate  Q.  This  result  has  been  verified  by  Silberman  and  recently 
by  Reischman  and  Holzmann  [10].  In  practice,  this  high  injection  rate 
limit  typically  applies  to  an  ejection  using  discrete  drilled  holes.  The 
physics  in  the  intermediate  regime  is  unknown;  an  analytic  formula  for  the 
bubble  size  cannot  be  easily  obtained.  As  the  injection  coefficient 
reduces,  we  move  into  the  single  bubble  regime,  i.e.,  during  the  bubble 
formation  the  gas  cavity  appears  to  resemble  a  bubble  geometry.  In  this 
regime,  two  distinct  force  balances  exist:  normal  and  tangential.  It  is 
intuitively  convincing  that  in  a  rapidly  flowing  liquid,  if  the  gas  exit 
velocity  equals  approximately  that  of  the  liquid  tangential  velocity,  the 
mechanism  of  bubble  breakaway  should  be  determined  by  a  normal  force 
balance.  As  the  gas  exit  velocity  reduces  further,  or  as  the  liquid  velocity 
increases  while  the  gas  exit  velocity  holds  constant,  the  dominant  force 
balance  switches  to  the  tangential  mode. 


In  the  normal  force  balance  mode,  at  least  two  possibilities  exist.  At 
the  high  vpore/U0  end,  the  Saffman  lift  force  balances  the  inertial  force 
surrounding  an  expanding  bubble.  From  (3)  we  find  from  the  modified 

ir2 

I  UUl _ 

Voloshko  equation  that,  for  this  case  sn 


12R 


=  CL7rpR  U0uT, 


where  ux  is  the  local  friction  velocity  and  p  the  liquid  density. 

i1/4 

d 


Rearranging,  we  find 


J  bubble 


Vporc 

,2u^ 

12CL  1 

.  U0  y 

'  u. 

which  does 


depend  on  the  injection  coefficient  to  the  Vi  power.  For  the  lower  vporc/U0 
case,  Saffman  lift  will  balance  the  surface  tension  between  the  gas  bubble 

r2  d 

and  water  on  the  wall,  i.e.,  27t-^-a  =CL7rpR2U0  uT,  or  bubblc  = 

K  Qpore 


4a 


Un 


.  1/3 


,  U0 
where  —  = 
uT 


1/2 


and  cf  is  the  local  skin 


lpU20CLdporc  uTy 

friction  coefficient  on  the  wall.  Notice  that  this  result  does  not  depend  on 
the  injection  coefficient.  The  question  of  whether  there  are  any  other 
normal  force  balances  could  arise  can  be  addressed  by  examining  the 
modified  Voloshko  equation  (3).  Dividing  equation  (3)  by  pU20  r2^,  we 
find 

3 

A  -  X  “  ^  ~~  f  t 

12 


+  7tCL 


Iporc  I 

f  VPorc  1 

!  ^  <y  v  _  47U  gfporc 

irJ 

l  U0  J 

*  Uo(i  RU0  3  Uj 

(  „  X 

2  /  \  1/2 

■  /  „  \2 

P  1  Vpore  I 

V  *porc  ) 

l  2  J 

P  l  uo  J  ' 

Substituting  sm=  32,  -?-= 7 ,  -^-=10+  cr  S3 x  lO'5 =  10+ 
U0p  U0K  UQ 

nCL  =  6.46,  —  SI  O'3,  for  U0  =  10  m/sec,  rporc  =  10pm,  we  can  write 
P 

the  above  equation  as  follows: 


+0.4  =  10-6f— 

■  ^0  J  V  rpore  y 


+  0.25 


x2 


+  10" 


V  ‘pore  J 


From  this  we  see  that  we  can  neglect  the  buoyancy  term  (first  term  on  the 
right-hand  side)  compared  with  the  Saffman’s  lift  term  (second  term  on 
the  right-hand  side).  The  balance  type  of  force  depends  on  the  magnitude 
of  only  two  parameters:  RA^  and  v^e/llo.  For  vpore/U0  =  1,  the  first  term 
on  the  left-hand  side  (i.e.,  the  water  inertia  surrounding  an  expanding 
bubble)  balances  the  Saffman  lift  and  gives  a  result  of  R/rporc  =  2.4.  For 
vpore/Uo  «  0.1,  again  the  Saffman  lift  force  dominates  the  right-hand  side 
of  the  equation,  while  the  dominant  term  on  the  left-hand  side  shifts  to 
the  surface  tension  term  (the  second  term)  and  gives  a  lower  result  of 


342 


R/i-pore  =  1.2.  No  other  physically  meaningful  possibility  seems  to  exist; 
thus  concludes  the  discussion  of  the  normal  force  balance. 

For  the  tangential  force  balance  case,  only  one  possible  combination 
exists:  the  water  drag  on  a  gas  bubble,  or  on  a  gaseous  cap,  balances  the 
surface  tension  between  the  gas  bubble  and  the  wall.  As  indicated  in 
figure  2,  two  bubble  breakaway  geometries  are  possible:  a  nearly 
spherical  bubble  case,  and  a  nearly  spherical  cap  case.  In  reality,  neither 
occurs.  In  fact,  unstable  waves  on  the  bubble  surface  should  be  present  as 
a  result  of  both  the  unsteady  forcing  of  the  turbulent  flow  over  them  and 
the  liquid  local  pressure  gradient  generated  by  the  growing  bubble. 
Whether  the  bubbles  will  break  away  as  a  result  of  this  unstable  wave 
growth  is  unknown.  A  water  tunnel  experiment  on  a  single  bubble 
formation,  visualized  at  close  range,  is  a  plausible  approach  to  address  this 
issue. 


For  the  spherical  bubble  case,  we  have  7tR2  xw  =  7ca~^*50,  where 


R 

60  =  0.17,  as  given  before,  and  xw  is  the  local  wall  shear  stress.  From  this 

V'3 

(4) 


we  fmd  Rubble.  = 

dnnrP 


2a80 


Uv^pore  J 


Alternatively,  we  can  replace  xw  with  (1  /  2)pUqCd,  where  CD  is  the  drag 
coefficient  over  the  bubble.  But  this  also  opens  questions  about  the 
validity  of  using  U0  as  the  relative  liquid  velocity  over  the  bubble,  and 
also  that  CD  is  not  known  until  the  bubble  Reynolds  number  is  known, 
which  requires  a  priori  knowledge  of  the  bubble  size.  As  the  injection 
coefficient  reduces,  we  move  into  the  spherical  cap  regime.  For  the 
tangential  force  balance,  the  tangential  surface  tension  force  is  described 
by  equation  (2).  The  shear  force  is  27iRhxw,  where 


h  =  R 


f 

(  ( r  Vi 

1/2  \ 

1- 

1_  Vl 

l  R  J 

V 

v  J 

or  h  =  Zi  rpore  rporc/R,  where  small  rporc/R  is 


applied.  Equating  them,  we  find  R  -  <rS0/xw.  Substituting  the  values  of  a, 
80,  and  iw  =  pu2T  at  10  m/sec,  we  fmd  R  =  74  pm,  which  is  7  times  greater 
than  the  pore  size  (10  pm),  consistent  with  our  assumption  that  rporc/R  <  1. 
The  bubble  diameter  after  breakaway,  dbubblc,  is  related  to  the  cap  height  h 
by  d3bubb)e  =  h3  +  Si^pore  h.  Substituting  h  and  carrying  out  simplifications, 


we  have  dJubWc 


/ 

'  _  \3>| 

3.522. +  | 

*pore 

2R  1 

,2Rj  , 

or  dbubbic  - 


(  A  \ 1/3 

r_ore »  ^"ubblc  =  —  —  Tw  pore  ,  an  interesting  result 

pore’  dpore  2U  a80  J  ’ 

because  the  shear  stress  dependence  is  the  reverse  of  that  for  the  single 
bubble  regime  case.  In  the  spherical  cap  regime,  bubbles  are  smaller  than 
the  pore  size  and  increase  in  size  with  iw;  while  in  the  single  bubble 
regime,  bubbles  are  greater  than  the  pore  size  and  decrease  with  local  xw. 

1.3  Estimation  of  Pore  Characteristics  of  a  Porous  Surface.  Porous 
shells  and  flat  plates  have  been  used  extensively  for  microbubble  drag 
reduction.  These  surfaces  typically  are  formed  by  pressing  and  sintering 
powdered  metal  particles.  The  void  space  among  the  powders  provide  the 
required  porosity.  Estimation  of  the  pore  characteristics  is  essential  for 
predicting  and  controlling  the  bubble  size.  In  this  subsection,  we  derive 
the  required  relationship  among  the  pore  size,  number  of  pores  per  unit 
area,  and  percentage  of  surface  porosity.  Porous  titanium  shells  and  plates 
traditionally  are  used  in  the  industry  for  filtration  purposes.  The  pore  size 
typically  is  specified  in  terms  the  size  of  the  smallest  particles  filtered  out, 
instead  of  the  pore  size  per  se.  In  liquid  flows,  titanium  filters  made  by 
Gould  will  normally  retain  particles  approximately  one-third  of  the  mean 
pore  size.  No  generalization  to  gas  flows  was  made,  but  the  retention  size 
is  known  to  be  much  finer. 


The  distribution  of  pore  size  is  not  available,  but  given  the  fact  that 
particles  three  times  smaller  than  the  mean  pore  size  are  filtered  out,  there 
must  be  a  sharp  drop-off  in  the  large  pore  size  end  of  the  spectrum.  The 
standard  deviation  in  pore  size  cxpore  must  be  smaller  than  the  mean  pore 


size  dpore  .  Therefore,  for  engineering  purposes  we  can  assume  that  apore  = 


Vi  d^  that  the  pores  follow  a  Gaussian  distribution,  i.e.,  p(dp0re)  = 


l[  dporc  “dporc 

i2 

1  p  °porc 

.  This  distribution  can  be  used  to  make 

v/2*ap0TC 

engineering  estimates  of  pore  size  and  bubble  sizes. 

Size  Range 

Smallest  Particle 

Grades 

Mean  Pore  Size 

Filtered  Out  in 

(Microns) 

Liquid  (Microns) 

Ti-2003 

3 

1 

Ti-2505 

5 

2 

Ti-4010 

10 

3 

Ti-5015 

15 

5 

Ti-6525 

25 

8 

Table  I.  Gould  Titanium  Standard  Filtration  Grades 


To  calculate  the  gas  flow  rate  through  individual  pores,  it  is 
necessary  to  know  the  surface  porosity,  i.e.,  the  percentage  of  area 
occupied  by  pores.  Typically,  a  “density”  is  given  that  indicates  the  ratio 
of  the  weight  of  the  porous  material  to  that  of  the  solid  material  of  the 
same  nominal  volume.  Let  us  denote  this  density  by  then  it  is  seen  that 

£  =  P??lid  %°!ifi  =  |  .-.gftU  ,  where  40lid  and  L  are  lengths  characterizing 
P  total  Ytotal  V  L  / 

the  solid  part  and  the  entire  porous  material,  respectively.  If 

^1*  +  *3vold  =  L3,  where  t  void  is  a  length  characterizing  the  void  portion 


of  the  porous  material,  then  ™id  =  (l  -  4)13,  so  the  surface  porosity  r| 

can  be  estimated  to  be  r\  =  “-j  =  (l  -  ^)2  3  •  Given  a  45-percent 

density  we  find  the  surface  porosity  to  be  67  percent. 


It  is  useful  to  relate  the  mean  powder  size  dp0wdcr  to  the  mean  pore  size 
dp0re.  This  is  possible  if  we  assume  that  there  are  as  many  pores  as  there 

1 


are  powder  particles.  Then  we  can  say 


Npowdcr”^ 


powder 


-  =  5.  or 


Npore  ^  ftdporc 


=  1  -  so  that 


upowder 


i-5. 


=  0.93  for  4  =  0.45. 


v  total  ^pore 

Once  dporc  and  *1  are  found,  the  number  of  pores  per  unit  surface  area, 

Npore  (1-4)2'3 


Nporc/S,  can  be  calculated  to  be 


-di 


For  dpore  =  10  pm  and 


£  =  45  percent,  we  have  porc  =  0.85  x  106  pores  /  cm2 . 

2.  BUBBLE  SIZE  DISTRIBUTION  IN  A  TBL 


From  analysis  of  the  bubble  size  spectrum  it  is  clear  that,  given  a 
flow  speed  U0 ,  by  keeping  one  of  the  two  parameters  Q  and  rpore  constant 
but  varying  the  other  one,  bubbles  of  different  sizes  will  be  generated  as  a 
result  of  different  physics  mechanisms  being  activated.  For  the  commonly 
used  porous  ejectors  made  of  pressed  and  sintered  metal  powders,  the  pore 
sizes  are  not  uniform,  and  the  gas  ejector  pore  size  spectrum  will  lead  to  a 
spectrum  of  bubble  sizes.  Furthermore,  in  a  TBL  environment,  even  if 
both  Q  and  rpore  are  held  constant,  the  wall  shear  stress  fluctuates.  The 
absolute  magnitude  of  the  fluctuating  shear  stress  is  greater  than  twice  the 
mean  shear  stress,  i.e.,  x^  *  2xw.  Since  the  local  instantaneous  xw 
determines  nearly  all  modes  of  balance,  bubbles  generated  in  a  TBL 
should  have  a  bubble  size  spectrum  with  a  bandwidth  equal  to  at  least  two 
times  the  mean  bubble  size.  In  this  subsection  we  discuss  the  shear  stress 
fluctuations,  analyze  a  bubble  size  spectrum  obtained  in  the  ocean, 
identify  possible  physics  affecting  bubble  formation  in  sea  water  versus 


343 


the  physics  in  fresh  water,  and  identify  the  possible  bubble  splitting  and 
coalescence  effects  on  a  bubble  size  spectrum. 

2.1  Shear  Stress  Fluctuation  in  a  TBL.  The  xw  in  a  TBL  in  terms  of  the 
probability  density  function  (PDF)  and  the  ratio  (Burton  [11])  of  the 

variance  g(tw)  to  the  mean,  xw , =  0.3 1 ,  were  given  by  Sandborn 

[12],  who  found  that  the  ratio  ranges  from  0.2  to  0.4.  Kreplin  and 
Ecklemann  [13]  determined  the  skewness  S(xw)  and  the  flatness  F(xxv)  on 
the  wall.  Several  sets  of  PDFs  of  xw  do  exist  but  were  measured  at  a  small 
distance  away  from  the  wall,  i.e.,  y+=  1  to  5.  Brodkey,  Wallace,  and 
Ecklemann  [14]  determined  individually  the  PDFs  of  u  as  a  result  of 
ejection,  sweep,  and  inward  and  outward  interactions,  and  they 
superposed  them  to  obtain  the  total  PDF(u),  at  y+  —  3.4.  Since  within  y+  = 
5  the  P(u)  =  P(xw),  we  can  regard  this  resultant  P(u)  to  be  representative  of 
P(xw).  Bhatia,  Durst,  and  Jovanovic  [15]  obtained  P(xw)  at  y+  -  3.7  to  6, 
while  Kreplin  and  Ecklemann  [13]  obtained  it  at  y+  =  1.6  to  100.  Figure  4 
shows  Sandborn ’s  PDF  (xw.)  data  versus  the  normalized  xw  /  xw  .  Inspired 
by  the  lognormal  distribution  suggested  by  Nakagawa  and  Nezu  [16]  for 
the  streak  spacing  and  also  by  the  fact  that  X+  and  xw.  are  both  positive 
variables,  we  have  attempted  to  fit  the  P(x„.)  data  by  a  lognormal 

/ 

distribution,  i.e.,  P(xw)  =  . — - exp 

V  2tioxw  l 

£nx„  and  a2  =(£nxw  -p)2.  Several  possibilities  exist;  the  most  obvious 
is  to  first  obtain  p  and  a2  from  the  raw  data.  As  shown  in  figure  4,  the 
curve  fit  to  the  data  mean  and  variance  is  poor.  As  a  comparison,  the  least 
square  fit  is  also  shown.  Sandborn  indicated  that  the  high  shear  end  of 
data  was  not  trustworthy;  therefore,  we  reduced  the  value  of  the  highest 
five  data  points  and  refitted  by  the  lognormal  distribution  and  the  least 
square,  both  of  which  are  also  shown  in  figure  4.  Due  to  the  reduction  of 
xvv,  using  the  normalized  abscissa  variable,  the  curves  are  shifted  to  the 
right;  but  as  we  can  see,  a  much  smaller  difference  exists  in  the  later 
approach  between  the  lognormal  and  the  least  square  fits.  In  fact,  xw  and  a 
variance  of  xw,  V(xw)  can  be  calculated  from  p,  a2  by 

("4)  2  2 

xw=ev  ,  V(xw)  =  e2(1[e2°  -ea  ].  From  the  values  given  in  figure  4 

we  fmd  (V(1"  » —  -  e  2  |^e2<l2  -  e0^  =  0.24,  from  the  raw  data  fit  and, 

similarly,  0.24  from  the  modified  Sandborn  data  set;  both  are  close  to  the 
value  accepted  in  the  turbulence  community.  Given  the  equation  that 
determines  the  bubble  breakaway  diameter  from  dp0rc  and  xw,  the 
knowledge  of  the  PDFs  for  the  pore  size  and  the  wall  shear  stress  will 
enable  the  determination  of  a  PDF  for  the  bubble  diameter. 

2.2  Gallagher’s  Bubble  Size  Distribution.  Gallagher  [17]  obtained  a 
microbubble  size  distribution  in  sea  water  at  typical  ship  speeds.  He  used 
an  underwater  camera  and  the  Bete-Fog  bubble  analyzer  to  obtain  bubble 
size  spectrum.  He  presented  one  bubble  size  distribution  for  a  ship  speed 
of  12  knots,  using  pores  of  3/64-inch  diameter  through  a  vertical  steel  pipe 
of  2  7/8-inch  outside  diameter  and  pumping  air  at  the  rate  of  0.027 
liter/sec/pore.  The  underwater  camera  was  located  2  feet  downstream  of 
the  vertical  pipe.  Figure  5  shows  Gallagher’s  data  in  terms  of  the  number 
of  bubbles  (dashed  line)  and  the  percentage  of  occurrence  (heavy  solid 
line)  versus  the  bubble  diameter  in  microns.  On  the  same  figure,  a 
normalized  Rayleigh  spectrum  is  also  shown  in  a  thin  dotted  solid  line. 

As  shown,  the  Rayleigh  spectrum  seems  to  fit  the  bubble  size  spectrum 
and  is  represented  by  a  simple  parameter  of  the  bubble  diameter  at  the 
maximum  percentage  occurrence  at  221  pm.  Also  illustrated  are  the 
bubble  sizes,  predicted  using  the  different  force  balances  described  in  the 
previous  subsection:  lift  =  surface  tension,  and  drag  =  surface  tension  for 
the  bubble  regime  and  jet  instability.  Assuming  xw  =  '/a  pU02CD  and  using 
CD  =  0.2  at  Red  =  4  x  105from  Schlichting  [18],  we  find  dbubble  =  206  pm 
from  drag  (tangential)  balance  and  dbubbIe/dporc  =  0.17,  while  dbubblc  =  317 
pm  from  the  lift  (normal)  balance  and  dbubble/dp0rc  =  0.26.  The  former 
balance  gives  a  result  that  is  fairly  consistent  with  the  observed  maximum 
percent  occurrence  value  (dmax)  at  221  pm.  The  bubble  size  indicated  by 


(lnxw  -  p) 
2o2 


,  where  p  : 


the  splitting  will  be  addressed  in  the  following  subsection;  suffice  it  to  say 
that  it  seems  to  occur  where  the  bubble  size  spectrum  data  deviate  the 
most  from  the  Rayleigh  spectrum.  The  bubble  size  due  to  jet  instability 
was  5000  pm  and  does  not  seem  to  be  relevant  here. 


An  attempt  to  fit  Gallagher’s  data  by  the  lognormal  distributions  was 
also  carried  out.  A  comparison  of  the  best  fits  of  the  Rayleigh  and 
lognormal  distributions,  shown  in  figure  6,  was  motivated  by  the 
following  consideration.  Given  that  P(xw)  follows  a  lognormal 
distribution  A(p,a2),  and  (from  the  force  balances)  that  P(dbubble)  = 


,  then  according  to  the  lognormal  distribution  (Aitchison  and 


Brown  [19],  p.  11)  P(dbubblc)  should  follow  a  lognormal  distribution  of 

A I  -  — ,  — I .  As  shown  in  figure  6,  the  lognormal  distribution  seems  to 
l  3p  9) 


fit  the  data  better  (except  for  the  secondary  peak  at  a  small  bubble 
diameter,  which  could  be  a  result  of  the  bubble  splitting  phenomenon).  By 
combining  the  force  balance  equations  with  the  PDF  of  fluctuating  shear 


stress  results,  and  assuming  that  P(dbubble)  =  P 


<ese 


vl/3A 


from  drag 


balance  and  P(dbubblc)  = 


if 


4°  C 

pUfc, 


Uof] 


from  lift  balance,  we  can 


construct  simulated  bubble  size  distributions.  These  results  are  shown  in 
figure  7  (the  solid  histograms  are  for  the  drag  balance  case,  and  the  blank 
histograms  are  for  the  lift  balance  case).  Initially,  CD  was  assumed  to  be 
0.2,  and  the  PDFs  were  generated.  As  shown  in  the  figure,  the  peak 
values  are  consistent  with  the  observed  dmax  value,  but  the  size  bandwidths 
are  one  order  of  magnitude  smaller  than  the  data  indicated.  Then,  since 
we  did  not  know  the  exact  geometry  of  the  pores  relative  to  the  pressure 
minimum  point  of  flow  over  a  long  cylinder,  we  reduced  the  CD  by  a 
factor  of  20.  The  resulting  pairs  of  bubble  size  spectrum  are  also  shown  in 
figure  7.  The  lift  balance  gives  significantly  greater  spread  in  the  bubble 
size,  but  the  peak  value  moved  out  of  the  observed  bubble  size  range.  The 
drag  balance  case  increases  the  bubble  size  of  maximum  population  by  a 
factor  of  2,  but  the  bandwidth  increased  very  little.  This  analysis  and 
comparison  of  data  clearly  indicated  that  some  physics  are  lacking  in  the 
modeling  presented  so  far.  Two  more  physical  phenomena  have  been 
identified:  the  sea  water  physics  and  bubble  splitting  in  a  TBL;  they  are 
discussed  below. 


2.3  Smaller  Microbubbles  in  Sea  Water.  As  early  as  1954,  Fox  and 
Herzfeld  [20]  found  that  minute  bubbles  are  stabilized  by  encapsulation  in 
an  organic  film.  Riley  [21]  found  a  coincidence  between,  stable 
microbubble  formation  and  the  seasonal  occurrence  of  natural  organic 
particles.  Blanchard  [22]  found  that  bubble  coalescence  is  much  more 
rapid  in  tap  water  than  in  sea  water,  and  Monahan  [23]  found  much 
smaller  bubbles  produced  in  sea  water  than  in  tap  water.  Scott  [24] 
conducted  a  rigorous  experiment  designed  to  determine  the  effects  of  salt 
versus  organic  materials.  He  purified  the  tap  water  by  distillation  from 
potassium  permanganate  solution  and  by  filtration  through  activated 
carbon.  He  heated  commercial  grade  salt  at  red  heat  sufficient  for  fusion, 
driving  off  any  organic  material,  and  then  blew  nitrogen  through  a  3-cm- 
diameter  porous  glass  membrane  (with  pore  sizes  in  the  5-pm  to  15-pm 
range).  He  found  that  a  rapid  decrease  in  the  bubble  size  resulted  from 
the  addition  of  the  pure  salt  to  the  purified  water.  He  also  found  the 
bubble  distribution  in  the  purified  salt  water  (35g/liter  concentration)  to  be 
visually  identical  to  that  formed  in  real  sea  water. 


Johnson  and  Cooke  [25]  set  out  to  prove  the  existence  of  and  to 
visualize  the  surface  organic  film  on  bubbles  formed  in  sea  water.  They 
formed  bubbles  in  air-saturated  sea  water  by  the  shear  produced  at  the 
surface  of  a  sintered  glass  frit  through  which  air  was  blown.  After  the 
bubble  dissolution,  a  small  transparent  particle  remained,  about  5  pm  in 
diameter  and  composed  of  the  material  originally  present  on  the  bubble.  It 
was  systematically  photographed,  and  the  organic  material  was  identified 
by  Detwiler  [26]  to  be  proteinaceous  molecules,  such  as  glycoproteins  and 


344 


protoglycans.  To  verify  the  above  facts,  we  equipped  an  axisymmetric 
model  with  air  ejectors  and  towed  it  in  a  tow  tank  in  both  tap  water  and 
salt  water;  figure  2.8  shows  the  bubbles  that  were  generated  in  each  by  the 
shearing  motion  of  the  water.  The  salt  water  was  prepared  by  putting  640 
lb.  of  fine  table  salt  in  3500  gallons  of  tap  water.  The  salinity  was 
calculated  to  be  21  percent  by  weight,  which  is  about  60  percent  of  the 
typical  sea  water  salinity.  As  shown  in  figure  8,  much  smaller  bubbles 
and  a  much  denser  bubble  cloud  were  formed  in  salt  water.  In  salt  water, 
bubbles  were  observed  to  stay  at  the  depth  (17  inches)  where  they  were 
generated  and  eventually  dissolved  into  the  ambient  salt  water;  in  tap 
water,  the  bubbles  rose  and  coalesced  to  form  larger  bubbles,  which  rose 
faster  and  eventually  burst  on  the  surface. 


predicted  mean  bubble  size.  Theoretically,  bubble  splitting  should  be 
considered  whenever  bubble  generation  is  taking  place  in  a  turbulent  flow. 
The  reason  that  in  a  laminar  boundary  layer,  the  maximum  shear  stress 
occurs  right  on  the  wall  and  is  a  steady  shear  stress,  so  once  the  bubbles 
are  generated  and  transported  away  from  the  wall,  they  do  not  encounter 
higher  stress.  In  a  TBL,  however,  the  maxima  of  Reynolds  stresses  =  iw 
and  the  turbulent  kinetic  energy  =  10  tw  both  occur  away  from  the  wall  at 
about  y+  =  30  to  100,  so  bubbles  must  encounter  greater  turbulence 
intensity  and  unsteady  stresses  than  the  stresses  very  near  the  wall,  which 
are  responsible  for  the  bubble  creation. 

In  principle,  three  splitting  stresses  can  be  identified:  the  mean  shear 


We  can  identify  three  major  basic  physics  mechanisms  as  possible 
origins  of  smaller  bubbles  in  sea  water:  reduced  surface  tension  between 
the  gas  bubble  and  water,  organic  film,  and  metalionic  film.  The  most 
intuitive  physics  mechanism  is  the  reduction  of  surface  tension  between 
the  gas  bubble  and  water.  Scott  [24]  stated  that  the  surface  activity  of  salt 
increases  the  surface  tension  of  the  solution,  consistent  with  the  formula 
given  in  Kraus  [27],  i.e.,  ascawatcr=  75.63  (dyne/cm)  -  0.144T(°C)  + 

0.22 IS.  On  the  other  hand,  it  is  well  known  (Batchelor  [28])  that  any 
absorbed  contaminant  molecules  at  an  air-water  interface  will  orient 
themselves  and  exert  on  each  other  a  repulsive  bimolecular  force  that 
partially  balances  the  surface  tension  of  the  pure  water,  so  the  net  effect  is 
that  the  surface  tension  value  is  smaller  in  sea  water  than  it  is  in  purified 
tap  water.  The  decrement  is  proportional  to  the  amount  of  surface 
contaminant  and  the  gradient  of  contaminant  concentration.  Davis  and 
Acrivos  [29]  analyzed  the  effect  of  varying  surface  tension  on  a  bubble 
aqd  found  that  the  drag  coefficient  of  a  bubble  covered  with  a  surface 
contaminant  is  consistent  with  the  experimental  data  if  the  maximum 
surface  tension  reduction  is  from  10  percent  to  45  percent.  The  only 
qualitative  way  to  resolve  this  seemingly  complex  issue  is  to  directly 
measure  the  surface  tension  value  for  each  sea  water  experiment. 

Effects  of  the  absorbed  organic  films  on  gas  bubble  radial 
oscillations  have  been  modeled  by  Fox  and  Herzfeld  [20],  Avetisyan  [30], 
and  Glazman  [31].  Fox  and  Herzfeld  modeled  the  film  as  an  isotropic 
elastic  shell,  so  no  surface  tension  dependence  was  found;  Avetisyan 
represented  the  absorption  film  as  a  non-Newtonian  liquid  characterized 
by  hypothetical  viscoelastic  properties;  Glazman  derived  a  new  term  at  the 
bubble-film-water  interface  to  include  the  nonuniform  surface  concen¬ 
tration  and  the  resultant  surface  tension  and  represented  the  film  as  a 
viscoelastic  film.  He  found  that  smaller  bubbles  are  formed  as  a  result  of 
the  film,  and  an  additional  restoring  force  induced  by  the  film’s  dilational 
elasticity  increases  the  bubble  resonance  frequency.  The  true  physics  of 
the  organic  film  on  the  bubble  are  far  from  being  completely  resolved,  but 
intuitively  we  can  see  the  following  effects  on  bubble  oscillation:  the 
organic  film  will  create  a  surface  tension  gradient  that  resists  bubble 
oscillation,  and  the  viscoelastic  nature  of  the  film  will  likely  damp  the 
high  frequency  bubble  oscillations.  In  either  case,  smaller  bubble 
oscillation  amplitudes  are  expected,  and  the  smaller  the  bubble,  the  greater 
the  damping  effects  of  the  surface  film  on  the  bubble  oscillation.  Another 
possible  effect  of  the  sea  water  surface  contaminant  on  bubbles  is  to 
increase  the  bubble  drag  coefficient,  making  the  bubbles  less  mobile  and 
hence  reducing  the  bubble  collision  speed,  collision  frequency,  and 
subsequent  coalescence.  Finally,  the  potential  for  the  resinous  surface 
film  to  be  stabilized  by  metal  ion  complex  was  suggested  by  Degens  [32], 
This  would  have  the  net  effect  of  making  the  bubbles  electrically  charged, 
so  that  bubbles  will  repel  each  other,  therefore  reducing  the  occurrence  of 
bubble  collision  and  subsequent  coalescence. 

3.  BUBBLE  SPLITTING  IN  A  TURBULENT  BOUNDARY  LAYER 

As  shown  in  figure  6,  Gallagher’s  data  show  a  secondary  peak  that 
exists  at  50  pm,  indicating  that  some  of  the  bubbles  greater  than  50  pm 
might  have  been  broken  up  into  smaller  bubbles.  Another  indication  of 
the  existence  of  bubble  splitting  can  be  seen  in  figure  7,  which  shows  the 
simulated  bubble  size  spectrum  using  the  shear  stress  spectrum.  By 
comparing  the  simulated  bubble  size  spectrum  with  Gallagher’s  data,  we 
found  that  the  peak  matches  but  the  bandwidth  does  not,  indicating  that 
other  mechanisms  exist  to  make  bubbles  larger  and  smaller  than  the 


stress  x,  the  turbulent  Reynolds  stresses  pu[u  V  ,  and  the  turbulent 


fluctuating  pressure  p'2  ,  which  is  proportional  to  the  turbulent  kinetic 


energy.  There  is,  however,  only  one  resistance  stress:  the  surface  tension 
a/dbubb!c.  Depending  on  the  bubble  (or  droplet)  Reynolds  number 

V/2 

,  (where  subscript  g  represents  gas  phase),  two  different 


vg  vPg/ 

force  balances  can  be  realized.  At  the  low  Reynolds  number  limit,  the 
mean  shear  stress  and  surface  tension  balance  each  other.  At  the  high 
Reynolds  number  limit,  the  discrete  phase,  the  bubbles  (or  droplets)  feel 
the  influence  of  turbulence  in  the  continuous  phase.  The  kinetic  energy  of 
the  turbulent  motion  in  the  continuous  phase  will  bring  about  the  breakup 
of  the  discrete  phase.  This  is  the  case  in  which  we  are  most  interested. 


Historically,  chemical  engineers  have  shown  the  greatest  interest  in 
this  problem,  since  they  are  concerned  with  the  problems  of  dispersion  of 
gas-liquid  systems  for  atomization  and  froth  formation,  and  with  liquid- 
liquid  systems  for  emulsification.  This  problem  had  the  attention  of  the 
most  distinguished  scientists  during  the  early  part  of  this  century.  Taylor 
[33]  developed  theories  and  experiments  to  study  the  “globule 
deformation”  in  the  Couette  and  plane  hyperbolic  flows.  The  globules  are 
stationary,  the  study  corresponds  to  the  Regk)bulc  <  1  limit,  and  it  is  valid  if 
the  drops  are  small  compared  with  the  local  regions  of  viscous  flow. 

These  facts,  however,  were  not  explicitly  stated.  Taylor  obtained  the 
results  of  We  -  xdglobuIc/a  versus  the  ratio  of  pd,  where  d  stands  for  the 
dispersed  phase,  ttrpc,  where  c  stands  for  the  continuous  phase.  His 
findings — that  no  breakup  will  take  place  either  at  the  low  pd/pc  <  3  x  10'4 
or  at  the  high  pd/pc  >  20  limits —  has  inspired  many  subsequent  studies, 
especially  those  by  Acrivos  [34]  and  Rallinson  [35].  Unfortunately,  none 
of  these  results  applies  to  our  case  of  interest. 


Hinze  [35]  laid  the  foundation  of  the  fundamental  physics  of  droplet 
breakup  in  a  moving  stream.  He  put  Taylor’s  work  (Reg,obu1c  <  1)  into 
perspective,  relative  to  a  droplet  breakup  in  an  air  stream  and 
emulsification  in  a  turbulent  flow,  for  the  Re^  >  1  case.  For  droplet 
breakup  in  an  air  stream,  Hinze  defined  a  new  Weber  number, 


We  = 


PcUod, 


droplet 


replacing  t  in  Taylor’s  expression  with  the  dynamic 


pressure  of  the  air  stream  pcUq.  He  found  that  the  mode  of  droplet 
breakup  was  very  different  for  We  greater  or  less  than  Wecritical.  For  We 
»  Wecriticaj,  droplets  were  stripped  off  the  drops  owing  to  the  waves  and 
ripples  generated  on  the  drops.  This  relevant  fact  could  have  its 
counterpart  for  bubbles.  For  emulsification  in  a  turbulent  flow,  Hinze 
pointed  out  that  the  critical  Weber  number  will  not  be  the  same  for  all  the 
globules — some  statistical  mean  value  will  determine  the  average  size  of 
the  largest  globules  that  can  withstand  the  breakup  forces.  For  an 
isotropic  and  homogeneous  turbulence  case,  Hinze  worked  out  the 
maximum  droplet  diameter  from  the  experimental  data  obtained  by  Clay 
[36].  Clay’s  data  were  obtained  in  an  apparatus  consisting  of  two 
concentric  cylinders  containing  two  immiscible  fluids.  The  inner  cylinder 
rotated,  and  one  of  the  fluids  formed  discrete  drops.  By  relating  his 
analytic  expression  and  Clay’s  data,  Hinze  [37]  found  that  the  maximum 
drop  diameter  is  determined  by  the  following  critical  Weber  number: 


Weaiucal  = 


P»'2  d  top 


a 


1.17.  From  Hinze’s  analysis  of  the  maximum  drop 


345 


3/5 


size  in  a  turbulent  flow,  i.e.,  ddropmax  = 


s  2/5 ,  we  can  obtain 


an  expression  for  the  corresponding  drop  size  in  a  TBL  if  we  assume  that 
the  isotropic  turbulence  assumption  still  applies.  From  Hinze  [37]  (p.  64) 

we  find  the  maximum  s  to  be  ,  where  6  is  the  local  boundary 

6 


layer  thickness.  Expressing  5  and  puT2  in  terms  of  Rex  and  substituting 
into  the  above  relationship,  we  obtain 

where  x  is  the  downstream  distance 

along  a  flat  plate.  Sleicher  [39]  did  turbulent  flow  experiments  using  two 
immiscible  liquids  in  a  48-ft-long  Lucite  pipe  with  a  l'A-inch  inner 
diameter.  He  found  that  the  fraction  of  drops  that  broke  up  was  very 
sensitive  to  flow  velocity,  and  in  every  case  the  breakup  occurred  very 
close  to  the  pipe  wall,  which  is  where  the  turbulence  was  the  least 
isotropic  and  homogeneous.  Although  Sleicher’s  data  do  not  deal  with 
bubble  breakup,  they  are  very  relevant  to  our  concern  here  because  they 
deal  with  breakup  in  a  TBL.  He  gave  the  following  results  for  the  critical 


drop  R 


Weber  number:  PcUoddr°Pma\  =  38r|1/2  (1  +  OJrf0 7),  where  q  =  a/pcU0, 

CT 

pc  is  the  viscosity  of  the  continuous  phase,  and  U0  is  its  velocity. 


Sevik  and  Park  [40]  conducted  a  study  of  air  bubbles  splitting  in  a 
turbulent  jet.  Their  apparatus  consisted  of  a  water  jet,  oriented  vertically 
upward,  with  an  air  nozzle  located  at  its  center.  The  water  nozzle 
diameter  was  1.5  inch,  and  the  water  velocity  at  the  nozzle  exit  varied 
from  7  ft/sec  to  16  ft/sec.  Air  was  injected  into  the  center  of  the  water  jet, 
and  air  nozzle  diameters  varied  from  0.071  inch  to  0.25  inch.  Bubbles 
with  diameters  varying  from  4  mm  to  5.8  mm  were  generated  in  the 
laminar  core  of  the  low  turbulence  jet  of  water  and  subsequently  were 
broken  up  by  the  jet  turbulence  downstream.  The  initial  bubble  sizes  were 
designed  to  be  greater  than  the  Kolmogorov  [41]  microscale,  which  was 
on  the  order  of  25  pm,  so  that  the  bubble  breakup  would  occur  and  would 
be  characterized  by  the  single  parameter  of  critical  Weber  number 
according  to  Kolmogorov  [41],  It  was  found  that  the  bubbles  remained 
near  the  center  of  the  water  jet  and  that  breakup  was  substantially 
completed  at  an  axial  distance  of  9  to  10  water  nozzle  diameters.  Beyond 
that,  no  additional  changes  in  bubble  size  took  place.  The  bubbles  were 
also  progressively  broken  into  smaller  and  smaller  ones  as  the  jet  velocity 
increased.  Sevik  and  Park’s  [40]  most  important  finding  was  that  if  a 
characteristic  frequency  of  the  turbulence  is  set  to  the  lowest  resonant 
frequency  of  the  bubble  oscillation  with  constant  volume,  the  critical 
Weber  numbers 'correspond  to  both  Clay’s  experimental  data  and  their 
own.  Furthermore,  they  stated  that  progressively  smaller  bubbles  were 
generated  when  the  critical  Weber  number  was  exceeded  and  when  the 
higher  frequencies  of  the  turbulence  excited  the  higher  modes  of  the 
bubble  oscillation. 


flow  speed.  We  can  see  that  all  three  curves  of 


pu'2d„ 


■  C,  with  C  = 


2.48  and  3,  are  nearly  identical.  The  y+  =  25  and  100  curves  are  provided 
to  indicate  the  boundaries  of  maximum  turbulence  production. 


As  the  majority  of  the  bubbles  become  smaller  than  y+  =  100,  we 
conjecture  that  more  microbubble  drag  reduction  can  be  expected. 
Interestingly,  we  see  that  at  5  m/sec  the  splitting  just  commences,  which 
might  be  relevant  to  the  observation  that  drag  reduction  begins  to  emerge 
at  this  speed.  At  20  m/sec,  more  bubbles  are  of  the  size  of  y+  =  25;  further 
increase  in  speed  should  ensure  that  most  of  the  bubbles  are  smaller  than 
y+  =  25,  therefore  increasing  the  opportunity  for  bubbles  interacting  with 
the  turbulence  production  that  would  normally  take  place  in  a  single  phase 
fluid  turbulent  flow.  It  is  intuitively  convincing  that  the  more  bubble 
splitting  taking  place,  the  more  the  turbulence  kinetic  energy  is  drained 
from  the  TBL;  therefore,  the  more  skin-friction  reduction.  Hinze’s 
isotropic  turbulence  result  for  droplets,  which  is  never  smaller  than  y+  = 
100,  is  also  shown.  The  curve  for  0.016  shows  that  at  speeds  less  than  10 
m/sec,  bubbles  larger  than  0.016  would  survive  the  splitting;  at  speeds 
greater  than  10  m/sec,  bubbles  would  be  much  smaller  than  0.015. 

4.  BUBBLE  TRANSPORT  IN  A  TBL 

One  of  the  tools  necessary  to  investigate  microbubble  drag  reduction 
is  a  method  of  determining  the  motion  of  microbubbles  in  a  TBL.  The 
model  employed  here  assumes  a  spherical  microbubble  in  a  mean  TBL 
velocity  profile.  Any  effects  of  the  rotation  of  the  bubble  are  ignored. 

The  forces  on  the  microbubble  are  calculated  as  if  the  bubble  were 
actually  a  rigid  particle.  This  assumption  is  based  on  evidence  that 
surface  phenomena  encountered  in  the  real  world  environment  make  this  a 
better  approximation  than  the  usual  free  surface  model  (see  Batchelor 
[28]).  The  fluid  is  assumed  to  be  Newtonian  and  incompressible.  We 
assume  that  the  time  scale  T  over  which  a  bubble  alters  its  breakaway  size 
by  diffusion,  splitting,  or  coalescence  is  such  that  T  »v/u2T.  We  can  then 
assume  that  the  bubble  size  remains  constant  during  the  calculation  of  its 
short  time  trajectory  in  a  TBL.  This  is  equivalent  to  stating  that  the 
bubble  size  does  not  change  significantly  until  the  bubble  has  traveled 
many  viscous  lengths. 

The  drag  of  the  microbubble  is  D  =  C£(Re)  •■ipUrcl7r2R2,  where 

the  drag  coefficient  CD  is  a  function  of  the  relative  velocity  bubble- 

U  R 

diameter  Reynolds  number  Re  =  2 — — — ,  and  Urd  is  the  difference 

v 

between  the  bubble  velocity  and  the  fluid  velocity.  The  drag  coefficient  is 
calculated  from  a  series  of  functional  fits  given  by  Morsi  and  Alexander 
[42].  A  microbubble  in  a  shear  flow  also  experiences  a  lift  force.  For 
small  Reynolds  numbers  this  force  is  L  =  6.46  p  Urel  R2  (vk),/2}  where  k  is 
the  magnitude  of  the  velocity  gradient  (Saffman  [4]). 


Sevik  and  Park  [40]  measured  Wecritica,  of  air  bubbles  generated  in  a 


water  jet  and  found  that 


PU’2db: 


-=2.6.  By  equating  bubble  and  flow 


frequencies, 


py 


^bubble  2^ 


(n  +  l)(n-  l)(n  +  2)cr 


P  ^bubble 


,  at  rl=2 


pu,2d 


=  2.48  ,  which  is 


they  found  the  following  theoretical  result: 

o 

close  to  the  experimental  result.  Inspired  by  these  results,  we  consider  the 
balance  of  the  turbulent  kinetic  energy  exerting  influence  on  a  bubble  to 
the  surface  tension  energy,  which  is  the  only  energy  resisting  the  breakup, 

i.e.,  pul2  — 1  =  — crd2ubb1e.  We  find  pU  dbubblc  =  3,  which  is 

3  V  2  )  2  a 

fairly  close  to  the  above  experimental  result.  Summarizing  all  these 
results,  we  show  in  figure  9  the  maximum  bubble  diameters  versus  the 


All  pressure  gradients  are  taken  into  account,  including  the  pressure 
gradient  due  to  gravity,  which  causes  buoyancy.  All  inertial  effects  are 
also  considered:  4he  mass  of  the  microbubble,  the  added  mass  of  the 
microbubble,  and  the  so-called  Basset’s  force: 


B  =  6pR(itv)l/2 


dt 

(t-T)'/2‘ 


The  basic  equations  thus  take  the 


form: 


■JTI R’  ^-{p'  u  +  CAp(u  -  u)}  =  -CD  ~p|v|(u  -  u)it  R2 

-6.46p(v-v)R2v1/2^  (5) 

-  C„p  R2  (itv)1'2 1 -j|-(u  -  u)  >  and 


346 


Bubble 

lOjj. 


Bubble 

10Q)i 


Bubble 

1000m. 


j  n  R3  A  {p'  v  +  CAp(v  -  v)}  =  -CD  •  Jp|v|(v  -  v)tiR2 

/  —  A  1/2 

-6.46p(u-u)R2  v1'2  —  7tR3  — +  p'— JtR3g  (6) 

(.ay;  3  5y  3 

-CHpR2(juv)1/2  f— (v-v) — , 
idx  (t-i)172 

where  the  velocity  of  the  bubble  is  given  by  V  =  u  i  +  v  j,  and  the  velocity 
of  the  fluid  in  the  absence  of  the  bubble  is  V  =  ui  +  vj.  The  coefficients 
CA  and  CH  are  the  added  mass  and  history  (or  Basset’s)  force  coefficients, 
respectively.  These  are  functions  of  the  “acceleration  number” 

|v-v| 

Ac  -  — - - as  given  by  Odar  and  Hamilton  [43]. 

2R—  V-V 
dt 


The  relative  importance  of  the  forces  on  a  microbubble  can  be  determined 
by  forming  their  ratios  and  calculating  the  numerical  values  of  the  ratios 
for  any  case  of  interest.  To  simplify,  we  can  use  the  drag  force  as  the 
basis  of  comparison,  since  even  a  cursory  examination  of  the  physics 
involved  serves  to  demonstrate  that  the  drag  force  must  always  be 
significant  in  any  case  of  interest.  Assuming  that  the  relative  velocity 
bubble  Reynolds  number  is  small,  the  form  of  the  drag  force  used  for 
comparison  with  other  forces  is  Hadamard’s  drag,  4  71  p  R  Urch  where  p  is 
the  fluid  viscosity,  R  is  the  microbubble  radius,  and  Urcl  is  the  relative 
velocity  between  the  fluid  and  the  microbubble. 


Forming  ratios  of  these  forces  with  the  drag  force,  we  find 


LIFT 

DRAG 


=  0.51R+(k+)1/2 


BASSET  CH  R+ 
’  DRAG  ”4ti1/2  U+ 


dx  + 


BUOYANCY  _  I  R+2G+  GRAVITY  _  1  R+2G+ 

DRAG  ”  3  U+  *  DRAG  ~  3 a  U+ 
R^dlT  ADDED  MASS  1  Q  R+2  dU+ 

3 a  U+  dt+  ’  ^  DRAG  3  A  U+  dt+  * 


INERTIA 
*  DRAG 

where  R+  = 

v 


where  uT  = 


l 

dy|wai 


■Ip 


u+ 


Urcl  ?  t+  = 

UT  ’  V  ’ 


G+  =  and  a  =  p ’/p. 

As  an  example,  let  us  assume  uT  =  1 .44  m/s  and  v  -  1  O'6  m2/s,  so  we 
find  G+  =  3.3  x  10"6.  Now  assume  that  for  a  bubble  in  ocean  water  a  =  2.2 
x  10'2.  To  estimate  the  nondimensional  relative  velocity,  acceleration,  and 
velocity  gradient,  it  is  necessary  to  consider  regions  where  these  quantities 
are  large,  that  is,  regions  where  the  forces  will  be  large.  As  an  order-of- 
magnitude  estimate  we  can  state  that  U+  =  10.0,  k+  =  1.0,  and  dU7dt+  = 
10.0.  In  order  to  estimate  Basset’s  force,  suppose  that  the  bubble  has 
experienced  a  roughly  constant  acceleration  during  the  last  At+  of  time, 
prior  to  which  it  was  moving  with  constant  velocity.  This  supposition 
yields  an  order-of-magnitude  estimate  for  most  cases  because  the  solutions 
of  the  above  equations  tend  to  behave  exponentially.  Hence,  the  periods  of 
high  acceleration  occur  over  short  time  intervals.  With  these  assumptions 
we  can  approximate  Basset’s  force  as 


?  dU+  dx* 

|  dt+  (t+-T+)1/2 


;2i*L(AtT2. 

dt+ 


show  that  we  can  state  At+  =  1 . 


In  addition,  the  above  arguments 


If  we  now  take  the  added  mass  coefficient  CA  and  the  history  or 
Basset’s  force  coefficient  CH  to  make  their  high  acceleration  values  CA  = 
1/2,  CH  =  6,  then  we  can  calculate  the  force  ratios.  Proceeding  with  the 
aforementioned  example,  with  microbubble  sizes  chosen  that  are  typical 
of  those  found  in  engineering  situations,  we  arrive  at  the  following  results: 


R+ 

14.4 

Lift 

Drag 

7.3 

Inertia 

Drag 

1.5 

Added  Mass 
Drag 

34.5 

Basset 

Drag 

24.4 

Gravity 

Drag 

5.0x1  O'7 

Buoyancy 

Drag 

2.3x1  O'5 

144.0 

1440.0 

73.5 

735 

152.1 

15210.0 

3450.0 

3.5x1 05 

243.8 

2437.5 

5.0xl0'5 

5.0x1 0'3 

2.3x1 0'3 

2.3xl0*1 

With  the  exception  of  gravity  and  buoyancy,  all  other  influences  on 
microbubble  acceleration  are  of  at  least  the  same  order  of  magnitude  as 
the  drag,  and  they  generally  dominate  the  drag  during  periods  of  high 
velocity  and  acceleration.  Of  particular  interest  is  the  lift  force,  which  can 
be  orders  of  magnitude  greater  than  the  drag  force  in  the  high  shear  flow 
of  a  boundary  layer.  The  lift  force  acts  in  the  direction  of  increasing 
relative  velocity  magnitude,  so  a  microbubble  released  at  the  wall 
experiences  a  strong  lift  force  that  pulls  it  away  from  the  wall.  Initially, 
the  lift  force  is  many  times  the  drag  force,  and  the  bubble  will  move 
almost  perpendicularly  away  from  the  wall.  As  the  drag  force  slowly 
brings  the  relative  velocity  between  the  microbubble  and  the  fluid  to  zero 
and  the  bubble  moves  to  regions  of  lower  shear,  the  lift  force  diminishes 
rapidly  and  the  bubble  eventually  moves  parallel  to  the  wall  (see  figures  10 
and  11). 

Outside  the  boundary  layer,  however,  the  lift  force  is  generally 
negligible  because  of  the  comparatively  small  values  of  velocity  gradient 
encountered  in  the  external  flow.  For  example,  the  maximum  velocity 
gradient  that  exists  in  the  potential  flow  about  a  circular  cylinder  is  on  the 
order  of  Uoo/a,  where  Uoo  is  the  freestream  velocity  and  a  is  the  radius  of 
the  cylinder.  If  we  assume  that  uT  =  1 .44  m/s,  and  if  a  =  1  m,  then  in 
terms  of  the  nondimensional  quantities  this  velocity  gradient  is 

■ii  =  =  1.7  x  10~5,  which  is  very  small  compared  to  the  value 

a  uT  /  v 

found  in  the  boundary  layer  where  k+  =  1 .  Hence,  outside  the  boundary 
layer  the  main  forces  to  be  considered  are  drag  force,  pressure  force, 
inertial  force,  and  added  mass  force. 

The  Advected  Particle  Trajectory  (APT-1)  program  takes  all  the 
relevant  forces  into  consideration  and  can  calculate  the  trajectories  of  the 
bubbles  from  the  time  they  depart  the  wall  to  their  long  time  asymptotic 
path.  Once  the  microbubble  size  spectrum  has  been  determined  (including 
bubble  splitting  and  coalescence  effects),  we  know  where,  in  diameter, 
most  of  the  microbubble  population  reside.  We  can  employ  the 
microbubble  diameter  probability  density  function  p(D)  to  describe  the 
distribution  in  bubble  sizes  passing  any  downstream  station.  From  this 
PDF  we  can  define  the  mean  bubble  diameter  pD,  the  variance  g2d,  and 
skewness  crD  of  the  distribution.  The  bulk  of  the  microbubble  population 
can  be  estimated  to  lie  between  the  diameters  pD  ±  gd.  The  trajectories, 
followed  by  bubbles  of  these  sizes  as  they  pass  through  the  TBL,  serve  to 
bound  the  portion  of  the  boundary  layer  containing  most  of  the 
microbubbles.  For  sufficiently  small  variance  and  skewness  these 
trajectories  also  bound  the  region  of  greatest  void  fraction;  hence  the 
magnitude  of  the  local  void  fraction  maximum  can  be  increased  by 
reducing  the  variance  in  bubble  diameters.  Similarly,  control  of  the 
location  of  this  void  fraction  maximum  can  be  accomplished  by 
controlling  the  mean  bubble  diameter. 


347 


In  order  to  examine  further  the  phenomenon  of  microbubble  drag 
reduction,  it  became  necessary  to  obtain  an  estimate  of  the  void  fraction 
variation  in  the  TBL.  In  the  first  attempt  the  APT-1  code  was  employed 
to  calculate  trajectories  for  bubbles  of  the  diameters  pD  and  pD  ±  ctd  for 
the  cases  of  three  microbubble  diameter  spectra,  for  which  the  means  and 
standard  deviations  (pD,  crD)  in  microns  were  (338,34),  (156,16),  and 
33,5,3.5,  respectively.  The  trajectories  for  these  three  cases,  shown  in 
figure  12,  were  calculated  with  a  mean  TBL  profile  produced  by  the 
axisymmetric  TAPS  code.  The  body  shape  was  that  of  an  axisymmetric 
body  with  a  length  Reynolds  number  of  UooL/v  -  8.9  xlO7  and  a  Froude 
number  of  Uoo/vgL  =  2.55.  Each  trajectory  was  calculated  from  three 
different  locations,  corresponding  to  x/L  =  0.1 1,  0.53,  and  0.82.  The 
trajectories  are  presented  in  terms  of  both  y/8  and  y+  versus  x/L.  For 
clarity,  only  the  trajectories  for  the  mean  bubble  size  are  shown  for  the 
case  pD  -  33.5  microns. 

The  microbubble  trajectories  can  be  used  to  obtain  estimates  of  the 
void  fraction  profile.  Consider  the  evolution  having  downstream  distance 
of  bubbles  with  diameters  in  the  interval  (D,  D,  +  AD)  in  proximity  to  a 
plane  or  nearly  plane  wall.  Following  typical  turbulence  modeling 
practice  we  consider  the  flow  to  consist  of  a  basic  steady  portion  (the 
mean  turbulent  flow  profile)  with  a  strong  spatially  varying  cross-stream 
diffusion  rate  (an  eddy  viscosity  model  vc=  vc  (y)).  If  for  the  moment  we 
neglect  the  diffusion,  we  can  easily  calculate  the  trajectories  of  the 
bubbles  of  diameter  D  and  D  +  AD  .as  though  the  flow  were  laminar.  For 
AD/D  «  1,  these  trajectories  are  separated  by  a  very  small  distance;  A  and 
all  the  bubbles  with  diameters  in  the  interval  under  discussion  have 
trajectories  that  lie  between  these  two  trajectories. 


microbubble  distribution  is  sufficiently  narrow  that  1/Uoo  duldy  «  1/A, 
then  any  dependence  of  u  on  D  can  be  ignored,  and  the  second 
integration  can  be  performed  to  arrive  at  Q  =  C  %  D^y  u  .  Therefore  the 
local  void  fraction  can  be  computed  as  a(x,y)  = 

— f  dDp(D)g(D,x,y),  or  s  Q — -  fdDp(D)  g(D,x,y). 
rcD^uJo  7tDbod).u(x,y)J» 

Examples  of  void  fraction  profiles  and  their  evolution  with  downstream 
distance  on  an  axisymmetric  body  are  shown  in  figure  13. 

5.  MICROBUBBLE  DRAG  REDUCTION  MECHANISM 

5.1  Decay  of  Drag  Reduction  Downstream.  Madavan,  Deutsch,  and 
Merkle  [44]  (abbreviated  MDM  hereafter)  indicated  that  the  ratio  ACf/cf 
decays  by  50  percent  over  a  distance  of  256,  where  8  is  the  boundary  layer 
thickness.  This  observation  raises  a  question  about  why  this  happens  and 
how  it  can  be  prevented  or  mitigated  in  practice.  Intuitively,  we  can 
suggest  three  basic  mechanisms  to  be  the  potential  origin  of  the  loss  of 
effectiveness  of  the  microbubble  drag  reduction:  growth  of  TBL 
thickness  reducing  the  local  void  fraction;  bubble  diffusion  away  from  the 
wall  due  to  the  turbulent  eddy  diffusivity;  and  bubble  coalescence  and 
subsequent  rise  away  from  the  wall  due  to  the  larger  buoyancy.  The  last 
mechanism  is  expected  to  be  greatly  reduced  in  sea  water,  especially  for 
higher  speeds.  The  second  mechanism  depends  upon  the  magnitude  of  the 
turbulent  eddy  diffusivity  uT8,  which  also  depends  on  8,  the  boundary 
layer  thickness.  This  fact  led  us  to  focus  our  discussion  on  the  first 
mechanism:  how  the  growth  of  8(x)  will  degenerate  the  effectiveness  of 
microbubble  drag  reduction. 


For  convenience  we  assume  that  all  the  bubbles  in  the  initial 
distribution  begin  their  trajectories  at  one  point  on  the  body,  with  the  same 
initial  conditions.  Each  of  the  trajectories  can  be  described  by  a  function 
of  the  form  y  =fD(x);  so  if  y  (D;x,y)AD  describes  the  void  fraction  at  (x,y) 
as  a  result  of  bubbles  in  the  interval  (D,D  +  AD),  then  the  above  initial 
condition  can  be  written  as  y  (D;  x,y)  AD  =  C  8(y  -  fD  (x))  p(D)  AD,  where 
C  is  an  as  yet  undetermined  constant,  and  8  is  the  Dirac  delta  function. 
Assuming  the  diffusion  process  obeys  the  linear  diffusion  equation  with 
diffusion  coefficient  vc,  the  void  fraction  y  will  then  evolve  downstream  as 

y(D,x,y)AD  =  expi — — — —  where  we  have 

2(7TVet)1/2  F1  4vet  J 

assumed  that  dvjdy  «  uA/L  in  the  regions  of  interest,  and  that  Uooy/vc 
»  1,  so  wall  effects  can  be  neglected.  The  coordinates  of  the  mean  bubble 
path  (xD,  yD)  are  related  by  yD  =  fD(xD)  and  can  also  be  expressed 
parametrically  by  xD  =  xD(t),  yD  -  yD(t).  Hence,  by  the  implicit  function 
theorem,  we  can  write  t  =  tD(x),  so  that 


y(D;x,y)  AD  = 


Cp(D)  AD 
2(*vctD(x))‘'2 


exp 


[-(y-fp(x))2] 
1  4vetD(x)  \ 


Then  the  local 


void  fraction  can  be  recalculated  by  a(x,y)  =  J  dDy(D;x,y).  The 

quantities  fD  and  tD  in  the  expression  for  y  are  implicit  functions  of  D.  In 
order  to  determine  the  value  for  C  we  require  that  the  total  void  flux  past 
any  downstream  plane,  perpendicular  to  an  axisymmetric  body  with 

diameter  Dbody,  be  conserved  so  that  Q-7tDbodvJo  dya(x,y)  u(x,y). 
Thus  we  see  that  Q  =  Cn  Dbodv  dy  u(x, y)  J* dD  p(D)  g(D; x, y),  where 


g(D; x, y)  = - ! - —  exp]—1 — — fp^  1.  Interchanging 

S  2(7TVetD(x)),/2  4  VctD(x)  J 

orders  of  integration,  we  can  write 

Q  =  Cn  D^  J" dD  p(D)  J* dy  u(x, y)  g(D;  x, y).  However,  if  u(x,y) 

I  ✓  x  1/2 


varies  slowly  enough  with  y,  that  is,  if  — L.~|yD  «|  I  ?  then  we 

dy  VveLJ 

can  approximate  u(x,y)  by  some  u  for  the  purpose  of  integration  over  y  to 
find  that  J*dy  u(x,y)g(D;x,y)  =  u.  If  we  further  assume  that  the  initial 


The  nominal  void  fraction,  i.e.,  the  average  void  fraction  in  a 
microbubble-laden  TBL,  was  suggested  by  MDM  as  Cv  = 

— - - ,  where  Qboundai>  laver  =  (1  ~  8*/8)U0b8,  and  b  is  the 

Lcgas  Lcboundan  lava- 

width  of  the  gas  ejector.  In  a  single-phase  liquid  TBL,  1  -  8*/8  =  0.87. 
Defining  Qgas  =  cqv0s  =  cqv0bL,  where  s  is  the  porous  surface  area,  b  =  7tD, 
and  L  is  the  length  of  ejection,  we  have 


0.878 


1  + 


(7) 


The  rates  of  change  of  Cv  and  8  are  then  related  by  = 

dx 


_  — ,  so  that  if  d8/dx  is  reduced,  so  is  dCv/dx;  hence  it  is 

CqL  v  dx 

expected  and  hoped  that  the  decay  of  the  microbubble  drag  reduction  can 
be  reduced.  The  following  discussion  focuses  on  whether  this  basic 
mechanism  can  be  identified  as  the  primary  one,  how  much  reduction  of 
d8/dx  is  needed  to  slow  the  decay  of  Cv,  and  how,  in  practice,  such  a 
mitigation  can  be  implemented. 


First  we  compare  the  decay  rate  of  Cv  with  the  MDM  data  on  the 
persistence  of  skin  friction  reduction  over  the  distance  downstream. 
According  to  MDM,  Ac/cf  decays  by  about  a  factor  of  2  over  a  distance  of 
308.  Since  the  MDM  data  show  that  Acj/cf  is  proportional  to  the  Cv,  we 
expect  that  Cv  should  be  reduced  by  a  factor  of  2  over  a  distance  of  308. 
Such  an  assumption  can  be  compared  with  equation  (7).  MDM  (in  their 
figure  17)  gave  the  following  key  parameters:  L  =  7  inches,  cq  =  0.02  for 
ACf/Cf  at  speed  U0  =  10  m/sec,  Cyo=  0.48  at  x0  =  409  mm  will  yield 

a— ^|0  =0.85,  at  Xj=575  mm,  ^-|2  =  0.4  with  an  equivalent  CVl  =0.20; 
cf  cf 

in  other  words,  a  nearly  50-percent  reduction  in  Ac/cf  for  a  50-percent 
reduction  in  Cv-  Using  8  =  0.37  x/Rex0  2  and  U0  =  10.8  m/sec,  we  find 
8(x0)  =  0.71  cm  and  8(x^  =  0.93  cm.  Substituting  into  (7),  we  find 
Cv  /CVo  =0.8,  certainly  not  sufficient  to  explain  the  50-percent  reduction 
observed  in  the  MDM  data. 


From  Migirenko  and  Evseev’s  [44]  void  fraction  profile  data,  we  see 
a  distinct  peak  in  the  void  fraction  at  y/8  =  0.1,  and  if  we  neglect  the 


348 


bubble-bubble  interactions,  then  theoretically  the  local  void  fraction 
should  follow  the  diffusion  equation.  In  other  words,  the  void  fraction 
should  follow  c(y)  oc  e'y2/4vet>  where  y  is  the  distance  from  the  void 
fraction  peak  and  ve  =  0.04  uT8  (Hinze  [37],  p.  645).  To  find  one  e-fold 
time  or,  equivalently,  the  distance  downstream,  for  c(y)  to  reduce  by  e1, 
we  set  4vct  =  (1/2  8)2.  Substituting  vc  into  the  above,  we  obtain  Ax  =  Vi 
U0t  5  1/1 .28  (2/cf)1/2  8  =  358  for  cf=  0.001,  where  Ax  is  not  very  different 
from  the  MDM  data  of  308.  This  indicates  that  diffusion  of  bubbles 
instead  of  growth  of  the  TBL  thickness  might  be  the  dominant  mechanism 
for  the  decay  of  microbubble  drag  reduction. 


The  next  relevant  question  is  how  much  growth  there  is  in  S(x)  over 
a  distance  of  308,  and  how  much  suction  is  required  to  reduce  its  growth. 

A8(x) 


From  the  expression  for  8(x)  we  find  at  the  same  speed, 


S(x) 


0.8  —  =  24  ,  so  that  at  Rex  =  107,  A8/8  =  0.3.  The  required 

x  x 


Re' 


7rDjo8(x)udy 


suction  coefficient  is  then  defined  as  Cqs  = 

“  0“ 

suction  area  and  D  is  the  diameter  of  the  axisymmetric  body. 
Equivalently,  the  above  equation  can  be  rewritten  as 

\  1/7*1 


,  where  A  is  the 


c  =-f03 

^  T  Jo 


/  \  1/7  /  \ 

1  -  1  -  —  d  —  ,  where  A  =  nDL  and 
v  5/  v8/ 


u/U0  -  1  -  (1  -  y/8)1/7  (Hinze  [37],  p.  632)  were  applied. 


5.2  Bubble  Splitting  as  a  Turbulence  Reduction  Mechanism.  From 
previous  discussion  about  bubble  splitting,  we  can  estimate  the  total 
amount  of  turbulent  kinetic  energy  needed  to  split  bubbles  in  a  TBL  and 
compare  that  with  the  total  energy  available  in  a  TBL.  From  this 
estimation,  we  can  identify  whether  the  bubble  splitting  is  a  plausible 
basic  mechanism  for  reducing  the  turbulence.  Furthermore,  if  it  is  indeed 
plausible,  we  could  identify  what  can  be  done  to  maximize  its  effects. 
From  the  energy  balance  point  of  view,  it  takes  a  Reynolds  stress 

pu’2  =3 a  /  dbubble  to  initiate  bubble  splitting.  Assuming  that  bubbles  stay 
spherical  in  shape,  the  work  needed  to  split  a  bubble  from  a  diameter  of 
4ubbie  into  bubbles  of  diameter  XA  dbubble  (abbreviated  henceforth  as  db)  is 

' 2  9 

ddb  =  —  7iadb,  and  the  energy  needed  to  split  N  bubbles 
8 


fd  3  f  c 

Ji  TT4*  “ 

2  dh  V 


is  9  /  87rcrdbN.  Assuming  the  bubble  size  spectrum  follows  a  Rayleigh 


spectrum,  as  shown  in  figure  5,  n(db)  =  N- 


-1/2  J*b_ 
,db0 


the  total 


amount  of  turbulence  energy  required  to  split  all  N  bubbles  into  bubbles 
with  diameters  of  half  their  original  sizes  can  be  calculated  from 


C-TIG 

db  e-l«( 

'  \ 

db 

Jo 

^db0  ) 

ddb  =  —  T(2)  rcaNd 
4 


where  dbo  is  the 


bubble  diameter  of  the  maximum  population  in  the  Rayleigh  spectrum. 
The  power  Ps  needed  to  split  all  N  bubbles  is  then  9/4  f(2)7icr  NdbQ  .  To 

relate  the  bubble  generation  rate  N  to  the  gas  ejection  rate  Q,  we  first 
integrate  the  Rayleigh  spectrum  to  find  the  total  gas  volume  and  then 
differentiate  it  with  respect  to  time  in  order  to  obtain  the  volumetric  gas 


flow  rate:  total  gas  volume  = 


Njjrc(A.) 


< 


(iC\m 

—J  Ndbo .  Thus  the  volumetric  gas  flow  rate  Q  can  be  expressed 


■«-(!)’ 


Ndb  ,  where  N  is  the  number  of  bubbles  generated  per 


time.  Expressing  N  in  terms  of  Q,  we  have  the  rate  of  turbulence  energy 
required  to  split  bubbles: 

P=— Trad2  f—l  orPs  =  — ^——Q.  This  power  should  be 

4  b°UJ  d{0  (2k)'12  db0  V 

compared  with  the  total  turbulence  power  available  in  a  TBL  over  an 
axisymmetric  body,  which  can  be  derived  as  follows. 


The  power  per  unit  width  (from  Hinze  [37],  p.  642,  figure  7-20)  is 
p^BL=£pq2dy,  where  q2  =  u’2  +  v'2  +  w’2,  and  ~  q2  =  8u2^l 


so  that  Pm  =  4pu2S,  where  8  is  the  boundary  layer  thickness. 
Multiplying  PTOL  by  7rDU0,  where  D  is  the  diameter  of  an  axisymmetric 
body  and  U0  the  body  speed,  we  have  P^  =  47ip28U0D.  The  ratio  of  Ps 


to  PTri  is  then 


ps  _  9 

f  \ 

a 

f  Q  ) 

J5 

r*  | 
1 

to 

To 

Lpufdb0  J 

Ud8U0/ 

(8) 


The  first  term  in  parentheses  represents  the  ratio  of  surface  tension  stress 
to  turbulent  wall  shear  stress  for  a  bubble  with  a  diameter  of  dbo ;  the 

second  term  in  parentheses  represents  the  ratio  of  gas  flow  rate  to  that  of 
the  TBL  axisymmetric  body.  To  estimate  the  first  term  in  parentheses,  we 

apply  the  following  facts:  pu'L  s9pu*,  d„  s  3dbo,  so  that 


pU  maxdbmax  =27  PM*)  .  an£,  _£ - s|Q  Equatjon  (g) 

a  °  PuXo 

represents  the  fraction  of  energy  expended  to  split  all  bubbles  from  db  into 
Vi  db.  In  practice,  this  ratio  should  be  equal  to  the  drag  reduction  ratio. 
Although  this  analysis  is  preliminary  in  nature,  it  does  indicate  that  bubble 
splitting  can  be  a  primary  cause  of  the  effectiveness  of  microbubbles  to 
reduce  turbulence.  To  increase  the  effectiveness,  we  can  increase  the 
surface  tension  between  the  water  and  the  gas;  therefore,  injecting  a 
certain  liquid  or  using  a  gas  with  higher  value  of  a  might  be  useful.  Since 
db0  decreases  with  flow  speed  U0,  by  increasing  U0  a  higher  reduction 
might  also  be  possible.  However,  we  must  also  increase  the  gas  flow  rate 
Q  proportionally. 


6.  CONCLUSIONS 

Hydrodynamic  forces,  both  tangential  and  normal  to  the  wall,  have 
been  identified.  Quantitative  relationships  with  gas-injection-induced 
bubble  formation  on  a  wall  are  obtained.  Fundamental  unknowns  are  the 
bubble  shape,  the  drag  force  over  it,  and  the  lift  force  on  a  bubble  in  a 
TBL.  Bubble  size  regimes  have  been  identified  to  be:  spherical  cap, 
single  bubble,  intermediate,  and  jet  disintegration  regimes.  The 
controlling  parameter  has  been  found  to  be  the  ratio  of  gas  exit  velocity  to 
the  external  flow  velocity.  At  very  low  injection  rate,  the  tangential  force 
balance  mode  determines  bubble  size,  i.e.,  water  drag  and  surface  tension 
balance  each  other.  At  higher  injection  rates,  the  normal  force  balance 
mode  takes  over,  i.e.,  the  lift  force  balances  the  surface  tension  or  water 
inertia  surrounding  a  bubble.  At  even  higher  injection  rates,  jet  instability 
determines  the  bubble  size.  There  are  still  unknown  regions  between  the 
gas  jet  and  bubble  regimes.  Effects  of  sea  water  have  been  identified  but 
not  quantified.  Effects  of  bubble  splitting  have  been  found  to  be  very 
significant  and  might  well  be  the  key  origin  of  microbubble  drag 
reduction  mechanisms.  Transport  of  bubbles  in  a  TBL  has  been 
simulated.  The  smaller  the  bubble,  the  more  likely  the  bubbles  will  stay 
near  the  wall.  The  unknowns  are  the  quantitative  lift  force  formulation, 
bubble  coalescence,  and  splitting  effects. 

7.  REFERENCES 

1 .  Al-Hayes  and  Winterton,  “Bubble  Growth  in  Flowing  Liquids,” 
International  Journal  of  Heat  Mass  Transfer ,  vol.  24,  pp.  213-221, 
1981. 


349 


2.  Al-Hayes  and  Winterton,  “Bubble  Diameter  on  Detachment  in  Flowing 

Liquids,”  International  Journal  of  Heat  Mass  Transfer ,  vol.  24,  pp. 
223-230,  1981. 

3.  1.  S.  Gradshteyn  and  I.M.  Ryzhik,  Table  of  Integrals,  Series,  and 
Products ,  A.  Jeffrey  (ed.).  Academic  Press,  New  York,  1980. 

4.  P.  G.  Saffman,  “The  Lift  on  a  Small  Sphere  in  a  Slow  Water  Flow,” 
Journal  of  Fluid  Mechanics,  vol.  22,  p.  385,  1965. 

5.  P.  G.  Saffman,  “Corrigendum,”  Journal  of  Fluid  Mechanics,  vol.  31, 

p.  625,  1968. 

6.  Voloshko,  et  al.,  Inzhenerno-Fizicheskii  Zhurnal,  vol.  35,  no.  6,  pp. 

1066-1071,  1978. 

7.  F.  MacIntyre,  “Bubble  Generation  on  a  Heated  Body,”  personal  notes. 

University  of  Rhode  Island,  Graduate  School  of  Oceanography,  1981. 

8.  E.  Silberman,  “Gas  Jets  in  Liquids,  Production  of  Bubbles  By  the 
Disintegration  of  Gas  Jets  in  Liquids,”  5th  Midwestern  Conference  on 
Fluid  Mechanics ,  p.  263,  1957. 

9.  Lord  Rayleigh,  “On  the  Stability  of  Cylindrical  Fluid  Surfaces,”  Phil. 
Mag.  of  London,  vol.  34,  pp.  177-180,  1892. 

10.  M.  M.  Reischman  and  J.M.  Holzmann,  “Digital  Image  Analysis  of 
Two  Phase  Flow  Data,”  NOSC  Technical  Report  502,  Naval  Ocean 
Systems  Center,  San  Diego,  CA,  1980. 

1 1.  T.  E.  Burton,  “The  Connection  Between  Intermittent  Turbulent 
Activity  Near  the  Wall  of  a  Turbulent  Boundary  Layer  with  Pressure 
Fluctuations  at  the  Wall,”  Report  No.  70208-10,  Acoustics  and 
Vibration  Laboratory,  MIT,  Cambridge,  MA,  1974. 

12.  V.  A.  Sanborn,  “Evaluation  of  the  Time  Dependent  Surface  Shear 
Stress  in  Turbulent  Flows,”  ASME  Publication  79-WA/FE-17,  1979. 

13.  H.R.  Kreplin  and  H.  Ecklemann,  “Bearer  of  the  Three  Fluctuating 
Velocity  Components  in  the  Wall  Region  of  a  Turbulent  Channel 
Flow,”  Physics  of  Fluids,  vol.  22,  no.  7,  p.  1233,  1979. 

14.  R.  S.  Brodkey,  J.M.  Wallace,  and  H.  Eckel  mann,  Journal  of  Fluid 
Mechanics,  vol.  63,  p.  209,  1974. 

15.  J.  C.  Bhatia,  F.  Durst,  and  J.  Jovanovic,  “Corrections  of  Hot-Wire 
Anemometer  Measurements  Near  Walls,”  Journal  of  Fluid 
Mechanics ,  vol.  122,  pp.  411-431,  1982. 

16.  H.  Nakagawa  and  I.  Nezu,  “Structure  of  Space-Time  Correlations  of 
Bursting  Phenomena  in  an  Open-Channeled  Flow,”  Journal  of  Fluid 
Mechanics,  vol.  104,  p.143,  1981. 

17.  J.  J.  Gallagher,  “Microbubble  Size  Distributions  Data  Collection  and 
Analyses,”  OCEAN  1984  Conference,  1984. 

18.  H.  Schlichting,  Boundary  Layer  Theory ,  McGraw-Hill,  New  York, 
1960. 

19.  J.  Aitchison  and  J.A.C.  Brown,  The  Lognormal  Distribution , 
Cambridge  University  Press,  Cambridge,  England,  1957. 

20.  F.  E.  Fox  and  K.F.  Herzfeld,  Journal  of  the  Acoustical  Society  of 
America,  vol.  26,  pp.  984-989,  1954. 

21.  G.  A.  Riley,  Limnology  Oceanography,  vol.  8,  p.  372,  1963. 

22.  D.  C.  Blanchard,  “The  Electrification  of  the  Atmosphere  by  Particles 
from  Bubbles  in  the  Sea,”  Progress  in  Oceanography ,  vol.  1,  pp.  72- 
202,  1963. 


23.  E.  C.  Monahan,  “Sea  Spray  and  Its  Relationship  to  Low  Elevation 
Wind  Speed,”  Ph.D.  Thesis,  MIT,  Cambridge,  MA,  1966. 

24.  J.  C.  Scott,  “The  Role  of  Salt  in  Whitecap  Persistence,”  Deep  Sea 
Research,  vol.  22,  pp.  653-657,  1975. 

25.  B.  D.  Johnson  and  R.C.  Cooke,  “Generation  of  Stabilized 
Microbubbles  in  Sea  water,”  Science,  vol.  213,  p.  209,  1981. 

26.  A.  Detwiler,  “Surface-Active  Contamination  on  Air  Bubbles  in 
Water,”  in  Surface  Contamination :  Genesis,  Detection,  and  Control, 
K.L.  Hittal,  ed.,  Plenum  Press,  New  York,  1979. 

27.  E.  B.  Kraus,  Atmosphere-Ocean  Interaction,  Clarendon  Press,  Oxford, 
England,  1972. 

28.  G.  K.  Batchelor,  An  Introduction  to  Fluid  Dynamics,  Cambridge 
University  Press,  Cambridge,  England,  1967. 

29. 1.  A.  Avetisyan,  Soviet  Physics  of  Acoustics,  vol.  23,  pp.  285-288, 
1977. 

30.  R.  E.  Glazman,  “Effects  of  Absorbed  Films  on  Gas  Bubble  Radial 
Oscillations,”  Journal  of  the  Acoustical  Society  of  America,  vol.  74, 
p.  980,  1983. 

31.  E.  T.  Degens,  in  The  Global  Carbon  Cycle:  SCOPE  Report  13,  B. 
Bolin  et  al.,  eds.,  pp.  57-77  Wiley,  New  York,  1979. 

32.  G.  I.  Taylor,  “The  Formation  of  Emulsion  in  Definable  Field  of  Flow,” 
Proceedings  of  the  Royal  Society,  London,  Series  A,  vol.  146,  p.  501, 
1934. 

33.  A.  Acrivos,  The  Breakup  of  Small  Drops  and  Bubbles  in  Shear  Flows, 
New  York  Academy  of  Sciences,  New  York,  1983. 

34.  J.  M.  Rallison,  Journal  of  Fluid  Mechanics,  vol.  109,  p.  456,  1981. 

35.  J.  O.  Hinze,  “Fundamentals  of  the  Hydrodynamic  Mechanism  of 
Splitting  in  Dispersion  Processes,”  American  Institute  of  Chemical 
Engineers  Journal,  vol.  1,  no.  3,  p.  280,  1955. 

36.  P.  H.  Clay,  Proceedings  of  the  Royal  Academy  of  Sciences,  vol.  43, 
pp.  852-979,  1940. 

37.  J.  O.  Hinze,  Turbulence,  Second  Edition,  McGraw-Hill,  New  York, 
1975. 

38.  C.  A.  Sleicher,  Jr.,  “Maximum  Stable  Drop  Size  in  Turbulent  Flow,” 
American  Institute  of  Chemical  Engineers  Journal,^  ol.  8,  no.  4,  p. 
471,  1962. 

39.  M.  Sevik  and  S.H.  Park,  “The  Splitting  of  Drops  and  Bubbles  by 
Turbulent  Fluid  Flow,”  Journal  of  Fluid  Engineering,  p.  53,  1973. 

40.  A.  N.  Kolmogorov,  “On  the  Disintegration  of  Drops  in  a  Turbulent 
Flow,”  Doklady  Akad.,  Nauk,  SSSR,  vol.  66,  p.  825,  1949. 

41.  S.  A.  Morsi  and  A.  J.  Alexander,  “An  Investigation  of  Particle 
Trajectories  in  Two-Phase  Flow  Systems,”  Journal  of  Fluid 
Mechanics ,  vol.  55,  p.  193,  1972. 

42.  F.  Odar  and  W.S.  Hamilton,  “Forces  on  a  Sphere  in  a  Viscous  Fluid,” 
Journal  of  Fluid  Mechanics,  vol.  18,  pp.  302,  1964. 

43.  N.  K.  Madavan,  S.  Deutsch,  and  C.L.  Merkle,  “Measurements  of 
Local  Skin  Friction  in  a  Microbubble  Modified  Turbulent  Boundary 
Layer,”  Technical  Memorandum  84-136,  Pennsylvania  State 
University  Applied  Research  Laboratory,  1984. 

'44.  G.S.  Migirenko  and  A.R.  Evseev,  “Turbulent  Boundary  Layer  with 
Gas  Saturation,”  Problems  of  Thermophysics  and  Physical 
Hydrodynamics  (in  Russian),  Novosibirsk,  Nauk,  1974. 


350 


SYMMETRIC  BUBBLE 


TOP  VIEW 


(a)  STATIC  ENVIRONMENT  (b)  ENVIRONMENT  WITH  EXTERNAL  FLOW 

Figure  1.  Bubble  Formation  Geometry  and  Nomenclature  in  Static  and  Flowing  Environments 


(a)  SHEARED  SPHERICAL  CAP 

•  FORMATION  TIME  OF  A 
SPHERICAL  BUBBLE  IS 
MUCH  LONGER  THAN 
THE  FLOW  TIME  OVER 
ONE  PORE  RADIUS 


(b)  SINGLE  BUBBLE 

•  BUBBLE  FORMATION 
TIME  IS  LONGER  THAN 
FLOW  TIME  OVER  THE 
PORE  RADIUS 


(C)  INTERMEDIATE 

.  CAVITY  FORMATION 
TIME  IS  COMPARABLE 
TO  FLOW  TIME  OVER 
THE  PORE  RADIUS 


(d)  JET  DISINTEGRATION 

•  JET  FORMATION  TIME 
IS  SHORTER  THAN 
FLOW  TIME  OVER  THE 
PORE  RADIUS 


Figure  2.  Bubble  Formation  Time  Analysis 


351 


PROBABILITY  DENSITY  pOw> 

0.00  0.50  1.00  1.50  2,00 


IMTERMEDIATE 

REGIME 


JET  REGIME  -►] 


I  TANGENTIAL  .^NORMAL 
FORCE  BALANCE  I  =ORCE  BALANCE 


FLOWING  LIQUID  LIQUID  AT  REST 


bubble 

d 

pore  1Q1  ■ 


WATER  DRAG  ON  SAFFMAN  LIFT 

WATER  DRAG  ON  BUBBLE  =  SURFACE  TENS 

A  SPHERICAL  CAP  »  SURFACE  TENSION  BETWEEN  GAS 

SURFACE  TENSION  BETWEEN  GAS  BUBBLE  AND 

BETWEEN  CAP  BUBBLE  AND  WATER  ON  WAI 

AND  WATER  ON  WATER  ON  WALL 
WALL 


1  (  3*wdpore 


SAFFMAN  LIFT  =  SAFFMAN  LIFT  « 

SURFACE  TENSION  ADDED  WATER 

BETWEEN  GAS  INERTIAL  FORCE 

BUBBLE  AND  AROUND  AN 

WATER  ON  WALL  EXPANDING 


PHYSICS  GAS  JET 
UNKNOWN  INSTABILITY 
|  PERPENDICULAR 

TO  WATER  FLOW 


,12CL\  Uq  /  gT 


Y>9d  porey 
BUBBLE 
BUOYANCY= 
SURFACE  TENSION 
BETWEEN  GAS 
BUBBLE  AND 
WATER  ON  WALL 


-M1' 

Uq  d2pore/ 


pore  / 

GAS  JET 

INSTABILITY  WITH 
BUOYANCY, 
WATER  AT  REST 


INCREASING  SPEED  INCREASING  GAS  INJECTION  RATE 


I  DISCRETE 
HOLES 


INJECTION  COEFFICIENT  PER  PORE  - Per  Pore- 

Uotc  d2pore 

Figure  3.  Approximate  Realms  of  Bubble  Diameter  Criteria 


vpore 

Uo 


©  SANDBORN  HOT-FILM  DATA  (1979) 

1  ,  (Lntw  _  v)* 

- 7 —  exP  (-  — TP - ) 

t  <j/2ir  2a 

w 

_  CURVE  FIT  TO  DATA  MEAN  AND  VARIANCE 

\x  =  1.02,  a  =  0.23 

LEAST  -  SQUARE  FIT  TO  DATA 

H  =  1.12,  a  =  0 . 2  9 

d  MODIFIED  SANDBORN  DATA 

—CURVE  FIT  TO  MODIFIED  SANDBORN  DATA 
MEAN  AND  VARIANCE  ,  n  =  i.53,  a  =  0.23 

— LEAST  SQUARE  FIT  TO  MODIFIED 
SANDBORN  DATA  ,  n  =  i.47,  a  =  0.23 


NORMALIZED  WALL  SHEAR  STRESS  Tw/tw 


Figure  4.  Normalized  Probability  Density  Distribution  of  Surface  Shear  Stress  over  a  Flat  Plate 


352 


UG  =  12  kts. 


Figure  6.  Comparison  of  Rayleigh  and  Lognormal 
Fits  to  GallagheFs  Bubble  Size  Spectrum 


Figure  5.  Bubble  Size  Spectrum  Obtained 
by  Gallagher  (1984)  with  an  MIT  Camera 
and  Bete  Fog  Analyzer 


15  ^ 


HI 

o 

z 

LU 

DC 

DC 

3 

O 

O 

o 


c  =0.2  at  Ren  =4x10 

D  D 

c  =  0.01 


200 


400  600  800  1000 

BUBBLE  DIAMETER  IN  MICRONS 


Figure  7.  Comparison  of  Simulated  Bubble  Size 
Spectra  with  Gallagher ys  Ocean  Data 


UQ  =  8  ft/sec 
Cq  =  0.002 


A)  TAP  WATER 


B)  SALT  WATER 


Figure  8.  Microbubbles  Ejected  Through  Two  Rings 


353 


Turbulent  Drag  Reduction 
Methods:  Electromagnetic 
Drag  Reduction 


357 


ENGINEERING  INSIGHT  OF  NEAR -WALL  MICROTURBULENCE  FOR  DRAG  REDUCTION  AND 
DERIVATION  OF  A  DESIGN  MAP  FOR  SEAWATER  ELECTROMAGNETIC  TURBULENCE  CONTROL 


J.C.S.  Meng 

Naval  Undersea  Warfare  Center 
Newport,  Rhode  Island  02841-1708 
mengjc@code80.npt.nuwc.navy.mil 

Abstract  -  The  latest  findings  regarding  the  dynamics  and  cause-effect  relationships  of  near-wall  microturbulent  events  are  summarized,  together 
with  quantification  of  the  sequence  of  microturbulent  events  and  a  description  of  the  geometric  pattern  of  microturbulent  events.  A  historical 
perspective  on  microturbulence  and  drag  reduction  is  given  in  terms  of  phenomenological  structural  models  and  the  effects  of  drag  reduction  on 
near-wall  microturbulence  events.  With  this  focus,  the  engineering  dynamics  of  the  key  microturbulent  events  are  expressed  in  terms  of 
microturbulent  spatial  (streamwise,  spanwise,  normal  to  wall)  and  temporal  scales  versus  Reynolds  number.  From  these  dynamics,  rudimentary 
estimates  of  the  force  and  energetics  of  each  event  are  derived  based  on  known  phenomenological  turbulence  structural  models.  The 
electromagnetic  turbulence  control  (EMTC)  and  drag  reduction  concepts  are  related.  The  spatial  distribution  of  the  control  elements  relative  to 
the  microturbulence  patterns,  the  electrical  field  actuation  frequency  versus  microturbulence  occurrence,  and  the  Lorentz  pressure  gradient  power 
and  EMTC  efficiency  in  terms  of  the  magnetohydrodynamic  interaction  parameter  and  load  factor  map  are  described.  The  conclusion  is  that  any 
methodology  for  control  of  turbulence  can  be  effective  only  if  it  is  built  on  a  robust  foundation  of  the  near-wall  turbulence  phenomenology. 


Emerging  techniques  in  drag  reduction  invite  a  fundamental 
question,  i.e.,  based  on  the  known  dynamics  and  cause-effect 
relationships  of  microturbulent  events,  where  should  the  turbulence 
production  chain  be  disrupted?  Any  effective  drag  reduction  strategy 
must  eventually  be  traced  to  the  root-cause  of  turbulence  production. 
To  address  this  question,  some  of  the  currently  known  cause-effect 
relationships  of  microturbulent,  near-wall  events,  the  turbulence 
production  cycle,  and  related  drag  reduction  strategies  are  summarized. 
The  insights  gained  should  be  very  useful  for  practical  engineering 
applications  of  drag  reduction. 

1.  CAUSE-EFFECT  RELATIONSHIPS  OF  MICRO¬ 
TURBULENT  EVENTS  AND  TURBULENCE  PRODUCTION 
CYCLE 

Smith  [1]  described  how  to  advance  from  descriptive  and 
empirical  results  to  a  synthesis  of  cause-effect  relationships  implied  by 
microturbulent  events.  He  illustrated  that,  because  of  the  high  shear 
flow  near  the  wall,  the  spanwise  line  vortex  is  distorted,  followed  by  the 
narrowing  of  the  streamwise  parts  and  broadening  of  the  bent  spanwise 
parts  of  the  hairpin  vortices  as  the  distortion  progresses,  leading  to  a 
universal  spanwise  spacing  in  viscous  units  of  about  100.  Multiple 
vortex  lines  interact  with  each  other,  resulting  in  migration  of  both 
vortices  and  vorticity  away  from  the  wall — a  mechanism  by  which 
smaller  initial  vortices  evolve  into  larger  and  more  visible  vortex 
structures.  The  well  observed  low-speed  streaks  can  be  explained  in 
terms  of  the  trailing  part  of  the  interacting  hairpin  vortices.  The 
bursting  of  the  vortices  is  simulated  as  a  result  of  the  interaction 
between  the  essentially  inviscid  vortex  and  the  viscous,  erupting,  near¬ 
wall  fluid  and  in  response  to  the  passage  of  wall-region  vortices.  The 
response  is  made  visible  in  terms  of  the  sudden  increase  in  the 
displacement  thickness  due  to  the  interaction.  If  the  vortex  is  strong 
enough,  it  leads  to  a  burst;  if  not,  streaks  may  form.  Impingement  of 
vortices  on  the  streaks  creates  the  appearance  of  a  waviness  and 
swaying.  Regeneration  of  the  vortices  is  simulated  as  a  result  of  the 
similar  three-dimensional  unsteady  interaction  creating  an  adverse 
streamwise  pressure  gradient  in  the  region  between  the  trailing  vortex 
lines.  As  the  vortex  moves  progressively  closer  to  the  wall,  the  adverse 
pressure  gradient  intensifies  and  local  flow  separates,  leading  to 
ejection.  Subsequent  displacement  of  the  ejected  fluid  is  counteracted 
by  an  inflow  of  higher  momentum  fluid  from  immediately  upstream, 
which  appears  as  the  sweep  event,  thus  completing  the  streak,  ejection, 
burst,  and  sweep  cycle.  Numerical  simulations  carried  out  by  Robinson 
[2]  also  supported  Smith’s  cause-effect  relationships  and  showed  that 
less  than  50%  of  lifted  streaks  roll  up  to  form  a  new  vortex;  the  others 
dissipate  and  disappear.  Those  that  roll  up  and  erupt  penetrate  to 
distances  on  the  order  ofy+«100. 

Choi  [3]  provided  another  cause-effect  near- wall  turbulence 
model,  starting  from  his  observation  of  “near-wall  bursts,”  an  event 
similar  to  sweep  but  occurring  very  near  to  the  wall  at  about  y +  <15. 
These  near-wall  bursts  appear  in  a  staggered  pattern. 


In  search  of  a  unified  framework  to  unite  several  seemingly 
disjointed  concepts,  a  process  of  hairpin  vortex  growth  and  the 
formation  of  coherent  hairpin  packets  in  wall  turbulence  was  proposed 
by  Zhou  et  al.  [4].  Using  a  combination  of  particle  image  velocimetry 
and  numerical  simulations  Ree=  930,  they  found  that  the  hairpin  vortex 
dynamics  can  unify  several  earlier  models  and  quantify  the  dynamic 
conditions  under  which  they  can  occur.  Drawing  insights  from  both  the 
experiments  and  numerical  simulations,  they  showed  that  the  shear 
layer,  the  ejections,  the  low-speed  streaks,  liftup,  oscillation,  and  burst 
all  evolve  from  the  hairpin  vortex  packets.  The  hairpin  packet  forms 
low-speed  regions  extending  several  hundred  y+  above  the  wall  and 
several  thousand  viscous  lengths  downstream.  Above  a  critical  layer,  the 
hairpin  vortex  grows  and  multiplies,  while  below  a  critical  layer  the 
vortex  gradually  dissipates.  With  sufficient  strength,  a  single  hairpin 
can  grow  and  create  both  new  quasi-streamwise  vortices  and  new 
hairpin  vortices.  The  vortices  in  the  packet  advect  downstream  with 
little  dispersion. 

The  simulation  of  Zhou  et  al.  [4]  provided  a  detailed  account  of 
the  sequence  of  the  dynamic  events  leading  to  the  formation  of  an  re¬ 
shaped  vortex  and  sorted  out  the  causes  and  effects  of  the  generation 
mechanism.  By  subtracting  the  convection  velocity  and  using  the 
imaginary  part  of  the  eigenvalue  of  the  velocity  gradient  tensor,  they 
visualized  the  vortical  structure  with  great  clarity.  The  hairpin  vortex 
packet  creates  a  region  of  low-momentum  flow  between  itself  and  the 
wall.  This  low-momentum  region  impinges  on  the  upstream  high- 
momentum  fluid  to  form  an  upstream  shear  layer.  Beneath  this  low- 
momentum  region  and  within  the  horizontal  part  of  the  vortices  is  the 
low-speed  streak  between  the  wall  and  y+  *  20.  Beneath  each  primary 
hairpin  vortex  is  a  flow  induced  by  the  vortex  induction  away  from  the 
wall  and  upstream;  this  is  the  ejection.  Multiple  ejection  events  form  the 
burst.  The  hairpin  vortices  have  a  diameter  of  approximately  25-50 
viscous  units.  The  average  distance  from  wall  is  about  y+  -  78.  The 
spanwise  spacing  of  the  vortices  is  about  100  viscous  units  near  the 
buffer  region  and  decreases  to  about  40  away  from  the  wall  toward  the 
head  of  the  vortex.  The  streamwise  separation  between  the  hairpin 
vortices  is  about  100-150  viscous  units.  There  is  also  a  stagger  of  about 
25-50  spanwise  spacing  units,  leading  to  a  12°  pattern.  The  envelope  of 
the  hairpin  vortex  packet  makes  an  angle  of  15°  to  17°  with  the  wall.  It 
takes  about  /+  «  25  for  the  hairpin  vortex  to  evolve  into  a  shear  layer.  It 
takes  another  /+  ~  25  for  the  ejection  flow  to  evolve  at  a  height  of  about 
y+  «  85.  Overall,  it  takes  about  f  *  120  to  complete  the  cycle  of  the 
creation  of  a  new  hairpin  vortex.  This  populates  the  entire  boundary 
layer  with  hairpin  vortices  and  streamwise  vortices. 

One  may  argue  that  all  of  these  results  have  been  derived  from 
relatively  low  Reynolds  number  flow  visualizations  and  numerical 
simulations,  and  that  extrapolation  to  higher  Reynolds  numbers  needs  to 
be  validated.  In  a  very  innovative  experiment  conducted  over  a  flat 
plate  over  the  Great  Salt  Lake  Desert,  Klewicki  et  al.  [5]  showed  that  at 


359 


Ree  «  1.5  x  10  6  the  mean  spanwise  spacing  of  low-speed  streaks  was 
approximately  100.  In  addition,  they  also  found  that  the  crescent¬ 
shaped  pocket  pattern  width  is  *  127,  which  follows  a  scaling  law  of 
Ree  n ,  and  that  the  mean  time  between  pocket  events  is  f  «  36. 
Ferguson  et  al.  [6]  presented  a  Markov  state-transition  analysis  of 
turbulence  structure  above  a  gravel  bed.  The  Markov  states  were 
interpreted  as  the  four  quadrants  defined  by  Lu  and  Willmarth  [7]  of 
the  fluctuating  streamwise  and  normal  velocity  components.  Ferguson 
et  al.’s  measurements  of  transition  probabilities  illustrated  a  Markov 
probability  methodology  for  characterizing  the  sequence  of  the  wall 
layer  turbulence  phenomenology.  They  showed  that  a  statistically 
significant  preference  for  the  wall  layer  undergoes  acceleration, 
declination,  deceleration,  and  then  inclination,  i.e.,  through  quadrants  1 
,2,  3,  4,  1.  This  sequence  suggests  the  coherent  structure  of  streak, 
ejection,  burst,  sweep,  and  back  to  streak.  Gyr  and  Muller  [8]  showed 
that  bedforms  reflect  the  interaction  of  coherent  flow  structures  with  the 
size  of  the  grains  and  the  bedform  height.  Depending  on  the  size  and 
height  in  viscous  units,  smooth  bed,  ripple,  bedform,  and  dunes  are 
characterized.  Consistent  with  intuition,  sweeps  are  shown  to  be  the 
mechanism  for  sediment  transport  and  are  responsible  for  grain  motion. 
Grain  height  patterns  are  then  considered  to  be  a  visualization  of  the 
ejection-sweep  events.  Gyr  and  Muller  showed  that,  using  the 
convective  velocity,  the  sweep  frequency  can  be  translated  into  a  length 
scale  to  form  a  rhomboidal  pattern,  with  periodic  streamwise  length  in 
viscous  units  of  about  500,  and  spanwise  spacing  viscous  scale  of  about 
100,  again  producing  a  pattern  of  12°.  This  pattern  also  inspires  the 
hypothesis  that  the  sweeps  are  synchronized  in  the  statistical  sense. 

Figure  1  combines  the  above  information  and  extends  the 
conceptual  schematic  of  near-wall  phenomenology  (Meng.[9]). 

2.  NEAR-WALL  EVENTS  AND  DRAG  REDUCTION 
STRATEGIES 

All  of  these  findings  are  very  illustrative,  but  how  do  we  make 
them  useful  for  engineering  applications?  Since  we  concluded  earlier 
that  any  practical  drag  reduction  approach  must  focus  on  affecting  near¬ 
wall  structures,  and  since  we  know  the  complete  cycle  of  near-wall 
events  and  their  relevance  to  turbulence  production,  the  question  is 
which  event  should  be  inhibited  to  achieve  maximum  drag  reduction. 

One  approach  can  be  derived  by  observing  that  the  fundamental 
fluid  dynamic  cause  of  high  drag  or  momentum  loss  is  the  sweep,  which 
results  from  ejection  and  burst,  which  in  turn  results  from  an  adverse 
pressure  gradient  in  the  near-wall  region  caused  by  viscous/inviscid 
interaction.  Therefore,  to  control  the  turbulence  or  to  achieve  drag 
reduction,  one  would  rely  on  controlling  (at  the  microscale  level) 
creation  of  the  adverse  pressure  gradient.  This  may  lead  to  the  concept 
of  microcells  of  a  streamwise  favorable  pressure  gradient  to  determine 
where  and  when  it  detects  a  strong  enough  microflow  separation. 
Before  proceeding  to  the  drag  reduction  strategy,  let  us  first  examine  the 
empirical  facts  of  the  drag  reduction  effects  on  near-wall  events. 

2.1  Drag  Reduction  Effects  on  Microturbulent  Events.  Tiederman 
and  Luchik  [10]  injected  polymer  into  the  sublayer  and  found  increases 
in  A+  and  in  the  time  between  bursts  T b-  Using  wall  pressure 
measurements,  they  also  established  that  the  increase  in  A+  and  T b 
corresponds  to  drag  reduction.  The  upward  shift  in  the  log-law  velocity 
profile  has  been  well  observed  in  polymer  flows.  Sirmalis  [11]  observed 
dyed  turbulent  boundary  layers  with  low  concentrations  of  polymer  and 
found  that  the  fine-scale  turbulence  was  eliminated,  leaving  only  coarse 
turbulence,  and  that  the  boundary  layer  thickness  was  thinned. 

For  passive  control,  Choi  [3]  examined,  as  an  example,  the 
relevance  of  the  near-wall  turbulence  structures  over  the  drag-reducing 
riblets.  He  found  that  the  mean  velocity  profile  shifted  away  from  the 
wall,  and  he  found  an  increase  of  viscous  sublayer  thickness  similar  to 
that  produced  by  drag-reducing  polymer.  The  duration  of  the  near-wall 
burst  was  reduced  by  a  factor  of  two,  whereas  the  frequency  was 
increased.  The  average  spanwise  spacing  between  the  vortex  pairs  over 
a  riblet  surface  was  two  times  larger  than  that  over  a  smooth  surface. 


Choi  et  al.  [12]  applied  direct  numerical  simulations  of  turbulent  flows 
over  riblet  surfaces  and  showed  that  riblets  mitigate  the  Reynolds  shear 
stress-producing  events  by  restricting  the  location  of  the  streamwise 
vortices  above  the  wetted  surface,  so  that  only  a  limited  area  of  the 
riblets  is  exposed  to  the  sweeps,  and  by  impeding  the  spanwise  cross¬ 
stream  flows  necessary  to  replace  the  near-wall  fluid  ejected  away  from 
wall  during  ejection.  Effects  on  the  mean  velocity  and  turbulence 
statistics  are  limited  to  the  inner  region  of  the  boundary  layer.  The 
observed  global  effects  are  an  upward  shift  in  the  log-law  velocity 
profile,  increased  sublayer  thickness,  displaced  virtual  origin  of  the  wall, 
reduced  momentum  thickness,  and  an  increase  in  mean  streak  spacing. 
Through  simulations,  Kim  et  al.  [13]  found  that  the  center  of  the 
streamwise  vortex  is  located  on  average  at  /  *  20,  with  a  diameter 
about  (f  «  30,  so  that  the  optimal  spacing  of  the  riblets  is  /  *  20,  with 
an  included  angle  of  60°.  This  is  probably  the  most  direct  example  of 
how  basic  near-wall  turbulence  understanding  was  used  to  design  a  drag 
reduction  scheme.  Recently,  Tang  and  Clark  [14]  showed  that  the  peak 
value  w'nm  is  lower  by  10%,  the  peak  in  the  w'rms  profile  shifts  from  /  « 
15  for  the  plain  surface  to  /  «  25  for  the  riblets  and,  correspondingly, 
the  peak  location  of  turbulence  production,  defined  as  the  Reynolds 
stress  multiplied  by  mean  flow  gradient,  is  also  pushed  toward  /  *  25. 
The  probability  density  functions  show  a  dramatic  reduction  in  the 
occurrence  of  ejections  and  sweeps  as  compared  with  a  smooth  surface. 

For  the  active  control  case,  Kim  [15]  described  a  numerical 
experiment  of  active  turbulence  control  by  suppressing  the  sweep  and 
ejection  events  associated  with  the  streamwise  vortices  using  out-of- 
phase  blowing  and  suction.  The  results  showed  that  the  out-of-phase 
blowing  prevents  the  formation  of  high  vorticity  regions  on  the  surface. 
These  regions  are  located  away  from  the  surface,  and  the  strength  of  the 
vorticity  is  reduced,  resulting  in  a  reduction  of  the  surface  viscous  drag. 
The  structure  of  the  wall  layer  streaks  has  also  been  changed,  with  their 
strength  reduced  considerably  and  increased  physical  spacing,  while 
mean  spacing  in  wall  units  stays  approximately  the  same.  Using  well- 
established  numerical  simulations,  Choi  et  al.  [16]  showed  that 
significant  drag  reduction  is  achieved  when  the  surface  boundary 
condition  is  modified  to  suppress  the  dynamically  significant  coherent 
structures  present  in  the  wall  region.  They  identified  two  key  drag- 
reduction  mechanisms:  first,  deterring  the  sweep  motion  without 
modifying  the  primary  streamwise  vortices  above  the  wall,  so  that  the 
high  shear  rate  regions  on  the  wall  are  moved  to  the  interior  of  the  flow; 
and,  second,  stabilizing  and  preventing  lifting  of  the  spanwise  vorticity 
near  the  wall,  thereby  suppressing  a  source  of  new  streamwise  vortices 
above  the  wall.  The  apparent  outward  shift  of  turbulence  statistics  in  the 
controlled  flows  indicates  a  displaced  virtual  origin  of  the  boundary 
layer  and  a  thickened  sublayer.  It  was  found  in  numerical  simulations 
with  active  control  that  there  is  an  upward  shift  in  the  log-law;  namely, 
the  intercept  of  the  log-law  with  u  =/  is  increased  from  /  *  10  in  the 
natural  state  to  /  »  15.  Peak  locations  of  all  turbulence  intensities, 
production,  and  dissipation  are  shifted  away  from  the  wall  by  the  same 
amount.  The  viscous  sublayer  is  thickened  and  the  displacement 
thickness  increased,  while  the  momentum  thickness  is  decreased,  which 
is  related  to  the  skin-friction.  The  streaky  structures  below  /  *  5  are 
clearly  diminished,  and  the  streak  spacing  above  /  *  5  is  increased  by 
the  control.  The  local  maximum  of  the  streamwise  vorticity  fluctuations 
in  the  controlled  flows  is  farther  away  from  the  wall  compared  with  that 
in  the  natural  flows,  suggesting  that  the  sweeps  are  attenuated. 

2.2  Strategies  for  Near-Wall  Turbulence  Modification  for  Drag 
Reduction.  Jimenez  and  Moin  [17]  carried  out  numerical  experiments 
by  reducing  the  spanwise  spacing  of  the  computational  domain  below 
100v/wr  and  found  that  the  flow  does  not  remain  turbulent  unless  the 
spanwise  domain  is  increased.  Jimenez  and  Moin  suggested  that 
without  streaks  there  would  not  be  turbulence.  Kim  [15]  suggested  that 
reducing  the  streaks,  or  the  longitudinal  vortices  that  create  the  streaks 
due  to  interaction  with  the  wall,  is  the  best  strategy  for  turbulence 
control.  Choi  [3]  concluded  that  given  the  strategy  of  restricting  the 
spanwise  movement,  the  effectiveness  can  be  maximized  by  choosing 
the  optimal  spacing  of  the  riblets  so  that  it  is  nearly  equal  to  the  gap 
between  the  longitudinal  vortices  during  the  near-wall  bursts. 


360 


A  useful  observation  by  Choi  et  al  [12]  is  that  sweep  dominates 
Reynolds  stress  production  near  the  wall,  while  ejection  dominates  away 
from  wall.  This  finding  raises  a  possibility  for  efficient  wall  skin- 
friction  reduction  methodologies;  i.e.,  should  the  focus  be  solely  on 
reducing  sweeps  rather  than  on  both  primary  microturbulent  events. 
Choi  et  al.  [16]  stated  that  drag  is  reduced  mainly  by  deterring  the 
sweep  motion  without  modifying  the  primary  streamwise  vortices  above 
the  wall,  so  that  the  high-shear-rate  regions  on  the  wall  are  moved  to  the 
interior  of  the  flow  y+  >  5.  Active  control  changed  the  evolution  of  the 
wall  vorticity  layer  by  stabilizing  and  preventing  lifting  of  the  spanwise 
vorticity  near  the  wall,  thus  weakening  a  source  of  new  streamwise 
vortices  above  the  wall.  It  was  also  observed  that  active  control 
schemes  do  not  alter  the  structure  of  the  outer  wall  turbulence,  but 
simply  attenuate  its  strength  and  move  the  effective  origin  outward. 

Kim  [15]  suggested  an  active  scheme  that  detects  sweeps  or 
ejections  and  that  disturbs  their  sequence  of  energy-producing  activities 
each  time  the  sweeps  or  ejections  are  seen  to  affect  the  turbulent  events, 
it  is  possible — based  on  numerical  simulations — to  achieve  20%  and 
40%  drag  reductions,  respectively,  for  suction/blowing  at  the  wall 
surface  and  for  spanwise  wall  oscillation.  Choi  et  al.  [16]  compared 
their  results  from  active  blowing  and  suction  with  those  of  Narasimha 
[18]  from  unsteady  blowing  and  suction  and  showed  that  the  former  has 
a  significant  effect  on  turbulence  statistics  away  from  the  wall,  while  the 
latter  has  only  marginal  effects  in  the  interior  of  the  flow.  The 
difference  appears  to  be  due  to  the  use  of  a  feedback  control.  Even  in 
cases  where  the  mass  input  at  the  wall  is  applied  passively  at  the 
bursting  frequency,  useful  interaction  may  not  take  place  between 
control  inputs  and  flow  structure  because  of  the  spatial  and  temporal 
randomness  of  turbulence  structure  (Bushnell  and  McGinley  [19]). 

Choi  et  al.  [16]  also  investigated  a  variety  of  strategies  for  active 
control  of  dynamically  significant  coherent  structures  to  achieve  skin 
friction  reduction.  It  was  found  that  wall  pressure  alone  is  not  an 
adequate  detector  of  the  flow  toward  the  wall  or  away  from  it.  Surface 
shear  stress  correlates  better  with  the  normal  velocity,  although  the  best 
indicator  is  the  spanwise  derivative  on  the  wall  of  the  normal  gradient  of 
spanwise  velocity,  which  has  little  practical  application  potential. 
Handler  et  al.  [20]  investigated  use  of  phase  randomization.  By 
selectively  randomizing  the  largest  length  scales  of  the  turbulence,  they 
found  a  50%  drag  reduction,  a  phenomenon  similar  to  that  of  polymer 
injection.  Figure  2  summarizes  the  foregoing  observations. 

Reasoning  that  the  spatial  dimensions  and  time  periods  of  the 
near-wall  events  are  not  identical  in  each  occurrence  but  rather  they 
evolve,  grow,  and  dissipate  as  a  function  of  time  and  they  do  not  advect 
in  a  frozen  pattern  (as  Taylor’s  hypothesis  holds)  but  can  be  statistically 
determined,  Meng  [21]  invoked  a  strategy  to  capture  the  events  in 
probabilistic  sense  and  advocated  utilizing  a  Markov  process  in  the 
active  control  of  turbulence.  He  reasoned  that,  given  the  short  duration 
of  the  events,  simply  detecting  them  will  not  be  effective  and  a 
predictive  methodology  is  necessary.  In  other  words,  given  the  present 
state,  a  prediction  of  what  will  be  the  most  likely  events  to  be  taking 
place  over  a  fairly  large  area  of  repeatable  patterns  is  required  so  that 
counteractions  can  be  remotely  applied.  He  illustrated  this  strategy  by 
applying  it  to  the  electromagnetic  control  of  turbulence. 

3.  CONCEPTS  OF  ELECTROMAGNETIC  CONTROL  OF 
TURBULENCE  IN  TERMS  OF  NEAR-WALL  TURBULENCE. 

3.1  Laminar  MHD  Stability.  MHD  stability  of  an  incompressible, 
electrically  conducting  fluid,  boundary  layer  flow  along  a  flat  plate  in 
the  presence  of  a  transverse  magnetic  field  without  imposed  electric 
field  was  analyzed  by  Watanabe  [22]  and  later  by  Watanabe  [23]  with 
uniform  suction  or  injection.  The  neutral  stability  curves  of  Tollmien- 
Schlichting  waves  and  the  critical  Reynolds  numbers  were  calculated  for 
various  values  of  the  MHD  interaction  parameter  and  the  suction  or 
injection  parameter.  He  concluded  that  stability  increases  with 
increasing  MHD  interaction  and  increasing  suction  parameters,  and  that 
the  friction  coefficient  decreases  with  increasing  MHD  and  increasing 
injection  parameters,  while  displacement  thickness  increases  with 
increasing  MHD  and  increasing  injection  parameters. 


3.2  Streamwise  Vorticity  Inhibit  Theory  Based  on  Wall  Layer 
Conductance  by  Electrolyte  Injection  and  Counter  Vorticity 
Generated  by  Wallward  Lorentz  Pressure.  Nosenchuck  and  Brown 
[24]  were  the  first  to  introduce  the  concept  of  populating  the  boundary 
layer  with  discrete,  independent,  electromagnetically  controlled  regions. 
Their  hypothesis  was  based  on  direct  control  of  the  coherent  motions 
responsible  for  turbulence  production — the  normal  velocity  fluctuations 
and  the  Reynolds  stresses  in  the  near-wall  region — and  they  postulated 
that  a  relaxation  time  after  the  removal  of  the  Lorentz  force  would 
exceed  the  time  to  respond  to  it.  Their  theoretical  basis  was  that  the 
counter-vorticity  generated  by  the  Lorentz  force  would  inhibit  coupling 
between  the  inner  and  outer  regions  in  the  boundary  and  suppress  the 
amplification  of  the  streamwise  vorticity.  The  details  were  provided  in 
Nosenchuck  and  Brown’s  patent  [25]  for  the  single-tile  concept.  Their 
experiment  was  conducted  in  a  fresh-water  channel  on  a  flat  plate 
turbulent  boundary  layer,  Re$  *  1100;  the  conductance  a  of  the 
boundary  layer  was  enhanced  by  supplying  a  small  flux  of  dilute  NaOH 
electrolyte  with  the  optimal  conductivity-enhancing  layer  thickness  to 
be  10  <y+  <  30.  For  the  single-tile  experiment,  the  magnetic  flux  was 
Bz  »  0.05  tesla,  steady-state  electrical  current  density  j  <  20  mA/cm2 
over  a  dimension  on  the  order  of  x*  «  1000,  z  *  500,  and  the  laser  sheet 
illumination  was  at  a  height  of  y+  *  1.  The  flow  visualization  results 
indicated  complete  lack  of  vertical  transport  from  the  near-wall  region 
with  the  electric  field  turned  on,  thereby  substantiating  the  observation 
of  the  reduction  of  the  time-series  axial  velocity  fluctuations.  It  was 
expected  that  the  relaxation  time  after  the  electric  field  is  turned  off 
would  also  be  long  compared  with  the  time  for  the  flow  to  respond  to 
the  Lorentz  force  and  the  EMTC  on  time  would  be  short  compared  with 
the  relaxation  time.  Conversely,  Nosenchuck  and  Brown  [25]  stated 
that  by  reversing  the  Lorentz  pressure  away  from  the  wall  one  can 
destabilize  the  flow  in  the  boundary  layer  and  induce  turbulence. 

For  the  three-tile  experiment,  the  electrodes  were  sequentially 
activated  at  10  Hz,  1/3  duty  cycle,  flow  speed  at  0.15  m/s,  Ree  «  1350 
in  a  test  tank  1.5  m  wide,  0.5  m  high,  and  6  m  long.  The  magnetic  flux 
was  Bz «  0.016  tesla,  and  the  maximum  electrical  current  density  j  <  10 
mA/cm2.  Three  tiles  cover  a  total  dimension  of  0.24  m  streamwise  by 
0.18  m  spanwise,  or  in  terms  of  viscous  units  x+  «  1500  by  z+  *  1150, 
and  the  individual  tile  dimension  is  on  the  order  of  x+  »  500,  z  *  1150. 
The  laser  sheet  illumination  was  at  a  height  of/1'  *  20.  When  the  tiles 
were  activated,  little  dye  was  seen  in  the  laser  sheet,  indicating  a 
decrease  of  vertical  transport,  with  an  expected  attenuation  of  near-wall 
turbulent  motions.  A  turbulent  spot  was  also  artificially  generated 
upstream  of  the  EMTC  region,  and  the  turbulence  disappeared  once  it 
entered  the  EMTC  region.  The  injection  of  conductivity-enhancing 
electrolyte  was  still  believed  to  be  necessary. 

3.3  Spanwise  Rolling  Vortices  Resonance  Theory.  Nosenchuck  and 
Brown  [26]  presented  another  patent  using  a  multiple,  sequentially 
activated  EMTC  tile  concept.  The  ability  of  generating  a  Lorentz 
pressure  gradient  normal  to  the  wall  by  the  injection  of  a  wall  layer  of 
electrolyte  was  eliminated  and  replaced  by  the  pulsing  phase  control  of 
the  EMTC  cells.  Conceptually,  pulse  phasing  creates  a  series  of 
rotational-flow  regions  in  the  boundary  layer,  and  these  rotational  flow 
regions  continually  reinforce  the  small  amount  of  vorticity  created  by 
the  gradients  of  the  Lorentz  pressure  vector.  It  was  conceptualized  that 
a  “critical”  velocity  profile  could  be  maintained  that  would  reduce  the 
drag  to  that  between  the  laminar  flow  and  the  uninhibited  turbulent 
flows.  The  spacing  of  the  EMTC  cells  was  described  to  be  10  times  the 
height  of  the  maximum  field  strength  based  on  the  Maxwell  equations. 
The  optimal  frequency  of  the  equal-phase  tiles  was  determined 
experimentally.  It  was  found  that  there  is  a  critical  frequency  at  which  a 
condition  analogous  to  resonance  is  attained,  and  it  is  expressed  as: 
f critical  «  UJdcen,  where  Uoo  is  the  free-stream  velocity  and  dceu  is  the  cell 
spacing.  In  experiments  without  electrolyte  injection  over  a  different 
eight-cell  array  0.3  m  in  length  streamwise  by  0.4  m  spanwise  with 
magnetic  flux  of  0.6  tesla  J  *  100  mA/cm2,  each  equal-phase  tile  was 
actuated  for  0.75  s  at  1/4  duty  cycle  and  the  flow  velocity  was  0.3  m/s 
so  that  /critical  *  3  Hz,  the  measured  drag  was  reduced  90%  from  0. 1 
N/m2  to  about  0.01  N/m2. 


361 


Nosenchuck  [27]  later  conducted  more  experiments  without 
electrolyte  injection  in  a  small  water  tunnel  with  NaOH  solution  of 
electrical  conductivity  cr  *  2.5  S/m.  The  8x8  array  EMTC  plate  was  8 
in.  x  15  in.  in  size,  with  center-to-center  spacing  of  0.7  in.  between 
stainless  electrodes  and  neodymium  boron  iron  magnets.  Altogether 
there  were  64  electrodes  arranged  with  8  electrodes  per  spanwise  row 
and  8  rows  streamwise.  At  speeds  from  0.075  to  0.3  m/s,  Rex «  5  -  7.5 
x  105,  the  flows  ranged  from  the  laminar  to  the  transitional  flow 
regimes.  By  injecting  dye  from  the  leading  edge  and  laser-induced 
fluorescence  of  disodium  fluorescein,  Nosenchuck  clearly  visualized  the 
ability  of  the  Lorentz  pressure  gradient  to  create  wavelike  rotational 
flows  near  the  wall.  With  the  maximum  magnetic  induction  of  0.7  tesla 
and  applying  4  to  7  volts  (0.5  to  2  amps)  for  laminar  flow,  7  to  15  volts 
(2  to  4  amps)  for  transitional  flows,  and  15  to  38  volts  (4  to  12  amps) 
for  turbulent  flows,  they  determined  empirically  the  critical  frequencies 
from  4  Hz  (0.075  m/s)  to  900  Hz  (4  m/s).  When  EMTC  was  activated, 
hot-film  probe  output  traces  were  shown  to  indicate  80%  reduction  at 
0.525  m/s  and  25%  to  55%  reduction  at  4  m/s.  The  basic  premise  was 
that  vorticity  rotating  counter  to  that  naturally  generated  on  the  wall 
would  push  the  maximum  vorticity  away  from  the  wall.  The  maximum 
effect  occurs  when  the  vorticity  source  on  wall  generates  a  wave  pattern 
that  resonates  with  the  natural  vorticity  source  and  therefore  reduces  the 
skin  friction.  It  was  also  shown  that  the  “critical  frequency”  (above 
which  no  bubbles  were  generated)  was  about  300  Hz  at  1  m/s 

Subsequently,  Nosenchuck  [28]  showed  refined  experimental 
results  using  surface  hot-film  probes  to  measure  the  spanwise  variation 
of  streamwise  shear  stress,  cylindrical  hot-film  probes  traversing  normal 
to  the  wall  to  measure  streamwise  velocity,  and  a  pitot  tube  for  free- 
stream  characteristics.  At  low  speed,  0.07  m/s,  Rex  «  6  x  104  ,  with 
streamwise  magnets  and  cross-stream  electrodes  operated  at  3  volts  (0.2 
amps)  and  from  2  to  3.5  Hz,  results  of  streamwise  velocity  profiles 
revealed  the  expected  near-wall  jet-like  feature.  Coefficients  of  friction 
versus  Reynolds  number  showed  that  results  were  substantially  lower 
than  the  well-established  laminar  flow  lines,  which  raised  questions 
about  the  tunnel  flow  ambient  pressure  gradient.  By  showing  the  drag 
reduction  ratio  versus  the  power  ratio  defined  as  the  ratio  of  EMTC 
power  to  that  naturally  occurring,  Nosenchuck  expected  that  the 
maximum  drag  reduction  ratio  would  be  obtained  at  the  point  where  the 
power  ratio  equals  1.  In  laminar  flows  at  speeds  of  0.1  and  0.3  m/s,  the 
drag  ratio  is  larger  than  1,  meaning  a  drag  increase,  while  in  turbulent 
flows  at  speeds  of  1.0  and  3.0  m/s,  the  drag  ratio  is  less  than  1,  meaning 
a  drag  reduction  even  as  the  power  ratio  increases  beyond  1 . 

Nosenchuck  [29]  presented  some  other  tests  results  for  a  novel 
axisymmetric  model.  A  roughly  10-in. -diameter,  3-foot-long  model 
with  a  teardrop  tail  cone  and  numerous  tiles  was  released  for  buoyant 
rise  in  a  15-  to  20-foot-tall  pipe  filled  with  salt  water.  The  model  breaks 
over  the  water  surface  and  drops  back  into  the  water.  Using  magnets 
affixed  to  the  buoyant  model  and  tracking  the  time  history  of  the 
trajectory  as  the  model  lifts,  acceleration  due  to  the  activation  of  EMTC 
was  interpreted  as  a  50%  net  drag  reduction. 

Krai  [30]  modeled  turbulence  over  an  EMTC  flat  plate.  Her 
results  show  regions  of  significant  MHD  interaction  parameter  where 
drag  reduction  vanishes,  with  50%  drag  reduction  levels  over  the  region 
in  between.  Crawford  and  Kamiadakis  [31]  conducted  direct  Navier- 
Stokes  equations  simulation  in  a  fully  developed  turbulent  channel  flow 
to  simulate  Nosenchuck's  experiment  on  inclined  waves  and  pulsed 
powering.  Crawford  &  Kamiadakis’S  calculations  show  a  drag 
reduction  on  the  order  of  5%.  These  channel  flow  numerical  simulation 
results  are  progressively  more  realistic  and  therefore  significant,  as  a 
fine  resolution  EMTC  experimental  drag  measurement  is  practically 
very  challenging. 


feedback  closed-loop  control.  They  proposed  that  the  Lorentz  pressure 
over  the  tile  will  generate  a  Stokes  layer  of  vorticity  with  a  height  on  the 
order  of  V( 2  vlf),  which  is  equal  to  a  thin  wall  layer  with  a  height  of  1 
mm.  From  this  a  resonance  frequency  was  derived  to  be  70  Hz,  which 
is  in  reasonable  agreement  with  their  5x5  array  of  microtiles.  This 
observation  can  actually  be  further  extended  to  a  more  general 
relationship  between  the  Stokes  layer  and  the  ideal  height  of  the 
microturbulent  events,  or  the  height  y+  «  10,  where  maximum 
turbulence  production  takes  place.  In  other  words,  V(2v/<y)  *  10  v/uT  or, 
/  a  wr2/(100;ri;),  so  that  a  quadratic  dependence  of  the  resonance 
frequency  on  the  speed  is  expected. 

3.4  Theoretical  Spanwise  Resonance  Theory.  A  convincing 
“resonance  mechanism”  for  a  natural  turbulent  boundary  layer  without 
MHD  effects  was  derived  by  Jang  et  al.  [33].  Benney  and  Gustavsson 
[34]  first  introduced  the  “direct  resonance  concept”  that  a  three- 
dimensional  disturbance  with  certain  wave  numbers  can  grow  to  a 
relatively  large  amplitude.  This  theory  draws  from  the  empirical 
observation  by  Morrison  et  al.  [35]  of  wavelike  streamwise  fluctuations 
so  that  a  weakly  nonlinear  perturbation  around  the  mean  velocity  might 
be  applicable  to  the  turbulent  boundary  layer  bursting  process  and  from 
the  observation  by  Blackwelder  [36]  of  the  similarity  between  bursting 
and  the  laminar-turbulent  transition  phenomenon.  Guided  by  this,  Jang 
et  al.  [33]  replaced  the  Blasius  profile  with  the  mean  turbulent  profile 
including  the  sublayer,  law  of  the  wall,  and  logarithmic  law  of  wake 
profiles,  and  examined  the  Orr-Sommerfeld  and  vertical  vorticity 
equations.  The  linearized  vertical  vorticity  equation  contains  a  forcing 
term  related  to  the  vertical  velocity  that  provides  the  physical  link. 
Wherever  eigenvalues  of  both  equations  in  wave  number  space  are 
identical,  resonant  growth  occurs  at  the  streamwise  wave  number  ct * 
0.0093,  spanwise  wave  number  «  0.035,  and  frequency  a)+  »  0.09. 
Note  that  tan A(jFla+)  «15°  for  the  wedge  pattern  well  known  in  the 
transition  regime.  These  theoretical  results  agree  well  with  experimental 
data  obtained  by  Morrison  et  al.  [35].  Further,  by  applying  a  nonlinear 
perturbation  method,  Jang  et.  al.  [33]  showed  that  this  resonance 
mechanism  produced  a  mean  flow  of  counterrotating  streamwise 
vortices  in  a  turbulent  boundary  layer. 

Relating  this  well-established  theoretical  foundation  to  the  near¬ 
wall  microturbulence  phenomenology,  there  appears  to  be  a  physics- 
based  validity  to  the  theory  that  if  the  naturally  occurring  frequency  and 
the  wave  pattern  are  detected  and  countered  by  the  applied  EMTC  force 
90°  out  of  phase,  a  significant  reduction  of  turbulence  and  drag 
reduction  can  conceivably  be  achieved.  The  question  then  is:  How  can 
a  design  map  be  derived  by  relating  EMTC  to  the  near-wall  turbulence. 

4.  ESTIMATION  OF  DYNAMIC  SCALING  LAWS 


The  heuristic  kinematics  and  dynamics  of  microturbulent  events 
and  EMTC  can  be  related.  In  principle,  once  the  dominating  physics  of 
a  microtubulent  event  is  understood,  an  imposed  Lorentz  pressure 
gradient  can  be  tailored  spatially  and  temporally  to  relate  the  imposed 
EMTC  Lorentz  pressure  in  a  Eulerian  control  volume  on  an  evolving 
Lagrangian  microturbulent  fluid  element  subject  to  all  naturally 
occurring  fluctuating  forces. 

4.1  Natural  Microturbulent  Ejection  Power  Scaling.  Let  us  derive 
dynamic  scaling  law  relationships  for  all  microturbulent  events, 
especially  the  power  scaling  for  ejection  and  sweep  events  for  practical 
application.  The  power  required  for  a  microvortex  ejection  can  be 
derived  from  basic  dynamics  principles.  One  starts  with  the  definition 
of  power: 


A(mu)  _  AxAyAz  „ 

F  u~  — — —  •  u  ~  p — - (A u  +  Av) •  u 


At 


At 


Note  that  all  EMTC  experiments  conducted  so  far  have  been  based 
on  open-loop  control;  in  other  words,  all  experimental  investigators  are 
basically  exploring  trial -and-error  matrices  without  a  quantitative 
theoretical  means  to  optimize.  Bandyopadhyay  and  Castano  [32] 
explored  the  possibility  of  a  higher  payoff  in  a  more  rational  and 


-P 


(lOO)2  -50 


s  6.2  x  10 5 pup. 


362 


where  it  is  assumed  that  Ax+  =  100,  A y+=  50,  A z  =  100,  A/+  =  25,  Aw  = 
w  0+  =  80)  -  u  (y+  =  30)  =  2wr,  Av  =  wr,and  the  local  velocity  vector  is 
assumed  to  be  w  =  15wr,  v  =  ur.  From  this  relationship,  one  can  easily 
calculate  the  energy  per  ejection  by  multiplying  the  above  expression  of 

v3 

power  per  ejection  by  25v/wr2  to  obtain  1.5  x  \07  p — .  The  ejection 

power  per  unit  area  in  a  natural  burst  cycle  is  then  equal  to 
energy/ejection  x  number  of  bursts/span/second/burst  separation: 

=  1.5  x  107p~I.5  x  10~4  —2 -  _  =  230/teflO73pw3,  or  in  terms  of 

uT  v  Tb15ut 

length  Reynolds  number  =  2.6  x  103  Ref 584 pu* .  From  these 

relationships,  the  natural  microturbulent  ejection  scaling  for  5  x  105  < 
Re,  <  107  can  be  summarized: 


Dynamics: 

Vortex  liftup  force  per  ejection  =  6.2  x  10 5pv2 
Vortex  liftup  power  per  ejection  =  6.2  x  10 5puTv2 
Vortex  liftup  energy  per  ejection  =  1.5  x  \07pv3/uT 
Power: 

Natural  microejection  power  required  per  unit  area 
=  230Red'°  73puT\ 

It  is,  however,  important  to  point  out  that  ejections  contribute 
significantly  to  Reynolds  stress  but  account  for  only  a  small  fraction  of 
the  dynamics,  as  would  be  expected.  This  fact  can  be  demonstrated  by 
comparing  ejection  power  per  unit  area  with  1/2 pU  3c>  and  examining 
the  ratio,  which  can  be  expressed  as  ~  29 Ree0*55  s  0.08  and  =  0.01  for 
Reo=  103  and  104,  respectively. 

4.2  Natural  Microturbulent  Sweep  Power  Scaling.  Assuming  the 
frequency-per-span  information  for  sweeps  is  identical  to  that  of  the 
ejection,  the  power  scaling  for  sweep  events  can  also  be  carried  out.  The 
power  required  for  a  single  sweep  can  be  derived  from  basic  dynamics 
principles.  One  starts  again  with  the  definition  of  power: 


F  u  =  p(200)--100  -l]  f(4.6 . 15ar2)  +  h2]  =  2.8  x  10 6pu,v2, 
inn—  1 


100  2 
K 


where  it  is  assumed  that  Ax+  =  200,  A y+~  200,  A z+  =  100,  A/+  =  100,  Aw 
=  w  (y+  =  200)  -  w  (y+  =  30)  =  4.6wr,  Av  =  wr,  and  the  local  velocity 
vector  is  assumed  to  be  w  =  15wr,  v  =  wr.  The  energy  per  sweep  is  then 
*  v3 

=  2.8x10  p — •  The  sweep  power  per  unit  area  in  a  natural  burst 

"r 


v3  w3  1 

cycle  is  =2.8x10*/? — 1.5x10  4— —  =  4 x  l03ReBO73pu3 

wT  vz  Tb\5ut 

From  these  relationships,  the  natural  microturbulent  sweep  scaling  for  5 
x  105  <  Re,  <107  can  be  summarized: 


Dynamics: 

Force  per  sweep  =  2.8  x  10 6/?v2 
Power  per  sweep  =  2.8  x  106/?wrv2 
Energy  per  sweep  =  2.8  x  10 8/?v3/wr 
Power : 

Natural  microturbulent  sweep  power  required  per  unit  area 
=  4  x  103W07W  or  4.5x  104/?er-°-58473/?wr3 

It  is  interesting  to  see  that  sweeps  not  only  contribute  significantly 
to  Reynolds  stress  and  but  also  account  for  a  major  fraction  of  the 
dynamics.  Comparing  sweep  power  per  unit  area  with  1/2 pV  3c,  and 
examining  the  ratio  504/tefl0  8?5,  we  find  it  is  a  1.39  and  a0.17  for  Ree  = 
103  and  104,  respectively. 

4.3  Threshold  Lorentz  Pressure  Power  for  Electro-magnetic 
Turbulence  Control.  The  threshold  Lorentz  pressure  required  for 
EMTC  can  be  derived  by  comparing  the  Lorentz  pressure  power  per  unit 
area  with  the  power  per  unit  area  in  natural  microturbulent  burst  cycles. 


Conceptually,  the  threshold  is  where  this  ratio  equals  1 .  Before  one  can 
proceed  to  derive  this  ratio,  one  must  establish  the  length  and  time  scale 
assumptions,  which  are  summarized  below: 

EMTC  Length  Scales: 

Spanwise  spacing  of  Lorentz  pressure:  1 00v/wr 
Distance  normal  to  wall  of  Lorentz  pressure:  30v/wr 

EMTC  Time  Scales  (if  pulsed  or  ac): 

Lorentz  pressure  frequency:  1  !T» 

Lorentz  pressure  pulse  duration:  20v/wr2. 

Since  it  is  not  clear  a  priori  that  thresholds  would  be  identical  for  the 
cases  of  Lorentz  pressure  in  the  streamwise  direction  and  normal  to  the 
solid  wall,  calculations  will  be  carried  out  for  both  cases.  For  the 
normal  Lorentz  pressure,  the  Lorentz  pressure  power/area  =  A pu: 

r  40—  -  -  r  40—  _ 

AP  “  =  J„  “r  JxB  udy  =  J0B0}0  ’’e  -ey  udy, 


where  J  and  B  are  the  externally  applied  electrical  current  density  and 
magnetic  flux  density  vectors,  respectively. 

In  a  turbulent  boundary  layer  without  an  axial  pressure  gradient, 
the  local  vertical  velocity  has  zero  mean.  The  vertical  velocity  is  away 
from  the  wall  during  ejection  and  bursting,  and  it  is  toward  the  wall 
during  sweep.  Unless  the  Lorentz  pressure  is  sustained  long  enough  to 
give  rise  to  a  velocity  along  the  Lorentz  pressure  gradient  vector,  no  net 
work  would  be  done  to  the  flow.  In  practice,  this  implies  that  the 
EMTC  pulse  duration  should  be  longer  than  the  duration  of  bursting. 
Assuming  that  a  velocity  normal  to  the  wall  on  the  order  of  the  natural 
turbulence,  v  =  uT  in  the  active  MHD  region,  then 
.  „  f  81 


A pu  =  ~ 


l-e 


,  which  is  an  idealized  order-of-magnitude 


estimation.  The  threshold  Lorentz  power  normal  to  the  wall  must  then 
be  equal  to  or  greater  than  the  power  required  in  the  natural  ejection 
cycle.  In  other  words,  the  MHD  interaction  parameter  must  satisfy 

SOv'N 


d v,R(\Q 


1/2 pu] 


l-e 


1  x  10 

:  Re°r5*4 


For  the  streamwise  Lorentz 


pressure  gradient  case,  the  local  velocity  is  u  =  14  uT: 

yu 

uM  =  "r  — 

V 


C  40 — 

,  0  -W  °  u(y)dy. 


up  to  10 — ,  and  beyond  that  u(y)  =  wT^2.38  In  y+  +  5.2^,  so  that 


A p*u  =  J0B0uTa\ 


M 

4v 


f  20v> 

|  20v 

I 

f  20v  80v> 

l-e~u*a 
\  ) 

«-5e"w^ 

+  2 .6| 

e  ura  -e  uta 

k  y 

+  1.19  In 


+  1.19 


te) 


(  20v  80v 


80v 


80  v 
uta 


20v 

f  20v^| 

\ 

f  80v"| 

+  EA - 

—  £  - 

v  w  Ta  J 

l  uTa  J 

T  J 

( 


=  JAuA 


15  +  1.19  £. 


20v 


■Ei 


80v 

ufa 


where  E\  is  the  exponential  integral  function.  Given  the  power/area  in 
the  natural  sweep  cycle  =  4.52  x  104^e^°  584/?w3 ,  the  threshold 
streamwise  Lorentz  power  would  then  follow: 

9  x  104 


dpBoa  j  j  , 


1/2  pu] 


Re°r 


363 


where  {•}  represents  the  long  expression  of  the  geometric  factor  in  terms 
of  the  EMTC  cell  spacing  parameter  uxa/v.  It  is  interesting  to  note  that 
the  threshold  Lorentz  pressure,  in  terms  of  the  MHD  interaction 
parameter,  is  higher  for  the  Lorentz  pressure  gradient  normal  to  the  wall 
than  for  the  streamwise  case  along  the  flow. 

One  way  to  illustrate  this  threshold  condition  is  by  displaying  the 
ratio  of  the  left-hand  side  and  the  right-hand  side  as  a  function  of  the 
MHD  interaction  parameter  JBalpu J,  and  the  spacing  Reynolds  number 

uTa/v  as  a  function  of  the  length  Reynolds  number.  When  this  ratio  is 
close  to  or  greater  than  1,  the  turbulence  control  is  expected  to  be 
effective;  a  ratio  below  1  implies  less  effectiveness,  and  a  ratio  much 
above  1  may  mean  over-exertion  of  control,  implying  less  efficiency. 
Figure  3  presents  the  case  of  free-stream  Reynolds  number  =  105. 
Similarly,  figure  4  shows  the  case  where  Reynolds  number  =  107  over 
the  same  domain  of  cell  spacing  Reynolds  number  and  MHD  interaction 
parameter.  By  comparing  the  two  graphs,  one  can  see  that  as  the  free- 
stream  Reynolds  number  increases,  the  ratio  increases  for  the  same  cell 
spacing  Reynolds  number  and  MHD  interaction  parameter.  It  is 
interesting  to  note  that  the  ratio  is  the  highest  for  small  spacing  of 
electrodes  and  magnets  and  an  MHD  interaction  parameter  value  greater 
than  1.  The  ratio  decreases  as  spacing  increases  and  the  MHD 
interaction  parameter  decreases.  Both  trends  are  consistent  with  a 
rudimentary  understanding  of  EMTC  in  a  conducting  medium.  As  the 
free-stream  Reynolds  number  increases,  the  ratio  increases,  implying 
that  for  the  same  EM  cells  and  MHD  interaction  parameter  the 
turbulence  control  effectiveness  increases. 


By  setting  the  ratio  to  be  unity,  one  can  relate  the  EM  cell  spacing 
to  the  MHD  interaction  parameter  as  a  function  of  free-stream  Reynolds 
number,  thereby  defining  the  threshold  condition  as  a  function  of 
Reynolds  number.  Specifically,  this  can  be  expressed  as  Re .  =  - 
4t5.9/te,°'/ln(l  -  3124AU?e*0584)  or 

f  lxlOJ  1 

Re  fl  =  -80/ln  1-— - ^7  for  the  anti-ejection  normal  Lorentz 

^  V  A imRex  ) 

pressure  gradient  (figure  5),  and  N,m  =  6.02  x  103  584  for  the  anti¬ 

sweep  streamwise  Lorentz  pressure,  and  can  be  considered  to  be  the 
design  map. 


4.4  EMTC  Efficiency.  One  seeks  an  analytic  expression  that  will  relate 
some  basic  design  parameters  expressed  in  terms  of  nondimensional 
parameters  to  the  flow’s  nondimensional  parameters,  such  as  the 
Reynolds  number,  MHD  interaction  parameter,  load  factor,  and 
electrode  parasitic  voltage  losses.  This  expression  can  be  used  to  guide 
the  point  design  as  more  practical  approaches  are  introduced.  First,  the 

.  .  Power  Saved  by  EMTC 

ideal  efficiency  is  defined  as  77,  = - - - - — . 

Input  Power  to  Electrodes 


The  power  saved  by  EMTC  per  unit  area  =  1/2 pi?  Ac,,  where  c,  is 
the  friction  coefficient,  and  the  power  input  to  the  electrodes  per  unit 
area  =  IV,  where  /  is  the  electrical  current  and  V  is  the  voltage,  so  that 

\pU^cf 

rj.  =  — — - .  This  ratio  can  be  decomposed  into  products  of 

efficiencies  of  several  dominant  physical  processes;  namely,  77,  =  (power 
saved  by  EMTC  per  unit  area  /  power  expended  due  to  natural 
turbulence  production  per  unit  area)  *  (power  expended  due  to  natural 
turbulence  production  per  unit  area  /  Lorentz  pressure  power  per  unit 
area)  *  (Lorentz  pressure  power  per  unit  area  /  electrical  power  delivered 
in  seawater  per  unit  area)  *  (electrical  power  delivered  in  seawater  per 
unit  area  /  input  electrode  power  per  unit  area). 

In  other  words,  the  above  expression  can  be  interpreted  as  the 
product  of  several  intermediate  efficiencies:  77,  -  (turbulent  drag 
reduction  efficiency)  *  (drag  /  Lorentz  power  ratio)  * 
(electromagnetohydrodynamic  efficiency)  *  (seawater  electrode 
efficiency) 


Turbulent  Drag  Reduction  +  Natural  Turbulent  Drag 
Natural  Turbulent  Drag  Lorentz  Presure  Power 


Lorentz  Pressure  Power  +  Electrical  Power  in  Water 
Electrical  Power  in  Water  Input  Electrode  Power 


A  cf 
77  =  — 
CI 


-pU'c, 


J«B0a\ 


l-e 


10  ur 


JoM  1  e 


-Wv\ 


10  ur 


i{v-K) 


. i(y-v,)  _Acf . 

IV  cf  yC/  -AA  a  E 


It  is  interesting  to  note  that  the  major  physical  dimensionless 
parameters  —  imposed  MHD  interaction  parameter  Nm  =  (JoBoa)lpux2, 
electrical  load  factor  L  s  EI(uxB),  and  potential  ratio  V/Vo  —  emerge  in 
these  expressions.  The  same  results  can  also  be  obtained  by  a  rigorous 
application  of  the  pi-theorem.  Examining  these  expressions,  one  can 


Ac.  1  2  1 

see  that  rji  oc  — - - - ,  so  that  as  AC  -»  0  and  Z,  0,  would 

cf  Nin  11  ^  1 


approach  infinity.  This  simplistic  argument  neglects  the  fact  that  as  AC 
and  L  — >■  0,  meaning  that  no  EMTC  is  applied,  A c,l  cs  —>  0;  therefore,  77 
-»  0.  The  real  behavior  of  77,  -►  0  as  AC ,  and  L  ->  0  must  await  more 
detailed  experimental  observation;  however,  an  asymptotic  theoretical 
analysis  of  small  AC  and  L  parameters  is  described  below. 


Note  that  A cfc,  is  a  function  of  AC,  c,,  and  L.  Since  c,  is  a  function 
of  Ree,  A c,!c,  is  a  function  of  Ree,  AC,  and  L,  and  can  be  obtained  only 
via  systematic  experimental  measurements.  The  dependence  of  A c,  !c, 
on  AC  and  L  must  be  consistent  with  its  behavior  near  the  origin  of  the 
AC  ,  L  coordinates.  In  other  words,  Ac,  !c,  should 

b =  so  that  rj,  =  N°mLb f{Ree,N 

cf 

where  a  and  b  are  any  positive  values.  To  satisfy  the  large  AC,  L  value 
limit  behaviors,  i.e.,  dr),fdNm  <  0  with  AC  »  0,  L  »  0,  one  expects  that 
d\n  ft  ^InA L  <  a  and  d\wf  l  d\xil  <  b.  Based  on  experience  with 
seawater  MHD  propulsion  tests  and  the  above  observations,  one  can 
conjecture  77,  to  be  of  the  form  rji  oc  V,"  Lbe~Sime~L,  which  has  a  single 
peak  at  (AL ,  L)  -  {atb).  These  conditions  can  guide  experimenters  in 
analyzing  measurement  data. 


5.  REFERENCES 

[1]  C.R.  Smith,  “Coherent  Flow  Structures  in  Smooth-Wall 

Turbulent  Boundary  Layers:  Facts,  Mechanisms,  and 

Speculation,”  in  Coherent  Flow  Structures  in  Open  Channels , 
K.S.  Choi,  K.K.  Prasad,  and  T.V.  Truong  (eds.),  John  Wiley  & 
Sons  Ltd.,  Chichester,  England,  1996. 

[2]  S.K.  Robinson,  “The  Kinematics  of  Turbulent  Boundary  Layer 
Structure,”  NASA  Technical  Memorandum  103859,  National 
Aeronautics  and  Space  Administration,  Washington,  DC,  1991. 

[3]  K.S.  Choi,  “Near-Wall  Structure  of  a  Turbulent  Boundary  Layer 
with  Riblets,”  Journal  of  Fluid  Mechanics,  vol.  208,  1989. 

[4]  Zhou,  Meinhart,  Balachandar,  and  Adrian,  “Formation  of 
Coherent  Hairpin  Packets  in  Wall  Turbulence,”  in  Chapter  6  of 
Self-Sustaining  Mechanisms  of  Wall  Turbulence,  R.L.  Panton 
(ed.),  Advances  in  Fluid  Mechanics ,  Volume  15,  Computational 
Mechanics  Publications,  Southampton,  UK,  and  Boston,  1997. 

[5]  J.C.  Klewicki,  M.M.  Metzger,  E.  Kelner,  and  E.M.  Thurlow, 
“Viscous  Sublayer  Flow  Visualizations  at  R$  =  1  500  000,” 
Physics  of  Fluids,  vol.  7,  no.  4,  April  1995. 


364 


[6]  R.I.  Ferguson,  A.D.  Kirkbride,  and  A.G.  Roy,  “Markov  Analysis 
of  Velocity  Fluctuations  in  Gravel-Bed  Rivers,”  in  Coherent 
Flow  Structures  in  Open  Channels ,  P.J.  Ashworth,  S.J.  Bennett, 
J.L.  Best,  and  S.J.  Mclelland  (eds.),  John  Wiley  &  Sons  Ltd., 
Chichester,  England,  1996. 

[7]  S.S.  Lu  and  W.  .  Willmarth,  “Measurements  of  the  Structure  of 
the  Reynolds  Stress  in  a  Turbulent  Boundary  Layer,”  Journal  of 
Fluid  Mechanics,  vol.  101,  1973. 

[8]  A.  Gyr  and  A.  Muller,  “The  Role  of  Coherent  Structures  in 
Developing  Bedforms  During  Sediment  Transport,”  in  Coherent 
Flow  Structures  in  Open  Channels ,  P.J.  Ashworth,  S.J.  Bennett, 

J. L.  Best,  and  S.J.  Mclelland  (eds.),  John  Wiley  &  Sons,  Ltd., 
Chichester,  1996. 

[9]  J.  Meng,  “Experimental  Study  of  the  Span  wise  Vortex 
Resonance  Hypothesis  for  Turbulent  Drag  Reduction  Over  a  Flat 
Plate  in  Salt  Water,”  NUWC-NPT  Technical  Report,  Naval 
Undersea  Warfare  Center  Division,  Newport,  RI,  1997. 

[10]  W.G.  Tiederman  and  T.S.  Luchik,  “Wall  Structure  and  Drag 
Reduction,”  Report  PME-FM-82-2,  School  of  Mechanical 
Engineering,  Purdue  University,  Lafayette,  IN,  1982. 

[11]  J.E.  Sirmalis,  “A  Study  of  the  Drag  Characteristics  and  Polymer 
Diffusion  in  the  Boundary  Layer  of  an  Axisymmetric  Body,” 
NUSC  Technical  Report  4860,  Naval  Underwater  Systems 
Center,  Newport,  RI,  1976. 

[12]  H.  Choi,  J.P.  Moin,  and  J.  Kim,  “Direct  Numerical  Simulation  of 
Turbulent  Flow  Over  Riblets,”  Journal  of  Fluid  Mechanics,  vol. 
255,  1993. 

[13]  J.  Kim,  J.P.  Moin,  and  R.  Moser,  “Turbulent  Statistics  in  Fully 
Developed  Channel  Flow  at  Low  Reynolds  Number,”  Journal  of 
Fluid  Mechanics,  vol.  177,  1987. 

[14]  Tang  and  Clark  (1996)  “Near-Wall  Flow  Structure  in  a  Low 
Reynolds  Number  Turbulent  Boundary  Layer  Over  Misaligned 
Riblets,”  in  Emerging  Techniques  in  Drag  Reduction,  K.S.  Choi, 

K. K.  Prasad,  and  T.V.  Truong  (eds.).  Mechanical  Engineering 
Publications  Ltd,  Edmunds,  England,  1996. 

[15]  J.J.  Kim,  “Study  of  Turbulence  Structure  Through  Numerical 
Simulations:  The  Perspective  of  Drag  and  Reduction,”  Advisory 
Group  for  Aerospace  Research  &  Development  (AGARD) 
Report  786,  Special  Course  on  Skin  Friction  Drag  Reduction,  2- 
6  March  1992,  VKI,  Brussels,  Belgium. 

[16]  H.  Choi,  J.  Moin,  and  J.  Kim,  “Active  Turbulence  Control  for 
Drag  Reduction  in  Wall-Bounded  Flows,”  Journal  of  Fluid 
Mechanics ,  vol.  262,  1994. 

[17]  J.  Jimenez  and  P.  Moin,  “The  Minimum  Flow  Unit  in  Near-Wall 
Turbulence,”  Journal  of  Fluid  Mechanics,  vol.  225,  1991 . 

[18]  R.  Narasimha,  “The  Turbulence  Problem:  A  Survey,”  Journal  of 
the  Indian  Institute  of  Science,  vol.  64(A),  no.  1,  1983. 

[19]  D.M.  Bushnell  and  C.B.  McGinley,  “Turbulence  Control  in  Wall 
Flows,”  Annual  Reviews  in  Fluid  Mechanics,  vol.  21,  1989,  pp. 
1-20. 

[20]  R.A.  Handler,  E.  Levich,  and  L.  Sirovich,  “Drag  Reduction  in 
Turbulent  Channel  Flow  by  Phase  Randomization,”  Physics  of 
Fluids  A,  vol.  5,  1993. 

[21]  J.C.S.  Meng,  “Wall  Layer  Microturbulence  Phenomenological 
Model  and  a  Semi-Markov  Probability  Predictive  Model  for 
Active  Control  of  Turbulent  Boundary  Layers,”  in  Self- 
Sustaining  Mechanisms  of  Wall  Turbulence ,  R.  L.  Panton  (ed.), 
Computational  Mechanics  Publications,  Southampton,  England, 
and  Boston,  1997  (also  in  NUWC-NPT  Technical  Report  10434, 
Naval  Undersea  Warfare  Center  Division,  Newport,  RI,  1995). 

[22]  T.  Watanabe,  “Magnetohydrodynamic  Stability  of  Boundary 
Layers  Along  a  Flat  Plate  in  the  Presence  of  a  Transverse 
Magnetic  Field,”  Z  Angew.  Math.  Mech.,  58,  1978. 


[23]  T.  Watanabe,  “Magnetohydrodynamic  Stability  of  Boundary 
Layer  Flow  with  Suction  or  Injection  Along  a  Flat  Plate,”  Z. 
Angew.  Math.  Mech.,  vol.  67,  no.  1,  1987,  pp.  27-30. 

[24]  D.M.  Nosenchuck  and  G.L,  Brown,  “Discrete  Spatial  Control  of 
Wall  Shear  Stress  in  a  Turbulent  Boundary  Layer,”  Proceedings 
of  International  Conference  on  Near-Wall  Turbulent  Flows, 
C.G.  Speziale  and  B.E.  Lauder,  eds.,  Arizona  State  University, 
1993. 

[25]  D.  Nosenchuck  and  Garry  L.  Brown  ,  “Electromagnetic  Device 
and  Method  for  Boundary  Layer  Control,”  U.S.  Patent 
5,320,309,  1994. 

[26]  D.  Nosenchuck  and  Garry  L.  Brown,  “Multiple  Electromagnetic 
Tiles  for  Boundary  Layer  Control,”  U.S.  Patent  5,437,421, 1995. 

[27]  D.M.  Nosenchuck,  Technical  Discussion  at  Princeton  University, 
Princeton,  NJ,  24  March  1995. 

[28]  D.M.  Nosenchuck,  Technical  Discussion  at  San  Diego,  CA,  27 
July  1995. 

[29]  D.M.  Nosenchuck,  “Boundary  Layer  Control  Using  the  Lorentz 
Force  on  an  Axisymmetric  Body,”  Abstract  of  paper  presented  at 
the  ASME  Fluids  Engineering  Meeting,  Active  Control  Section, 
Ithaca,  NY,  1996. 

[30]  L.  Krai,  “Numerical  Simulations  of  Electromagnetic  Control  of 
Turbulence,”  Abstract  of  a  paper  presented  at  the  ASME  Fluids 
Engineering  Meeting,  Active  Control  Section,  Ithaca,  NY,  1996. 

[31]  C.  Crawford  and  G.  Kamiadakis,  “Reynolds  Stress  Analysis  of 
EMHD-Controlled  Wall  Turbulence,  Part  I:  Streamwise 
Forcing,”  Center  for  Fluid  Mechanics,  Turbulence  and 
Computation  #96-8,  Brown  University,  Providence,  RI,  1966. 

[32]  P.R.  Bandyopadhyay  and  J.M.  Castano,  “Micro-Tiles  for 
Electromagnetic  Turbulence  Control  in  Saltwater,  Preliminary 
Investigations,”  Symposium  on  Turbulence  Modification  and 
Drag  Reduction,  ASME  Summer  Meeting,  San  Diego,  CA,  FED 
vol.  237(2),  7-11  July  1996,  pp.  415-421. 

[33]  P.  Jang,  D.J.  Benney,  and  R.L.  Gran,  “On  the  Origin  of 
Streamwise  Vortices  in  a  Turbulent  Boundary  Layer,”  Journal  of 
Fluid  Mechanics,  vol.  169,  1986. 

[34]  D.J.  Benney  and  L.H.  Gustavsson,  “Direct  Resonance  in 
Turbulent  Boundary  Layers,”  Studies  in  Applied  Mathematics, 
vol.  64,  1981. 

[35]  W.R.B.  Morrison,  K.J.  Bullock,  and  R.E.  Kronauer, 
“Experimental  Evidence  of  Waves  in  the  Sublayer,”  Journal  of 
Fluid  Mechanics,  vol.  47,  pt.  4,  1971. 

[36]  R.  F.  Blackwelder,  “Similarity  Between  the  Laminar  Turbulent 
Transition  and  Turbulent  Boundary  Layer  Bursting,”  Physics  of 
Fluids,  26,  1983. 


6.  BIBLIOGRAPHY 

Akhavan,  R.,  R.D.  Kamm,  and  ATI.  Shapiro,  “An  Investigation  of 
Transition  to  Turbulence  in.  Bounded  Oscillatory  Stokes  Flows,  Parts 
1  and  2,”  Journal  of  Fluid  Mechanics,  vol.  225,  1991. 

Alfredsson,  P.  Henrik,  and  Arne  V.  Johansson,  “Time  Scales  in 
Turbulent  Channel  Flow,”  Physics  of  Fluids,  vol.  27,  no.  8,  August 
1984. 

Astolfi,  J.A.,  and  B.E.  Forestier,  “Study  of  the  Influence  of  External 
Manipulations  on  the  Near-Wall  Turbulence  Structure  Using  Wall 
Pressure  Fluctuations,”  1996. 

Bandyopadhyay,  P.R.,  “Turbulence  Spot-Like  Features,”  4th 
International  Conference  on  Physicochemical  Hydrodynamics , 
Reprinted  from  Annals  of  the  New  York  Academy  of  Sciences, 

Blackwelder,  R.F.,  and  H.  Ecklemann  ,  “Streamwise  Vortices 
Associated  with  the  Bursting  Phenomenon,”  Journal  of  Fluid 
Mechanics,  vol.  94,  pt.  3,  1979. 


365 


Cantwell,  Brian,  “Future  Directions  in  Turbulence  Research  and  the 
Role  of  Organized  Motion,”  Stanford  University,  Stanford,  CA. 

Choi,  Kwing-So,  “Turbulent  Drag  Reduction  Strategies”  in  Emerging 
Techniques  in  Drag  Reduction ,  by  K-S  Choi,  K.K.  Prasad,  and  T.V. 
Truong,  Mechanical  Engineering  Publications  Ltd.,  London,  1996. 

Falco,  R.E.,  “Coherent  Motions  in  the  Outer  Region  of  Turbulent 
Boundary  Layers,”  Physics  of  Fluids ,  vol.  20,  no.  10,  pt.  II,  October 
1977. 

Head,  M.R.,  and  P.  Bandyopadhyay,  “New  Aspects  of  Turbulent 
Boundary-Layer  Structure,”  Journal  of  Fluid  Mechanics,  vol.  107, 
1981. 

Hijikata,  Kunio,  Yuji  Sizuki,  and  Kenji  Iwana,  “Flow  Visualization  by 
Velocity-Pressure  Cross-Correlation,”  Transactions  of  the  ASME, 
vol.  118,  September  1996. 

Hinze,  J.O.‘,  Turbulence ,  2nd  Edition,  McGraw-Hill,  New  York,  1975. 

Kim,  H.T.S.,  S.J.  Kline,  and  W.C.  Reynolds,  “The  Production  of 
Turbulence  Near  a  Smooth  Wall  in  a  Turbulent  Boundary  Layer,” 
Journal  of  Fluid  Mechanics,  vol.  50,  pt.  1,  1971. 

Kirkbride,  Alistair  D.,  and  Rob  Ferguson,  “Turbulent  Flow  Structure  in 
a  Gravel-Bed  River:  Markov  Chain  Analysis  of  the  Fluctuating 


Velocity  Profile,”  Earth  Surface  Processes  and  Landforms ,  vol.  20, 
1995. 

Kline, S.,  W.  Reynolds,  F.  Schraub,  and  P.  Runstadler,  ”The  Structure  of 
Turbulent  Boundary  Layers,”  Journal  of  Fluid  Mechanics ,  vol.  30, 
pt.  4,  1967. 

Morrison,  W.R.B,  K.J.  Bullock,  and  R.E.  Kronauer,  “Experimental 
Evidence  of  Waves  in  the  Sublayer,”  Journal  of  Fluid  Mechanics, 
vol.  47,  pt.  4,  1971. 

Nakagawa,  Hiroji,  and  Iehisa  Nezu,  “Structure  of  Space-Time 
Correlations  of  Bursting  Phenomena  in  an  Open-Channel  Flow,” 
Journal  of  Fluid  Mechanics,  vol.  104,  1981. 

Offen,  G.R.,  and  S.J.  Kline,  “Combined  Dye-Streak  and  Hydrogen- 
Bubble  Visual  Observations  of  a  Turbulent  Boundary  Layer,” 
Journal  of  Fluid  Mechanics,  vol.  62,  1974. 

Praturi,  Ananda  K.,  and  Robert  S.  Brodkey,  “A  Stereoscopic  Visual 
Study  of  Coherent  Structures  in  Turbulent  Shear  Flow,”  Journal  of 
Fluid  Mechanics,  vol.  89,  pt.  2,  1978. 

Wark,  C.,  and  H.  Nagib,  “Experimental  Investigation  of  Coherent 
Structures  in  Turbulent  Boundary  Layers,”  Journal  of  Fluid 
Mechanics,  vol.  230,  1991. 


(Regs  10  -  10  ) 

3asjd/'bn: 

^line,  Reynolds,  Schraub  & 
Runstadler  (1967) 

Morrison,  Bullock  &  Kronauer  (1971) 
Kim,  Kline  &  Reynolds  (1971) 

Hinze  (1975) 

Brown  &  Thomas  (1977) 

Falco  (1977) 

Blackwelder  &  Ecklemann  (1979) 
Nakagawa  &  Nezu  (1981) 

Head  &  Bandyopadhyay  (1981) 
Bandyopadhyay  (1983) 


Wark  &  Nagib  (1991)  Choi  (1996) 

Astolfi  &  Forestier  (1996)  Zhou,  Meinhart,  Balachandar 
Smith  (1996)  &  Adrian  (1997) 


Figure  1.  Conceptual  Turbulent  Boundary  Layer  Near-Wall  Phenomenology 


366 


Observed 

Phenomena 


Burst 

i 


Streaks 

l 


Liftup 

i 


Ejections 

4- 


Breakup 

i 


Sweeps 

i 


2  11.0E-1  ■ 


Microturbulent  Activities 


Near-wall  burst  deforms  a 
spanwise  vortex  element 


Legs  of  counterrotating, 
streamwise  vortices  form  low- 
speed  streaks  between  the 
legs 


Stretched  vortex  evolves  into 
a  hairpin  vortex  loop 


Ejection  of  low-momentum 
fluid  away  from  wall 


Fluid  Dynamic 
Mechanisms 


Nonlinear  self-interaction 


Sweep  of  high-momentum 
fluid  toward  wall 


Near-wall  bursts  renew  under 
the  vortices,  forming  a 
staggered  pattern  relative  to 
the  previous  near-wall  burst 
and  completing  the  cycle 


Figure  2. 


Nonlinear  vortex  mutual 
induction 


U(y f)  inflectional  profile 
leads  to  instability 


Large-scale  outer 
structure  and  advection 
of  mean  shear 


Viscous-inviscid 

interaction 


Drag  Reduction  Strategies 


Riblets  impede  spanwise  movement  of  longitudinal  vortices,  reduce 
momentum  flux  within  riblet  valley,  impede  energy  redistribution  from  u ' 
to  w'  and  reduce  near-wall  burst  duration  and  intensity  (Choi,  1996). 
Spanwise  movement  of  A z+  =  50  disrupts  formation  of  longitudinal 
vortices  and  reduces  turbulence  production  (Akhavan  et  ah,  1991) 


Lorentz  pressure  gradient  suppresses  amplification  of  streamwise 
vorticity  (Nosenchuck  and  Brown,  1993) 


Polymer  injection  damps  vortical  motions,  increases  spacing  of  streaks, 
and  reduces  ejection  and  sweep  frequencies  and  intensities  (Tiederman 
and  Luchik,  1982). 

Suction-blowing  out  of  phase  with  sweep  and  ejection  inhibits 
longitudinal  vortex  interaction  with  wall  (Kim  et  ah,  1990) 


Microbubble  splitting  in  turbulence  provides  an  additional  energy 
dissipation  in  small  scale  activities  (Meng,  1985) _  _ 


Compliant  coating  motion  counters  local  fluid  motion  and  interrupts  the 
turbulence  production  cycle  (Choi,  1996).  Deferring  the  sweep  without 
modifying  the  streamwise  vortices  (Choi  et  al.,  1994) 


Randomization  of  largest  length  scale  (Handler  et  ah,  1993) 


Near-Wall  Turbulence  Activities  and  Drag  Reduction  Strategies 


MHD 

5.0E  -  4  Interaction 
Parameter 


MHD 

5.0E  -  4  interaction 
Parameter 


EMTC  Cal!  Spacing  or 
Reynolds  Number 

Figure  3.  Threshold  of  EM  Control  of  Microturbulent  Ejection  vs. 
Interaction  Parameter  and  EMTC  Cell  Spacing  at  Free-Stream 
Reynolds  Number  =  10s 


EMTC  Cali  Spacing 
Reynolds  Number 


Figure  4.  Threshold  of  EM  Control  of  Microturbulent  Ejection  vs. 
Interaction  Parameter  and  EMTC  Cell  Spacing  at  Free-Stream 
Reynolds  Number  =  107 


MHD  Interaction 
Parameter 


6.0E+6 

3.5  E+ 6  Length 
~  1.5E+6  Reynold* 

®  Number 


Figure  5.  Anti-Ejection  EMTC  Cell  Spacing  Reynolds  Number  Based  on  uT  at 
Threshold  Condition  vs.  MHD  Interaction  Parameter  and  Length  Reynolds  Number 


367 


Experiments  on  Turbulent  Channel  Flow  with  Electromagnetic  Turbulence  Control 

Xuejun  Fan  and  Garry  L.  Brown 
Department  of  mechanical  and  Aerospace  engineering 
Princeton  University 
Princeton,  New  Jersey  08540 
xfan@princeton.edu 


I.  INTRODUCTION 

The  possibility  of  controlling  the  wall  shear  stress  in  a  turbulent 
boundary  layer,  by  applying  a  Lorentz  force  J  x  B  perpendicular  to  the 
wall,  was  demonstrated  in  the  paper  by  Nosenchuck  and  Brown  (1).  A 
large  reduction  in  the  Reynolds  stress  was  found.  While  the 
measurements  and  flow  visualization  showed  a  substantial  effect,  the 
results  were  from  an  early  experiment  and  raised  a  number  of  questions. 
Two  particularly  important  issues  to  be  resolved  were:  firstly,  the  role 
that  3-dimensionality  had  played  due  to  the  arrangement  of  electrodes 
and  magnetic  poles;  and  secondly,  the  non-dimensional  scaling  to  much 
larger  free  stream  velocities  and  to  boundary  layers  of  different 
thickness.  The  aim  of  the  present  experiments  is  to  avoid  some  of  the 
complexity  of  the  earlier  experiments  and,  as  a  result,  to  more  clearly 
illuminate  the  underlying  physics  of  a  body  force  acting  on  near  wall 
turbulence,  to  impose  an  organized  structure  on  the  near  wall  flow  and 
to  explore  the  effects  of  scaling.  A  special  purpose  water  tunnel  has 
been  built  and  arranged  to  produce  a  two-dimensional  channel  flow  both 
with  and  without  wall  injection  of  an  electrolyte  or  a  fluid  of  different 
density  from  water.  The  flow  structure  near  the  wall  of  a  channel  flow  is 
known  to  be  very  similar  to  that  of  a  boundary  layer  having  the  same 
shear  stress.  The  particular  advantages  of  a  fully  developed  channel  flow 
are  that  the  shear  stress  is  a  linear  function  of  the  distance  from  the  wall 
and  can  be  readily  measured  from  the  pressure  drop  along  the  channel; 
measurements  of  the  velocity  profile  and  pressure  drop  along  the 
channel  can  be  used,  in  principle,  to  infer  the  eddy  viscosity.  Thus  the 
direct  effects  of  a  Lorentz  force  acting  on  the  flow  can  be  measured.  A 
channel  flow  also  has  the  advantage  that  a  wide  range  of  maximum  flow 
velocities  and  Reynolds  numbers  can  be  achieved.  In  the  present 
experiments  reported  here,  we  have  made  measurements  of  the  effect  of 
a  buoyancy  force  on  the  mean  flow  velocity  profile.  Nosenchuck  and 
Brown  called  electromagnetic  turbulence  control  in  which  the  effect  is 
produced  by  a  gradient  in  conductivity  “type  I”  and  the  case  of  uniform 
conductivity  ‘"type  II”.  In  the  type  I  case,  the  action  of  the  Lorentz  force 
is  analogous  to  a  buoyancy  force  with  a  corresponding  density  gradient. 
We  anticipate  presenting  the  corresponding  results  for  a  Lorentz  force  as 
well  as  the  present  results  for  a  buoyancy  force  at  the  meeting. 
Measurements  for  “type  IF’  electromagnetic  turbulence  control,  in 
which  the  conductivity  is  uniform  but  the  Lorentz  force  has  a  spatial  and 
temporal  variation,  will  also  be  made  shortly.  The  concept  of  an 
electromagnetic  riblet  is  introduced  in  this  paper. 


In  common  with  the  effects  of  buoyancy  on  a  turbulent  boundary 
layer,  an  important  parameter  for  type  I  electromagnetic  turbulence 
control  is  the  ratio  of  Lorentz  force  production  of  turbulent  kinetic 
energy  to  the  Reynolds  stress  production  of  turbulent  energy.  This 
parameter  is 

Ril  =-L'v'/ pu'v'-^- 
dy 

As  these  correlations  are  not  easily  measured  directly,  a  gradient 
Richardson  number  is  frequently  used,  i.e.  these  two  definitions  for  a 
Richardson  number  are  only  equivalent  if  the  turbulent  correlations  are 
assumed  to  be  approximated  by  eddy  viscosity  relationships  and  the 
eddy  viscosities  for  the  correlations  are  all  equal.  Thus, 

dz  dz 


)  for  the  buoyancy  case  and 


.  ,du  2 


for  the  electromagnetic  case. 


Previously  Fan  &  Brown  (2)  drew  attention  to  the  limitation  of  the 
analogy,  particularly  in  a  turbulent  flow,  between  the  buoyant  case  and 

the  electromagnetic  case  due  to  the  further  requirement  that  V  ■  J  =  0 
for  the  electromagnetic  case. 

For  the  experiments  for  the  type  1  case  a  novel  probe  has  been 
developed  and  used  to  measured  the  conductivity  profile  and  the 
corresponding  density  profile.  Measurements  of  the  Richardson  number 
and  the  corresponding  effect  on  the  mean  velocity  profile  are  reported. 

II.  APPARATUS  AND  MEASURING  TECHNIQUES 

A.  Water  tunnel 

A  sketch  of  the  water  tunnel  constructed  for  this  experiment  is 
shown  in  figure  1.  The  test  section  (5  ft.  long)  is  constructed  from  ’/i  - 
inch-thick  acrylic  plates.  The  channel  height  is  0.50inches  and  width  8.0 
inches.  The  flow  uniformity  and  quality  is  controlled  by  a  honeycomb  (1 
inch  long,  1/8  inch  in  diameter)  and  a  fiberglass  screen  (16  mesh/inch), 
followed  by  a  16:1  contraction.  At  the  downstream  end  of  the  test 
section  a  ten-degree  divergent  nozzle  was  used  as  a  diffuser. 


Figure  1.  Sketch  of  two-dimensional  water  tunnel. 

An  injection  slot  is  located  approximately  30  inches  downstream  from 
the  entrance  to  the  test  section.  This  carefully  designed  slot  spans  the 
test  section  and  has  a  0.055-inch  wide  outlet. 

The  tunnel  is  driven  by  a  3-horsepower  centrifugal  pump.  The 
Reynolds  number  (based  on  the  height  of  the  channel  and  the  maximum 
mean  velocity)  can  be  varied  typically  from  4,000  to  20,000.  Transition 
has  been  found  at  a  Reynolds  number  of  approximately  6,000-7,000. 

B.  Flow  Measurements 

All  velocity  measurements  reported  here  have  been  made  with  a 
Pitot  tube  and  the  wall  shear  inferred  from  Preston  tubes  calibrated 
against  the  static  pressure  drop  in  the  channel.  All  tubes  were  of  0.042 
inches  outer  diameter.  Measurements  were  at  locations  of  4  inches 
downstream  of  the  injection  slot.  A  programmable  traverse  gear  was 
used  to  move  the  Pitot  tube  across  the  channel. 

C.  Concentration/density  probe 

To  measure  solution  concentration,  a  bipolar  pulse  technique  has 
been  developed  by  Johnson  an  Enke  (3)  which  eliminated  many  of  the 
classical  problems  encountered  with  other  A.  C.  bridge  methods.  It  was 
capable  of  measuring  very  rapid  changes  in  conductivity.  It  has  been 
improved  for  the  measurement  of  small  solution  resistance  (high 
concentration)  by  Daum  and  Nelson  (4).  This  method  involves  the 
sequential  application  of  two  successive  constant  current  pulses  of  equal 
magnitude  but  of  opposite  sign  across  a  conductance  cell.  The  resulting 
voltage  can  be  electronically  rectified  and  integrated  to  determine  the 
area  under  the  curve.  Under  some  assumptions,  the  solution  resistance  is 


369 


directly  proportional  to  the  area  for  a  given  pulse  magnitude  and 
duration. 

Though  the  system  worked  extremely  well  for  a  uniform 
conductivity  cell,  the  application  of  the  technique  to  the  measurement  of 
concentration  profiles  in  the  present  channel  flow  was  not 
straightforward.  The  difficulty  arises  from  the  fact  that  the  solution 
resistance  of  a  conductance  cell  is  an  integral  quantity  which  makes  it 
impossible  to  localize  the  measurements. 

To  resolve  this  problem,  a  novel  probe  has  been  developed.  Two 
0.005-inch-diameter  platinum  wires  are  inserted  lA  inch  apart  into  a 
plastic  tubing  of  0.04  inch  OD.  A  pressure  drop  in  this  tubing  is 
established  and  a  Poiseuille  flow  with  a  maximum  velocity  of 
approximately  1  m/sec  then  enables  the  concentration  of  the  stream  tube 
to  be  continuously  sampled. 

A  pulse  duration  of  20  ps  was  chosen.  The  system  was  calibrated 
using  standard  NaCl  solutions  of  known  concentration.  The  results  are 
shown  in  figure  2  where  the  concentration  has  been  converted  to  the 
density.  The  probe  gave  highly  repeatable  results. 


0  12  3  4 

Sensor  Output  (V) 


Figure  2.  Calibration  of  the  concentration  probe  for  NaCl  solution. 

III.  EFFECTS  OF  DENSITY  GRADIENT 

In  the  first  set  of  experiments,  the  effect  of  buoyancy  (density  gradient) 
in  the  channel  flow  was  investigated.  The  density  gradient  was 
established  by  injecting  of  4.0M  NaCl  solution  through  the  injection 
slot.  Measurements  were  also  made  with  fresh  water  injection.  Injection 
rates  were  carefully  measured  using  an  accurate  flow  meter  calibrated 
for  fluids  of  different  density  and  viscosity. 

Mean  velocity  profiles  were  measured  at  Re  -11,000  as  shown  in 
figure3-4.  Due  to  the  size  of  the  Pitot  tube,  measurements  closer  to  the 
wall  were  not  made.  The  velocity  u  is  calculated  from  the  Pitot  pressure 
and  the  local  fluid  density  measured  with  the  concentration  probe.  At 
the  same  time,  the  upstream  flow  velocity  was  recorded.  It  was  found 
that  this  velocity  was  unchanged  with  or  without  injection.  The  average 
velocity  based  on  the  total  volume  flux  has  then  been  used  to  non- 
dimensionalize  the  velocity  profile  measurements. 

The  density  probe  was  traversed  with  the  Pitot  tube.  The  output 
during  the  traverse  of  the  probe  is  shown  in  figures  5  and  6  for  two 
different  injection  rates.  In  these  plots  the  voltage  output  has  been 
converted  to  a  density  by  means  of  the  calibration  obtained  from  figure 
2.  It  can  be  seen  that  the  fluctuations  of  density  are  large.  The  mean 
densities  are  nevertheless  significantly  less  than  that  of  the  injected  fluid 

Pi  *"  P0 

(i.e. -  =  0.1 15)  due  to  turbulent  diffusion  into  the  bulk  fluid. 

P0 

Two  polynomials  were  fitted  to  the  data  to  determine  the  mean  density 
profiles  from  the  distributions  of  instantaneous  values. 

With  the  corresponding  velocity  and  density  profiles,  the  near  wall 
gradient  Richardson  numbers  were  calculated  and  are  shown  in  figure  7- 
8. 

At  an  injection  volume  flow  rate  of  1.4%  of  that  of  the  upstream 
volume  flow  rate,  the  change  in  symmetry  of  the  velocity  profile  was 
quite  small.  Figure  7  shows  that  the  local  Richardson  number  in  this 
case  has  a  maximum  of  approximately  1.1  at  y/h  =  0.27.  At  the  higher 
injection  rate,  as  shown  in  figure  5,  a  significant  change  in  symmetry  of 


0  0.2  0.4  0.6  0.8  1 

y/h 


Figure  3.  Velocity  profiles  for  flow  with  injection  rate  of  1 .4% 


0  0.2  0.4  0.6  0.8  1 

y/h 


Figure  4.  Velocity  profiles  for  flow  with  injection  rate  of  2.2% 


0  0.2  0.4  0.6  0.8  1 


y/h 

Figure  6.  Normalized  relative  density  profile  for  injection  rate  2.2%. 

velocity  profile  can  be  seen.  In  this  case  the  gradient  Richardson  number 
is  well  above  1.0  as  shown  in  figure  8.  There  is  a  local  maximum  of 
approximately  2.2  at  y/h  —  0.22.  The  large  Richardson  numbers  for  y/h  > 
0.4  are  a  result  of  the  small  velocity  gradient.  These  results  will  now  be 
compared  with  the  corresponding  effect  of  a  normal  Lorentz  force,  for 


370 


which  the  mean  conductivity  profile  is  expected  to  be  approximately 
similar  to  the  density  profile  for  the  corresponding  buoyancy  case. 


y/h 


Figure  7.  Gradient  Richardson  number  distribution  near  the  wall  at  1.4% 
injection  rate. 


Figure  8.  Gradient  Richardson  number  distribution  near  the  wall  at  2.2% 
injection  rate. 

IV.  PROPOSED  EXPERIMENTS  USING  ELECTRO¬ 
MAGNETIC  RIBLETS 

It  is  well  known  that  longitudinal  vortical  motion  is  a  principal 
mechanism  for  maintaining  the  Reynolds  stress  near  the  wall. 
Measurements  indicate  a  span-wise  scale  of  approximately  80-100  wall 
units.  The  principal  effect  of  a  dilute  polymer  in  reducing  the  wall  shear 
stress  (Thoms  effect),  has  been  attributed  to  a  change  in  this  near  wall 
structure  and  a  correspondingly  larger  span-wise  scale.  Similarly 
longitudinal  riblets  have  been  found  to  reduce  the  wall  shear  stress  for  a 
particular  span-wise  scale  and  riblet  geometry.  The  proposed 
experiments  are  intended  to  directly  control  this  near  wall  structure  by 
the  application  of  a  span-wise  periodic  Lorentz  force,  whose  span-wise 
scale,  in  wall  units,  can  be  varied. 

To  generate  such  a  structure,  a  stream-wise  magnetic  field  and  an 
electric  field  due  to  surface  electrodes  mounted  on  the  top  and  bottom 
surfaces  of  the  channel  are  applied.  Figure  9  shows  the  directions  of 
these  fields  and  the  resulting  flow  field  that  is  expected  as  a  result  of 
the  Lorentz  force  near  the  surface  that  is  not  opposed  by  the  pressure 
field.  In  the  two-dimensional  case  (electrodes  infinitely  long  in  the 
stream-wise  direction),  the  current  field  will  be  perpendicular  to  the 
magnetic  field,  and  if  the  curl  of  J  x  B  does  not  vanish  it  acts  as  a 
source  of  stream-wise  vorticity.  How  best  to  achieve  this  source  of 
vorticity  is  the  subject  of  present  research.  To  the  extent  that  it  can  be 
achieved,  the  fields  might  therefore  be  thought  of  as  electromagnetic 
“riblets”. 

In  the  proposed  experiment  the  electromagnet  shown  in  figure  10 
will  provide  a  large  periodic  axial  magnetic  field.  Similarly  the 
electrodes  will  be  provided  with  an  A.  C.  voltage.  Thus,  theLorentz  (J 
x  B)  at  each  electrode  remains  in  the  same  direction  as  each  field 
reverses.  The  alternating  current  at  each  electrode  will  ensure  that  the 
electrode  impedance  will  be  small,  due  to  the  large  interfacial 
capacitance,  and  bubble  formation  will  be  suppressed.  Both  the 


magnitude  of  each  field  and  the  phase  relationship  between  them  can  be 
varied.  The  electromagnet  has  been  built  by  the  Sandia  National 
laboratory  and  a  maximum  field  of  0.7T  has  been  measured. 


j 

A  A  A 

b  i 

+  T  V  t + 1+  +i  *'t~  1J 

1-  -  -  -  r 

A  A  ) 

■  -■-  =  ?  -  -  -  J 

A  A  A  A  A 

M-  4-  -4-  4-  -4-  4-  4-  +  4-  4-  +  +1 


FLOW 


Figure  9.  A  schematic  of  electromagnetic  riblets.  Top:  cross-section, 
bottom:  top  view. 


Figure  10.  An  oblique  view  of  the  AC  magnet  with  the  associated  power 
factor  correction  capacitor  bank. 

V.  CONCLUSIONS 

A  channel  flow  facility  with  an  electromagnetic  control  system  has 
been  built.  The  channel  flow  has  enabled  some  of  the  issues  raised  by 
the  early  experiment  of  Nosenchuck  and  Brown  to  be  studied.  Studies  of 
both  type  1  and  type  II  electromagnetic  control  are  being  pursued.  In  the 
type  I  case  comparisons  between  the  Lorentz  force  and  the  buoyancy 
force  as  sinks  for  turbulent  energy  can  be  made.  Measurements  in  the 
buoyancy  case  confirm  that  a  Richardson  number  of  order  one  is 
required  to  affect  the  symmetry  of  the  velocity  profile.  For  the  type  II 
case,  an  electromagnetic  riblet  concept  is  being  explored  along  with  an 
array  of  electromagnetic  tiles  as  originally  proposed  byNosenchuck  and 
Brown. 

References: 

1.  D.  M.  Nosenchuck  and  G.  L.  Brown,  Discrete  Spatial  Control  of 
Wall  Shear  Stress  in  a  Turbulent  Boundary  Layer,  Near-Wall  Turbulent 
Flows,  R.  M.  C.  So,  C.  G.  Speziale  and  B.  E.  Launder  (Editors), 
Elsevier  Science  Publishers,  689-698,1993 

2.  X.  Fan  and  G.  L.  Brown,  Experiments  on  the  Electromagnetic  Control 
of  Turbulence,  ALAA  97-2123,  June  1997. 

3.  D.  E.  Johnson  and  C.  G.  Enke,  Bipolar  Pulse  Technique  for  Fast 
Conductance  Measurements,  Analytic  Chemistry,  Vol.  42,  No.3,  March 
1970. 

4.  P.  H.  Daum  and  D.  F.  Nelson,  Bipolar  Current  Method  for 
Determination  of  Solution  Resistance,  Analytic  Chemistry,  Vol.  45, 
No.3,  March  1973. 


371 


DRAG  REDUCTION  EXPERIMENTS  ON  A  SMALL  AXISYMMETRIC  BODY  IN 
SALTWATER  USING  ELECTROMAGNETIC  MICROTILES 


Promode  R.  Bandyopadhyay 
John  M.  Castano, 

Daniel  Thivierge  and 
William  Nedderman 

Naval  Undersea  Warfare  Center 
Newport,  RI 02841 

bandyopadhyay@c80.npt.nuwc.navy.mil 


ABSTRACT 

Experiments  are  being  carried  out  on  the  drag  reduction  of  a 
small  axisymmetric  body  in  salt  water  using  Lorentz  forces  produced 
by  electromagnetic  microtiles.  Scaling  and  measurement  issues  are 
considered  from  the  early  stage  of  the  work.  The  experiments  are 
aimed  at  higher  Reynolds  number  turbulent  boundary  layer  flows  with 
a  freestream  developing  on  an  axisymmetric  body,  right  from  the 
preliminary  stage  of  planning.  A  wall-layer  scaling  of  the  phenomena 
is  assumed.  The  main  variable  of  interest  is  large  area  time- averaged 
viscous  drag.  A  small  diameter  (d)  axisymmetric  body  is  constructed 
that  has  a  long  (5d)  floating  section  for  measurement  of  viscous  drag. 
This  floating  section  is  filled  with  numerous  electromagnetic  microtiles. 
The  recent  progress  on  drag  measurements  and  modeling  of  the 
mechanism  is  reported. 

1.  INTRODUCTION 

Over  the  last  few  decades,  an  important  progress  has  been  made 
in  our  understanding  of  turbulence  production  in  a  turbulent  boundary 
layer.  It  is  now  known  that  such  processes  are  not  entirely  random. 
There  are  quasi-periodic  processes  in  play  which  are  masked  in  noise. 
The  discovery  of  this  orderliness  has  opened  the  possibility  of  a  rational 
control  of  the  turbulence  production  process  and  eventually  of  viscous 
drag.  In  1832,  Ritchie  (1832)  experimentally  demonstrated  that,  a 
conducting  liquid  can  be  pumped  when  electric  and  magnetic  fields  are 
crossed  within  its  bulk.  Due  to  high  salinity,  seawater  is  reasonably 
electrically  conducting.  In  principle,  by  crossing  magnetic  fields  with 
electrical  fields  within  a  boundary  layer,  Lorentz  force  can  be 
produced  to  pump  such  a  liquid  locally  whose  amplitude,  phase,  length 
and  time  scales  can  be  digitally  varied.  These  developments  open  up 
the  possibility  of  controlling  the  turbulence  production  process  and 
viscous  drag  in  an  ocean  going  vehicle. 

Several  years  ago,  NUWC  undertook  research  on  this  subject  although 
not  much  was  reported.  Drag  reduction  remained  elusive  although 
fluid  pumping  was  demonstrated  via  flow  visualization.  Later, 
Princeton  researchers  made  claims  of  large  drag  reduction  which 
generated  a  considerable  interest  (Nosenchuck  &  Brown  1993).  These 
drag  reductions  were  primarily  based  on  local  hot  film  sensor  response. 
Low  Reynolds  number  transitional  flat  plate  results  were  scaled  to  high 
Reynolds  number  axisymmetric  bodies.  The  mechanism  was  based  on 
outer  layer  scaling.  Flow  visualization  revealed  the  formation  of  large 
roller  eddies.  NUWC  efforts  at  reproducing  these  results  were  not 
encouraging  (Meng  et  al.  1997).  In  any  case,  the  NUWC  and 
Princeton  efforts  are  at  least  note  worthy  for  a  novel  approach  to  a 
difficult  problem. 

The  Princeton  efforts  are  now  directed  towards  understanding  the 
mechanism  (Fan  &  Brown  1997).  A  novel  single  infinite  tile  is 
produced  on  one  wall  of  a  channel  flow,  the  other  being  a  reference 
wall.  The  edge  effects  are  less  than  that  in  a  flat  plate  boundary  layer. 
Experiments  in  a  channel  flow  marks  a  departure  in  the  Princeton 
thinking  of  the  pursuant  mechanism  from  outer  layer  to  inner  layer 
dominated.  Preston  tube  and  pressure  drop  are  used  to  compute  drag 
reduction  on  the  electromagnetic  wall.  However,  pressure  drop  can  be 
used  to  compute  wall  shear  stress  only  if  the  flow  across  the  entire 
channel  is  fully  developed.  The  electromagnetic  perturbation  on  one 
wall  violates  this  condition,  raising  questions  on  accuracy  of  pressure 
drop  in  shear  stress  diagnosis.  In  spite  of  this  innate  ambiguity,  it  is 


intriguing  that  a  ‘Preston  tube’  registers  a  clear  drop  in  response  when 
the  electromagnetic  field  is  turned  on. 

A  clear  evidence  of,  whether  the  technique  of  electromagnetic  drag 
reduction  in  saltwater  does  indeed  lead  to  a  reduction  of  surface- 
integrated  viscous  drag  or  not,  is  lacking  so  far.  The  goal  of  the 
present  experiment  is  to  come  up  with  such  an  evidence.  The  first 
progress  report  was  given  in  Bandyopadhyay  &  Castano  (1996)  and 
this  is  a  follow-up. 

During  the  planning  stage,  the  present  work  has  been  influenced  by 
past  negative  experience.  Past  Navy  and  NASA  drag  reduction  efforts 
indicate  that  scaling  from  low  to  high  Reynolds  numbers,  and 
transitioning  from  laboratory  curiosities  to  field  tests  can  sometimes  be 
problematic.  Understanding  of  the  non-linear  turbulence  mechanism 
tends  to  be  a  controversial  and  slow  process.  Techniques  that  work 
well  in  a  turbulent  flow,  viz.,  polymer  and  microbubble  injection,  are 
probably  not  that  relevant  because  they  involve  large  changes  in  fluid 
properties. 

Because  the  flat  plate  experiments  indicated  a  strong  convergent- 
divergent  edge  effect,  the  present  experiment  concentrated  on  an 
axisymmetric  model.  This  eliminates  at  least  one  scaling  issue  and 
results  in  a  better  flow  quality.  Because  power  consumption  is  bound  to 
be  an  issue,  there  is  a  need  to  resort  to  Lorentz  forces  that  focused 
near  the  wall  where  turbulence  production  is  a  maximum.  As 
described  in  the  previous  report,  the  turbulence  production  statistical 
scales  were  examined  in  large  and  small  underwater  bodies  and  in  the 
NUWC  quiet  water  tunnel  based  on  wall  layer  scaling.  Fabrication 
limits  then  led  to  slightly  higher  dimensions.  The  wall  layer  scaling  is 
an  approximate  guideline,  and  a  mixed  layer  scaling  effect  is  allowed 
in  the  boundary  layer  nature  of  the  experiments. 

There  appears  to  be  few  general  traits  of  drag  reduction.  However, 
there  is  one  that  is  assumed  to  be  relevant.  The  riblet  work  of 
Wilkinson  &  Lazos  (1987)  showed  that  drag  reduction  is  not  uniquely 
related  to  the  suppression  of  streamwise  component  of  turbulence  (u). 
Crawford  &  Kamiadakis  (1998)  have  shown  via  the  DNS  of  riblet  flow 
that,  drag  reduction  is  uniquely  related  to  the  suppression  of  the 
surface-normal  component  of  turbulence  (v)  near  the  wall.  We 
assume  that  this  is  a  universal  property  of  drag  reduction.  A  structural 
modeling  of  a  vortex  in  a  unit  flow  domain  have  shown  that  vertical 
Lorentz  pressure  can  lead  to  a  suppression  of  wall  pressure  rms  levels 
(Bandyopadhyay  &  Balasubramanian  1996).  It  then  follows  that 
Lorentz  pressure  should  be  directed  towards  the  suppression  of  the  v- 
component.  This  results  in  an  orthogonal  array  of  magnets  of 
electrodes.  The  reality  however  is  far  more  complicated  -  the  Lorentz 
pressure  is  only  nominally  surface  normal  in  such  an  arrangement,  it  is 
in  fact  highly  three-dimensional.  A  recent  comparison  of  our  work 
with  that  of  Krai  (1998)  suggests  that  the  induced  flowfield  of  micro 
and  macrotiles  can  be  basically  different.  The  attempt  to  control  the  v- 
component  of  turbulence  is  hoped  to  further  reduce  the  necessary 
Lorentz  pressure  levels.  The  present  wall-layer  based  arrangement  of 
the  magnets  and  electrodes  has  been  called  microtiling  here  as  opposed 
to  the  larger  length  scale  based  original  Princeton  or  NUWC  approach. 
In  this  manner  we  attempt  to  build  the  present  work  on  our 
understanding  of  the  organized  nature  of  turbulence  production  in  a 
turbulent  boundary  layer. 


373 


The  measurement  problems  in  an  electrically  charged  saltwater 
medium  are  formidable.  Because  saltwater  is  extremely  corrosive,  the 
longevity  of  electrodes  and  sensors  is  a  problem.  Many  of  the 
conventional  diagnostics  do  not  work.  Because  saltwater  is  being 
electrically  charged,  ground  looping  can  be  a  serious  issue. 
Electrolysis  can  contaminate  the  response  of  hot  films  and  LDAs  and 
PIV  methods  of  diagnostics.  Because  the  wall-shear  distribution 
produced  by  each  microtile  is  three-dimensional,  one  would  like  to 
focus  on  the  surface  and  time  integrated  viscous  drag  to  clearly 
evaluate  the  drag  reduction  behavior.  To  be  able  to  measure  changes 
in  drag  due  to  the  application  Lorentz  forcing,  the  ratio  of  the  tiled  to 
the  total  surface  area  of  the  floating  segment  for  drag  measurement 
should  be  close  to  one.  Recently,  improvements  have  been  made  over 
past  drag  sensors  and  the  longevity  of  the  electrodes.  Even  then,  the 
present  results  should  be  treated  with  caution  and  further  verification 
and  detailed  measurements  are  imperative  before  the  present  results 
can  be  deemed  established. 


perturb  the  flow  locally.  A  Stokes’  layer  resonance  model  was 
proposed  which  suggested  that  “pillows”  of  vorticity  are  formed  over 
the  microtiles  when  the  applied  electric  field  is  pulsed.  Subsequently, 
DNS  simulation  was  carried  out  on  the  same  configuration.  It  showed 
that  the  “pillows”  of  vorticity  were  in  fact  ring  vortices,  the  induced 
flow  in  the  middle  being  wall  ward.  The  axial  vorticity  perturbation 
due  to  the  microtile  is  shown  in  Fig.  1.  The  basic  qualitative  nature  of 
the  vorticity  distribution  is  the  same  in  quiescent,  laminar  and  low 
Reynolds  number  turbulent  flows  and  with  several  different  kinds  of 
pulsing,  although  the  entire  parameter  space  is  not  yet  fully  explored. 

At  a  freestream  speed  of  5  m/s,  the  spanwise  scale  of  the  normal  and 
microtile  perturbed  vorticity  pairs  will  match  (Fig.  2).  The  suggestion  is 
that  the  microtiled  turbulent  boundary  layer  provides  a  layer  of  pillows 
of  vorticity  whose  sense  of  rotation  is  opposite  to  what  normally  occurs 
in  a  turbulent  boundary  layer.  It  remains  to  be  seen  whether  this 
translates  to  any  near-wall  vorticity  cancellation  or  drag  reduction. 


2.  MODELING  OF  MECHANISM 

A  model  of  the  microtile  flow  mechanism  is  given.  The 
mechanism  may  not  be  universal  and  applicable  to  other  tile  designs. 

2.1  Vorticity  Perturbations  Due  to  Microtiles 


MHD  CHANNEL  FLOW 
Re_h=300 

Streamwise  Vorticity 


2.2  Volume  of  Influence  of  One  Microtile 

The  distribution  of  Lorentz  force  over  the  present  microtile  is 
given  in  the  first  report.  Figure  3  shows  the  distribution  of  boundary 
layer  integral  quantities  on  the  floating  section  of  the  75  mm  diameter 
model  of  the  present  work  (Castano  1997).  (They  are  from  a  similar 
sized  model  carried  out  in  a  similar  water  tunnel).  The  volume  of 
influence  of  one  microtile  is  shown  in  Fig.  4.  It  encompasses  one  near¬ 
wall  vortex  pair  and  the  location  of  maximum  turbulence  production 
around  5  m/s.  The  depth  also  covers  the  region  of  overlap  between  the 
outer  and  inner  layer  (Fig.  3a). 


6 

A 

5 

& 

4 

*  Delta  (mm) 

Surface 

■  0.15  Delta  (mm) 

Normal  3 

°  100y+  (mm) 

Distance  4 

b  0.05  Delta  (mm) 

(mm) 

•  15y+  (mm) 

1 

■ 

a  8 

o 

0  i 

□ 

.  * - - 

0 

0  100  200  300 

400  500 

X  (mm) 

Figure  1.  DNS  Simulation  of  streamwise  vorticity  perturbation  induced 
by  the  microtiles,  after  Hatay  et  al.  (1997).  The  induced  flow  between 


oulwtrd 

Figure  2.  Conceptual  sketch  showing  how  an  incoming  regular  near 
wall  vortex  pair  in  a  turbulent  boundary  layer  will  encounter  an 
opposing  pair  near  wall  over  a  microtile. 

In  the  previous  report,  a  5x5  array  of  microtile  fabricated  on  a 
printed  circuit  board  was  described.  Dye  visualization  in  a  low 
Reynolds  number  subcritical  channel  flow  of  saltwater  was  carried  out. 
It  showed  that  that  the  microtiles,  although  small,  were  indeed  able  to 


% 

i- 


x  (mm) 


(C) 


.01 


x  (mm) 


374 


(d) 


x  (mm) 


Figure  5.  Drag  reduction  due  to  spanwise  oscillation.  DNS  of 
Akhavan:  line;  measurements  of  Laadhari  et  al.  and  Choi  et  al.  (1998): 
symbols. 


Figure  3.  Boundary  layer  integral  quantities  over  the  floating  section  of 
the  75  mm  diameter  model  (Castano  1997). 


Similarly,  propose  that  near-wall  vorticity  breakdown  will  be 
interrupted  if  spanwise  wall  or  spanwise  fluid  displacement  follows  the 
relationship  in  (5)  where  the  spanwise  dimension  is  given  in  Fig.  6. 


120  Wall  Units 


25  Wall  Units 


/ 


Flow:  5  m/s 


Figure  4.  Volume  of  one  microtile  in  wall  units  at  5  m/s,  over  which 
the  Lorentz  force  field  is  being  applied. 

2.3  Stokes’  Layer  Resonance  Model 


b+  >100 


Figure  6.  Sketch  of  microtile.  Dimension  b  is  width  of  microtiles. 

Strouhal  number  for  maximum  drag  reduction  (45%)  is  given  by: 

(6) 


10<^<15 

2"t 

blnfh 

10< - £-<15 


2/7 


(7) 


Assume  that  pulsed  Lorentz  pressure  is  analogues  to  oscillating 
the  wall  giving  rise  to  a  Stokes’  layer.  Turbulence  production  peaks  at: 

10<^£-<15  (1) 

v 

Propose  that  Stokes’  layer  viscous  wave  length  should  match  waves 
responsible  for  turbulence  production: 


3.2  <  Stb  <  4.8  (8) 

Here,  St y  is  a  Strouhal  number  and  fy  is  the  pulsing  frequency.  Note 

that  turbulence  reproduction  physics,  namely  viscosity  and  information 
about  structure  organization  are  already  accounted  for  in  (8).  In  the 
current  75  mm  diameter  model,  in  the  middle  of  the  floating  section, 
where  U  =  0.33w/5  ,  pulsing  frequency  is: 


Wv  <  2v  <  15t> 

ur  ~u~ut 

If  G7  =  2/g^  ,  where  fB 
314  <  ^^-<>101 


(2) 

is  pulsing  frequency,  then 

(3) 


Condition  (3)  is  calibrated  against  turbulence  production  structure 
statistics.  The  drag  reduction  consequence  is  not  clear  and  is  treated  in 
the  next  section. 


2\0Hz<fb<^\SHz  (9) 

The  range  of  fy  in  (9)  is  roughly  the  same  as  that  of  /g  in  (4).  This 

suggests  that  the  original  Stokes’  layer  resonance  hypothesis  in  the  first 
report  (Bandyopadhyay  &  Castano  1996)  is  calibrated  against  the  large 
drag  reduction  due  to  spanwise  wall  oscillation.  The  microtile  should 
be  able  to  generate  a  spanwise  fluid  oscillation  given  by  (8)  for  a  drag 
reduction  of  45%  to  occur. 

3.  EXPERIMENT 


At  a  freestream  speed  of  8  m/s,  in  the  middle  of  the  floating  section, 

—7  2 

U ^  =  0.33m Is  ,  and  V  =  11.4x10  m  fs  ,  the  pulsing  frequency 
should  be: 

\35Hz<fB  <304//z  (4) 

2.4  Condition  for  Electromagnetic  Drag  Reduction 

Assume  that  pulsing  of  the  electromagnetic  microtiles  is 
analogous  to  the  spanwise  wall  or  fluid  oscillation  of  Akhavan  (Jueng 
et  al.  1992),  Laadhari  et  al.  and  Choi  et  al.  (1998).  Their  low  Reynolds 
number  drag  reduction  result  is  reproduced  in  Fig.  5. 


The  5x5  microtiles  developed  on  a  printed  circuit  board  and 
described  in  the  first  report  was  taken  as  the  model  for  building  an 
axisymmetric  model  sketched  in  Fig.  7.  Figure  8  shows  the  model  in  the 
NUWC  Saltwater  Tunnel.  The  floating  section  is  microtiled.  The  front 
and  back  parts  of  the  model  rest  rigidly  on  a  hollow  stainless  steel  rod 
through  which  all  coiled  wires  pass.  The  electrodes  are  placed  in  a 
cross-stream  direction  while  the  three-dimensional  permanent  magnets 
(1280)  are  aligned  axially.  All  microtiles  are  pulsed  in-phase.  At  a 
speed  of  5.5  m/s,  the  interaction  parameter  defined  as  the  ratio  of 
applied  Lorentz  force  times  viscous  force  divided  by  square  of  inertia 


force,  N  =  - 


<7 VB 


is  0.6.  Here,  <7  is  electrical  conductivity  of  the 


fluid,  V  is  scalar  electric  potential,  B  is  magnetic  flux,  p  is  fluid  density, 
and  U  is  friction  velocity,  and  the  subscript  o  denotes  conditions  at 


the  wall. 


375 


3  Inch  Diameter  EMTC  Model  In  NUWC  Saltwater  Tunnel 

,2  mm  Dl«  Trip  ^  ^  ^ 


<1  1 

mum 

III!  CT  1 

n 

7.5  cm  Diameter 

1  l*T*  em  2.1  cm* 

L _  — J 

Micro-Tile* 

\  24.5  cm 

35.3  cm 

Floating  Section 
75%  Tiled 

Rex  s  1.13x10  6  it  5.3  m/s 
at  First  Knife  Edge 


At  5.3  m/e.  Estimated  Values: 
c.  =  0.0035  Rs  A  =  2300  U 


a  0.2  m/s 


Salinity  =  Half  That  of  Seawater 
Forced  Transition:  Schlichting  (p538)  o  =  4  mho/m;  Vo  =  +/-  lOVolts;  Bo  a  0.6  T 

p  =  1000  Kg/m*3;  Nt  a  W-  (oVo  Bo)/(p  IH*2)  =  0.6 


Figure  7.  Schematic  of  the  model  and  the  experiment. 


Figure  8.  Photograph  of  the  75  mm  (3M)  diameter  lm  long  model  in  the 
water  tunnel.  The  electromagnetic  floating  section  is  visible  in  the 
middle. 


3.1  Quality  of  Surface  Smoothness: 


Figure  9.  Impression  of  accumulation  of  rust  roughness  over  the 
magnets.  Top  ruler  numerals  are  in  inches  and  the  bottom  are  in  cm. 
The  dark  areas  below  the  ruler  are  from  the  rust  deposition.  The  flow 
is  from  left  to  right,  the  rust  forming  a  ramp  to  the  flow. 

In  the  water  tunnel,  the  model  is  mounted  on  a  sting  attached  to  a 
cruciform.  Due  to  sting  mounting,  at  high  tunnel  speeds  (7  m/s),  the 
model  nose  vibrates,  whose  effect  is  not  known.  The  test  section  is  30 
cm  x  30  cm  in  cross-section  and  causes  an  area  blockage  of  5%.  The 
boundary  layer  was  tripped  with  a  2  mm  diameter  o-sealing  ring. 
These  trips  do  not  last  long  in  the  saltwater.  The  estimated  boundary 
layer  integral  quantities  over  the  floating  section  at  5  m/s  are  given  in 
Fig.  3.  Although  not  visible  to  the  naked  eye,  the  seemingly  filtered 
water  contains  fine  rust,  which  is  smooth  to  the  touch.  In  course  of 


about  one  hour  of  run,  they  accumulate  over  the  magnets  in  a  the  shape 
of  a  ramp.  Figure  9  shows  an  impression  of  the  rust  deposition.  These 
magnets  should  bring  the  Lorentz  force  well  into  the  boundary  layer. 
This  rust  deposit  which  slightly  varies  with  filtering,  raises  question 
about  the  validity  of  smooth  wall  assumption  in  all  current  direct 
numerical  simulations  of  the  flow  field.  In  the  present  work,  the 
magnets  lie  below  a  thin  kapton  layer  on  which  the  electrodes  are 
electroplated.  Over  time,  these  electrodes  may  form  microscopic 
cracks  but  they  do  not  form  a  gouging  or  roughness.  In  the  present 
work,  rust  is  the  only  source  of  roughness  which  can  be  minimized 
after  intensive  filtering.  On  the  other  hand,  in  many  other  experiments, 
where  tile  fabrication  did  not  follow  the  electronic  fabrication 
procedure  as  here,  due  to  corrosion,  the  plates  are  far  from  being 
hydrodynamically  smooth. 

3.2  Drag  Balance: 

In  the  first  set  of  experiments  on  the  axisymmetric  model,  an  in- 
house  built  drag  sensor  was  used.  Later  on,  this  was  replaced  by  a 
commercial  balance,  further  developed  for  saltwater  application,  was 
used.  Accurate  drag  balance  measurements  in  saltwater,  that  is  also 
charged,  is  difficult.  Not  much  expertise  is  available  on  this  subject. 
These  two  drag  sensors  are  briefly  discussed. 


(b) 


0,005- 

ittKH 

.0005- 

fOiQ- 

Vp5-| 

A020-J 

•0.025- 

■•0.03G-; 


I  10  gm 

Ujt 


+  ve 

■ 

-  ve 

ate  Sec 

f 

onds  . 

4.000 

-2.000 

-0.000 

-4000 

—4000 

-•6.500 


Figure  10.  Time  trace  showing  uncertainty  in  response  of  ATI  Nano 
coated  sensor.  Left  axis:  drag;  right:  electric  field,  (a)  No  weight 
drag,  10V;  (b)  No  weight  drag  5V;  (c)  100  gm  weight  axial  force,  10V 
bipolar  pulsing.  30-31  mSi/m;  17-18  gm/1  of  salt;  18-19  deg  c.  Model  in 
a  sink. 

Drag  reduction  at  low  levels  of  drag  can  not  be  measured 
accurately  if  there  is  balance  stiction.  The  cables  from  the  electrodes 
and  the  strain  gages  can  cause  friction  inhibiting  the  freedom  of  the 
floating  element  particularly  at  low  speeds.  This  problem  was 
eliminated  in  an  in-house  sensor  where  four  parallel  flexures  were 
used  to  stiffen  and  support  the  floating  cylinder.  Two  thin  plates  were 
placed  in  a  plane  orthogonal  to  the  flexures,  at  the  center  of  which  two 
strain  gages  were  placed  to  measure  drag.  Internal  cables  were 
coiled.  The  balance  followed  a  linear  response  over  the  entire  drag 
(that  is,  speed)  range  and  displayed  no  stiction.  A  similar  linear 
response  is  also  achieved  when  the  calibration  is  carried  out  while  the 


376 


model  is  immersed  in  water  after  being  installed  in  the  tunnel  using  the 
cruciform.  Measurements  are  presented  here  with  this  in-house  drag 
sensor. 

In  spite  of  the  seeming  improvements  due  to  the  in-house  sensors, 
it  was  discovered  later,  that  they  were  fragile  and  buckled  frequently, 
did  not  always  have  a  hysteresis- free  linear  response  and  needed 
temperature  compensation.  The  floating  section  was  still  not 
adequately  stiff  opening  the  potential  for  buckling  the  strain  gage 
sensor.  Questions  about  sensor  insulation,  ground  looping  and  spurious 
body  forces  giving  rise  to  anomalous  balance  response,  were  raised. 
Due  to  these  reasons,  runs  were  made  with  two  sensors.  Those  runs 
where  they  were  in  qualitative  disagreement  were  discarded.  The 
measurements  reported  here  are  for  those  runs  where  the  two  sensors 
simultaneously  displayed  a  similar  consistent  behavior. 

The  in-house  sensor  has  recently  been  replaced  by  an  ATI,  Inc. 
Nano  sensor.  This  is  a  six-component  balance  of  integral  construction. 
The  gain  has  a  temperature  compensation,  but  the  intercept  does  not. 
The  sensor  and  the  cables  are  coated  for  electrical  insulation  and  use 
in  saltwater.  The  sensor  was  installed  in  the  model  and  dipped  for  days 
in  a  saltwater  bath  (30  mSi/m,  16.9  gm/1  of  salt,  18  deg  c).  The  model 
was  stiff  and  showed  no  visible  movement  when  drag  loads  were 
applied.  The  calibration  was  linear  in  both  air  and  saltwater  over 
periods  of  hours  during  which  the  electrodes  were  powered  on  or  off. 
Figure  10  shows  the  long  time  trace  of  the  sensor  output  for  5  V  and 
10V,  70  Hz,  positive  and  negative  unipolar  and  bipolar  pulsing  of 
electrode  power  (Fig.  11)  under  zero  axial  loading  and  a  loading  of 
100  gms.  There  is  a  maximum  uncertainty  of  5  gms  at  10V  26 A  total 
bipolar  pulsing  in  the  no  load  case.  When  there  is  a  loading  of  100 
gms,  bipolar  pulsing  may  appear  as  a  5%  drag  reduction  after  15 
minutes  of  powering.  These  are  the  minimum  levels  of  uncertainty 
achieved  so  far  and  seem  acceptable.  Drag  measurements  with  these 
Nano  sensors  in  a  water  tunnel  have  not  yet  been  carried  out. 

3.3  Electrode  Pulsing: 

The  present  experiments  are  being  carried  out  with  three 
kinds  of  pulse  shapes  shown  in  Fig.  11.  They  are  unipolar  positive  and 
negative,  and  also  bipolar.  The  present  experiment  was  designed  to 
keep  voltage  levels  as  close  to  3V  as  possible.  The  electrodes  are 
made  of  pure  copper,  and  nickel  and  gold  plating  are  given  to  reduce 
corrosion.  The  electrodes  were  electroplated  on  kapton  layers 
whereby  the  surface  discontinuities  were  of  electronic  industry 
resolution  rather  than  of  mechanical  or  electrical  engineering 
resolution.  This  fineness  of  surface  finish,  plus  choice  of  frequencies 
and  pulse  shapes  helped  to  minimize  or  eliminate  electrolysis.  Tie 
magnets  remain  under  the  kapton  layer  and  are  not  exposed  to 
saltwater.  The  bus  bars  inside  the  cylinder  are  insulated.  The  control 
circuit  was  software  programmed  to  vary  the  pulse  form  and 
frequency.  The  voltages  were  varied  between  ±  10V,  or  0  to  10V  or  0 
to  -10V,  or  0  to  5V,  or  0  to  -5V.  The  current  level  over  the  entire 
floating  section  was  a  maximum  of  24A‘.  Measurements  in  flat  plates  in 
a  saltwater  aquarium  in  our  laboratory  indicate  that  heating  of  water 
does  not  bring  a  sufficient  change  in  viscosity  to  cause  a  drag 
reduction.  Electrolysis  is  also  not  a  source  of  drag  reduction  or 
possible  noise.  The  model  and  the  AT  sensors  have  been  dipped  in  an 
aquarium  of  saltwater  for  several  days.  The  calibration  has  been 
checked  with  electrode  power  turned  on  and  off.  A  floating  cylinder 
was  also  fabricated  that  did  not  have  the  magnets  and  had  only  the 
electrodes- 

1TL 

Ground 


Figure  11.  Voltage  wave  forms  of  power  to  electrodes:  positive 
unipolar,  negative  unipolar  and  bipolar. 

4.  TENTATIVE  DRAG  BALANCE  MEASUREMENTS: 


The  drag  results  using  the  in-house  sensors  are  presented. 
Only  those  results  where  both  sensors  validated  each  other  and  trends 
were  reproduced  are  presented.  All  other  drag  response  is  treated  as 
anomalous.  The  results  presented  here  are  being  repeated  with  the 
newly  developed  Nano  sensor.  Until  then,  the  present  results  are 
deemed  tentative.  The  response  of  the  in-house  sensor  to  on  /  off 
electrode  power  cycles  is  shown  in  Figs.  12  -  14.  The  data  has  scatter, 
but  some  trends  can  be  observed.  The  electrode  power  is  represented 
as  the  product  of  voltage  and  current.  The  drag  sensor  zero  is  not  at 
zero  grams.  In  Fig.  12,  a  positive  unipolar  pulsing  increases  drag 
balance  output.  The  effect  of  negative  unipolar  is  weak,  but  so  is  the 
power  level.  The  negative  unipolar  effect  is  supported  in  Fig.  13  to  be 
the  opposite.  The  powering  sequence  is  reversed  in  Fig.  13.  The 
positive  unipolar  behavior  shown  in  Fig.  12  is  recovered.  The  sensor 
output  is  lower  in  negative  pulsing.  The  suggestion  is  that,  a  positive 
unipolar  pulsing  increases  drag,  whereas  a  negative  unipolar  pulsing 
decreases  drag,  and  there  may  be  threshold  levels  of  powering.  This 
result  should  be  treated  with  caution  until  verified  by  the  planned  Nano 
sensor  measurements. 


Drag  2  -  Power;  Unipolar  EPROM;  7321  UAA 


Figure  12.  Effect  of  unipolar  pulsing  on  drag.  Flow  speed  =  5.2  m/s. 


Drag  3  -  Power;  Unipolar  7321UAB  18.7  (pi  7S  Hz 


Figure  13.  Reproduction  of  results  in  Figure  12. 

Figure  14  shows  the  effect  of  bipolar  pulsing.  The  electrode  powering 
is  now  represented  by  the  absolute  value  of  the  peak  value  current. 
The  output  from  both  the  front  and  back  strain  gages  are  shown.  Both 
gages  have  generally  similar  behavior,  although  not  absolutely 
identical.  The  balance  response  is  similar  to  the  negative  unipolar 
pulsing  case  -  reduced  output  when  the  electrodes  are  powered. 


377 


Drag  2  Bipolar  EPROM  7321UAC 

16.7  fpi  W-10V  75  Hi  ♦/-14Amp» 


Figure  14.  Effect  of  bipolar  pulsing  and  sensor  independence:  (a)  drag 
balance  ‘A’,  (b)  drag  balance  2.  Symbols:  open  (power);  filled  (drag). 


turbulent  boundary  layer,  a  spanwise  array  pulsation  could  be  picked 
up  downstream  although  in  a  narrow  frequency  range,  and  only  near 
the  frequency  of  pulsation  (Singh  &  Bandyopadhyay  1997). 

5.  CONCLUSIONS: 

Laboratory  experiments  on  drag  reduction  are  being  carried  out 
in  saltwater  on  a  small  axisymmetric  body  at  a  reasonably  high  speed 
and  Reynolds  number.  The  variable  of  interest  is  surface  integrated 
long  time  averaged  viscous  drag.  Emphasis  has  been  laid  on  scaling 
issues,  measurement  accuracy  and  reproducibility.  Internally 
consistent  measurements  and  a  flow  mechanism  have  been  obtained. 
These  experiments  tentatively  indicate  that  a  positive  unipolar  pulsed 
Lorentz  field  increases  the  drag  balance  output  while  a  negative  and  a 
bipolar  pulsing  reduces  the  drag  balance  output.  Attempt  is  being  made 
to  verify  the  measurements  with  a  more  robust  drag  sensor  and 
microtiled  surface. 


4.1  Sans-Magnet  Experiment: 


(a) 


3  SPEC  1 

20Av< 

- ! - , 

i  ! 

3 _ SpfisUj 

3 _ Mar 

ftjljiill  jrd 

V 

i - 

— 

p-j-— j 

Yf 

_ | _ i _ 

Hz 

— 

— 

250 

(b) 


Figure  15.  Wall  pressure  spectrum  downstream  of  the  electrodes  in  the 
sans-magnets  experiment.  Freestream  speed:  5.3  m/s;  (a)  electrode 
power:  off:  (b)  electrode  power:  on,  ±  8V;  20 A  bipolar  at  75  Hz. 

A  question  was  raised  whether  thermal  heating  due  to  the 
electrodes  contributes  to  a  drag  reduction,  or  a  gage  response,  that  is 
similar.  Hypothetically,  thermal  plumes  could  trap  recirculating 
bubbles  which  could  then  generate  a  thrust.  An  axisymmetric  model 
was  fabricated  that  had  electrodes  but  not  the  magnets.  In  addition  to 
the  in-house  strain  gage  balance  as  used  before,  a  commercial  balance 
was  also  used  (Nano  balance  from  ATI,.  Inc.)  which  had  a  temperature 
compensation  for  gain  (not  an  intercept  compensation).  No  change  in 
drag  was  observed  in  absence  of  the  magnets. 

Measurements  of  wall  pressure  spectra  in  the  sans-magnets  case  are 
shown  in  Fig.  15.  The  wall  pressure  sensor  was  located  at  the 
downstream  end  of  the  floating  section  containing  the  rows  of 
electrodes.  There  is  question  whether  hot  film  is  reliable  in  the  present 
flow  field.  Due  to  its  inherent  construction  and  working  principle,  the 
wall  pressure  sensor  has  performed  well  so  far  and  will  be  used  more 
extensively  in  the  near  future.  In  an  average  of  20  spectra,  a  2.4  dB 
reduction  is  observed  at  75  Hz,  the  frequency  of  pulsation.  There  is  no 
other  significant  reduction  over  the  entire  frequency  range.  It  is 
intriguing  to  see  that  even  at  such  a  reasonably  high  Reynolds  number 


ACKNOWLEDGMENTS 

This  work  was  funded  by  ONR  (Program  Manager:  Dr.  L.  P. 
Purtell)  and  NUWC  IR  (Program  Manager:  Dr.  S.  Dickinson).  Their 
support  is  gratefully  acknowledged. 


REFERENCES: 

Bandyopadhyay,  P.  R.  &  Castano,  J.  M.  "Micro-Tiles  for 
Electromagnetic  Turbulence  Control  in  Saltwater  -  Preliminary 
Investigations",  ,  Symposium  on  Turbulence  Modification  and  Drag 
Reduction ,  AS  ME  Summer  Meeting,  July  7-11,  1996,  San  Diego,  CA, 
FED  Voi.  237,  Vol.  2,  53-60. 

Bandyopadhyay,  P.  R.  &  Balasubramanian,  R.  1996  "Structural 
Modeling  of  the  Wall  Effects  of  Lorentz  Force,"  ASME  Jou.  Fluids 
Engrg .,  V.  118,  412-414,  June  1996. 

Castano.  J.  M.  1997  Private  Communication. 

Choi,  K-S.,  DeBisschop,  J-R.  &  Clayton,  B.  R.  1997  “Turbulent 
Boundary- Layer  Control  by  Means  of  Spanwise- Wall  Oscillation,’' 
AIAA  Jou.  (due  to  appear). 

Crawford,  C.  &  Kamiadakis,  G.  1998  “Shear-stress  Modification 
and  Vorticity  Dynamics  in  Near-Wall  Turbulence,”  Jou.  Fluid  Mech. 
(due  to  appear).  * 

Fan,  X.  &  Brown,  G.  L.  1997  “Experiments  on  the 
Electromagnetic  Control  of  Turbulence,”  Paper  No.  AIAA  97-2123. 

Hatay,  F.,  O’  Sullivan,  P.  L.,  Biringen,  S.  &  Bandyopadhyay,  P.  R. 
1997  "Numerical  Simulation  of  Secondary  Flows  in  Channels  Driven  by 
Applied  Lorentz  Forces,"  AIAA  Jou.  Thermophysics  &  Heat  Trans/'. 
Vol.  11,  No.  3,  446-453. 

Jueng,  W.  J.,  Mangiavacchi,  N.  &  Akhavan,  R.  1992 
“Suppression  of  Turbulence  in  Wall-bounded  Flows  by  High 
Frequency  Spanwise  Oscillations,”  Phys.  Fluids,  vol.  A4.  No.  8,  1605- 
1607. 

Krai,  L.  1998  Private  Communication. 

Meng,  J.  C.  S.,  Huyer,  S.  A.,  Castano,  J.  M.,  Thivierge,  D.  P.  & 
Hendricks,  P.  J.  1997  “Experimental  Study  of  the  Spanwise  Vortex 
Resonance  Hypothesis  for  Turbulent  Drag  Reduction  Over  a  Flat  Plate 
in  Salt  Water,”  NUWC-NPT  Technical  Report  JO,  680. 

Nosenchuck,  N.  &  Brown,  G.  L.  1993  “Discrete  Spatial  Control 
of  Wall  Shear  Stress  in  a  Turbulent  Boundary  Layer,”  in  Near-Wall 
Turbulent  Flows,  (eds.  So,  R.  M.  C.  &  Speziale,  C.  &  Launder,  B.  E.) 
689-698,  Elsevir. 

Ritchie,  W.  1832  “Experimental  Researches  in  Voltaic  and 
Electromagnetism,”  Phil.  Trans.  Roy.  Soc.  (London),  vol.  122,  279-298. 

Singh,  S.  N.  &  Bandyopadhyay,  P.  R.  1997  “Linear  Feedback 
Control  of  Boundary  Layer  Using  Electromagnetic  Microtiles,”  Jou. 
Fluids  Engrg. ,  vol .  119,  852-858. 

Wilkinson,  S.  &  Lazos,  B.  S.  1987  “Direct  Drag  and  Hot-Wire 
Measurements  on  Thin-Element  Riblet  Arrays,”  IUTAM  Sympo.  on 
Turbulence  Management  and  Relaminarization,  Bangalore,  India,  Jan. 
19-23,  1987. 


378 


MHD  TURBULENCE  EXPERIMENTS,  DRAG  REDUCTION 
AND  APPLICATION  TO  NON-MHD  FLOW 

A.  Eidelman,  H.  Branover,  E.  Golbraikh  and  S.  Moiseev41 

Center  for  MHD  Studies,  Ben-Gurion  University,  P.O.B.653,  Beer-Sheva  84105,  Israel 
eidel@bgumail.bgu.ac.il 

*Space  Research  Institute,  Profsoyuznaya  st.,  84/32, 117810  Moscow,  Russia 
moiseev@mx.iki.rssi.ru 

Abstract  -  Experimental  data  on  drag  reduction  in  turbulent  magneto-hydrodynamic  flows  and  those  with  polymer 
additives  are  compared.  A  similar  behavior  of  drag  reduction,  velocity  profiles  and  spectra,  Reynolds  stresses,  turbulent 
intensity  is  an  argument  in  favor  of  a  universal  turbulence  mode  independent  of  the  physical  nature  of  the  acting  factor.  We 
examine  properties  of  such  turbulence  defined  by  helicity  and  possessing  a  number  of  features  favorable  for  the  formation 
of  a  drag-reduced  flow,  such  as  regularization,  reduced  turbulent  viscosity,  inverse  energy  transfer,  low  dissipation. 
Application  of  this  approach  to  problems  of  seawater  drag  reduction  under  various  conditions  will  be  fruitful. 


1.  Introduction 

After  the  paper  of  Toms  [1]  revealing  a  considerable  (more  than 
twice)  reduction  of  hydrodynamic  drag  due  to  the  addition  of  <  10 
ppm  of  polymers,  quantitative  incompatibility  of  these  two 
characteristics  aroused  interest  in  this  effect  having  a  certain  economic 
potential.  The  problem  including  basic  studies  of  turbulence  proved  to 
be  difficult.  Although  a  lot  of  experimental  data  has  been  accumulated 
and  theoretical  studies  carried  out  during  50  years,  there  is  no 
adequate  understanding  and  no  respective  model  of  this  phenomenon. 
We  believe  this  is  the  reason  of  the  failure  of  all  attempts  to  apply 
drag  reducing  surface  modifications  and  boundary  layer  devices, 
although  they  seem  attractive  for  external  overflow  conditions, 
particularly,  for  seawater  drag  reduction. 

Drag  reduction  can  be  achieved  by  different  means,  both  by  such 
additives  as  polymers,  surfactants,  asbestos  fibers,  etc.,  and  by 
applying  a  magnetic  field  in  magnetohydrodynamic  (MHD)  flows,  i.e. 
by  essentially  different  ways  of  the  interaction  between  the  acting 
factor  and  the  flow.  A  significant  and  approximately  equal  effect 
achieved  suggests  that  it  exists  due  to  a  universal  turbulence  mode  in 
drag-reduced  flows  that  can  be  achieved  by  various  means.  We 
believe  that  just  this  basic  approach  is  fruitful.  It  involves  the  study  of 
the  conditions  of  such  turbulence  mode  generation  and  its  properties, 
and  then  -  their  application  under  specified  conditions. 

Recent  studies  of  a  MHD  flow  [2]  have  revealed  a  turbulence  mode 
with  properties  closely  connected  with  drag  reduction.  The  appearance 
of  turbulence  possessing  a  certain  order  and  such  properties  as 
turbulent  viscosity  reduction  [3],  redistribution  of  kinetic  energy  [4], 
are  connected  with  turbulence  generated  under  the  conditions  of  non¬ 
zero  helicity.  Turbulence  of  such  a  type  arises  under  the  action  of 
constraint  by  various  forces:  electromagnetic,  Coriolis,  buoyancy,  and 
also  under  the  conditions  of  shear  flow.  The  properties  of  this 
turbulence  are  determined  by  another  (along  with  energy)  non-viscous 
invariant  -  helicity,  characterizing  its  topology  [5]. 

The  properties  of  such  helical  turbulence  allow  us  to  have  a  new 
insight  into  experimental  studies  of  MHD  flows,  where  under  the 
action  of  the  magnetic  field  so  called  laminarization  is  observed.  The 
latter  term  is,  in  the  first  place,  due  the  observed  drag  reduction  that 
was  attributed  to  turbulence  suppression  up  to  its  total  disappearance, 
as  expected  according  to  some  theories  of  MHD  flow  stability.  In  fact, 
this  mode  remains  turbulent,  and  we  suppose  that  turbulence  mode  is 
close  to  that  observed  at  the  reduction  of  hydrodynamic  drag  at  the 
expense  of  additives,  such  as  polymers,  etc. 

Principal  features  of  turbulent  flow  parameters  with  a  reduced  drag 
are  the  following.  Their  friction  drag  is  bounded  between  a  usual 
value  and  the  maximum  drag  reduction  asymptote.  Mean  velocity 
profile  involves  a  thicker  viscous  sublayer  than  usual.  Longitudinal 
velocity  fluctuations  grow,  whereas  transverse  ones  and  Reynolds 
stresses  greatly  decrease.  A  similar  behavior  of  a  number  of  main 
characteristics  of  MHD  turbulent  flow  obtained  in  experiments  is  an 
argument  in  favor  of  a  universal  key  mechanism  of  significant  drag 
reduction  caused  by  various  factors. 

2.  Integral  characteristics  of  channel  flows  with  drag 
reduction 

The  principal  manifestation  of  the  flows  under  study  is  the  decrease 
in  hydrodynamic  drag  coefficient  X  =  8tw/pU02  =  8(U  /U0)2  by  AX. 
Here  p  is  density,  t  w  is  wall  shear  stress,  U*  and  U0  are  dynamic  and 
mean  flow  velocities,  respectively.  Drag  reduction  (DR)  is  expressed 


as  DR  =  AX/X.  Hydrodynamic  drag  in  a  turbulent  flow  in  channels, 
specifically,  in  smooth  pipes  of  circular  cross-section  (see  Fig.  1, 
curve  7)  can  be  well  approximated  by  Blasius  formula 

XB  =  0.3164  Re-025  (1) 

from  the  critical  Reynolds  number  Re  =  U0d/v  >  2300  to  Re  =  1 .5  x 
105.  The  relation  (1)  and  laminar  flow  range  characterized  by  the 
dependence  X  =  64/Re  are  shown  in  Fig.  1.  The  remaining  data 
presented  in  Fig.  1  have  been  obtained  in  MHD  flows  [6,  7,  8]. 
These  experiments  were  carried  out  in  circular  pipes  of  various 
diameters  in  uniform  magnetic  fields,  the  direction  of  the  field 
coinciding  with  mean  velocity  direction. 

The  amount  of  experiments  carried  out  in  such  a  configuration  is 
rather  small,  but  they  are  of  specific  interest.  Such  a  flow  does  not 
exhibit  the  coupling  between  the  magnetic  field  and  mean  flow, 
which  is  of  such  great  importance  when  the  field  is  transverse.  A 
longitudinal  field  has  no  effect  on  the  fully  developed  laminar  pipe 
flow  because  the  field  and  the  flow  are  parallel.  Therefore,  the  field 
should  influence  the  flow  only  when  the  flow  becomes  turbulent,  or 
when  small  disturbances  exist  in  an  otherwise  laminar  flow.  Since 
the  longitudinal  field  cannot  exert  longitudinal  forces  on  the  flow,  it 
does  not  affect  the  mean  velocity  profile  directly.  However,  it  does 
affect  the  mean  velocity  through  modification  of  the  turbulent 
structure  of  the  flow.  Consequently,  flows  of  this  type  reveal 
directly  the  influence  of  the  fields  on  the  turbulent  structures. 

A  longitudinal  magnetic  field  was  generated  by  a  solenoid  with 
the  axis  parallel  to  the  test  section.  Test  section  diameter  varied 
from  5  mm  [6]  to  32  mm  [7],  and  the  magnetic  field  reached  1.8  T 
[8].  Various  liquid  metals  were  used  as  working  fluid:  NaK  eutectic 
mixture,  mercury  [6,  8].  To  describe  MHD  experiments,  the 
following  dimensionless  parameters  are  used:  Hartmann  number 

Ha  =  Bd(a/pv),/2  (2) 

and  interaction  parameter 

N  =  a  B2d/p  U0  (3) 

where  B  is  the  applied  field,  c  is  the  electrical  conductivity,  Ha2  and 
N  are  the  ratios  of  magnetic  forces  to  viscous  forces  and  to  inertial 
forces,  respectively.  Due  to  low  viscosity  and  high  electrical 
conductivity  of  liquid  metals,  comparatively  high  Re  and  Ha  values 
are  reached  (3.4  x  105  and  1350)  [7]. 

The  dependence  of  drag  coefficient  on  Re  at  a  constant  Ha  has  a 
characteristic  shape  (see  Fig.  1).  With  increasing  Re,  drag  reduction 
is  first  decreased  more  rapidly  than  in  a  usual  turbulent  flow  (1). 
Above  a  certain  Re  value  depending  on  Ha  number,  the  magnitude 
of  X  is  2-3-fold  smaller  than  XB.  Drag  reduction  reaches  its 
maximum  value  at  a  certain  critical  Ha/Re  parameter  amounting, 
according  to  experimental  data,  to  0.025-0.035.  With  further  Re 
increase,  drag  coefficient  grows  abruptly  at  first,  and  then  more 
smoothly,  tending  to  the  dependence  (1).  Curves  14  in  Fig.  1  show 
maximum  drag  reduction  dependencies  obtained  in  MHD 
experiments  [6-8].  For  the  sake  of  comparison,  in  the  same  figure, 
Virk’s  asymptote  [9]  is  plotted  according  to  experimental  data 
obtained  with  polymer  additives.  It  is  approximated  by  the 
expression 


379 


X- 2.32  Re*0  58  (4) 

within  the  range  of  Reynolds  numbers  Re  =  (4  -5-  40)  x  103.  We  have 
approximated  the  maximum  drag  reduction  obtained  in  the  experiment 
[7]  by  the  curve  6  in  Fig.  1  and  by  the  expression 

X  =  2.39  Re*0  56  (5) 

very  close  to  Virk’s  asymptote. 

Note  that  in  a  transverse  magnetic  field  drag  reduction  is  observed 
just  as  in  a  longitudinal  one.  In  [1 1]  plots  of  relative  drag  coefficient 
XIX B  =  f(Re)  and  XJXB  -  f(Ha)  are  shown  (see  Figs.  6-18,  7-23  [1 1]). 
The  qualitative  character  of  the  dependencies  is  as  in  Fig.  1;  maximum 
drag  reduction  is  50-70%  at  (Ha/Re)  x  103  -  6.6,  and  its  dependence  is 
close  to  (5). 

The  mentioned  similarity  of  the  data  on  drag  reduction  in  MHD 
case  and  in  case  of  additives  is  also  observed  in  the  mean  velocity  U 
distribution  across  the  channel  cross-section.  Figs.  2  and  3  show  mean 
velocity  profiles  formed  at  the  decrease  in  hydrodynamic  drag  due  to 
polymer  additives  [10]  and  in  MHD  flows  [6].  Here  we  observe  a 
number  of  common  properties  of  profiles  in  both  cases.  The  profiles 
are  presented  in  near-wall  coordinates 

u+=  U/U*,  y+~y  U*/v  (6) 

where  y  is  the  distance  from  the  wall.  The  profiles  u+  =  f(y+)  measured 
in  the  case  of  drag  reduction  by  a  polymer  additive  of  5  wppm  at  Re  - 
3.5  x  104  were  obtained  at  various  distances  downstream  of  the 
polymer  injection  site  x/d  =  8  +  214  [10].  The  principal  feature  of  the 
profiles  at  DR  <  60%  is  a  nearly  parallel  shift  AB  of  their  logarithmic 
portion 

u+  =  5.75  log  y++  5.5  +  AB  (7) 

The  larger  drag  reduction  (curves  1-4,  Fig.  2),  the  larger  this  shift. 
At  AB  =  0  logarithmic  profile  (7)  fits  its  linear  portion  u+  =  y+;  then, 
with  growing  AB,  another  range,  similar  to  logarithmic  one,  appears 
between  them.  It  has  a  slope  increasing  with  growing  drag  reduction. 
This  portion  of  the  profile  tends  to  a  limiting  asymptote  [9] 

u+  =  26.9  y+  -  1 7  (8) 

shown  by  curve  7  in  Fig.  2. 

Mean  velocity  profiles  shown  in  Fig.  3  have  been  obtained  in  MHD 
mercury  flow  for  different  Ha  numbers  up  to  614  at  various  Re 
numbers.  Logarithmic  portion  of  the  profile  can  be  approximated  by 
the  relation  (7)  shown  by  curve  6  (Fig.  3).  With  increasing  Ha/Re 
ratio,  AB  grows  (7)  and  reaches  10  at  103  Ha/Re  =  32.  Just  as  in 
profiles  of  flows  with  drag  reduction  induced  by  polymer  additive,  a 
range  with  the  slope  close  to  the  limiting  asymptote  (8)  appears  in  the 
profile;  it  is  shown  by  curve  7  in  Fig.  3a.  It  is  noteworthy  that  here 
velocity  u+  values  remain  much  below  those  corresponding  to  a 
parabolic  profile  of  a  laminar  flow  shown  by  curve  8  in  Fig.  3a. 

Having  emphasized  a  marked  analogy  in  the  behavior  of  drag 
coefficient  and  mean  velocity  profiles  of  flows  with  drag  reduction 
caused  by  additives  and  MHD  flows,  we  pass  to  structural  properties 
of  MHD  turbulence  resulting  in  drag  reduction. 

3.  Helical  turbulence  of  a  drag-reduced  MHD  flow 

MHD  turbulence  has  a  specific  nature  that  results  from  the 
interaction  with  a  magnetic  field.  Since  we  are  interested  in  turbulence 
properties,  field  orientation  is  not  very  important,  and  longitudinal 
field  has  no  preference  with  respect  to  a  transverse  one.  Therefore,  we 
make  use  of  data  on  MHD  turbulence  in  a  transverse  magnetic  field, 
which  provide  for  a  more  complete  insight. 

Our  experiments  were  conducted  in  a  mercury  flow.  The 
experimental  facility  involves  a  test  channel,  a  pump,  an  overflow 
constant  level  tank  with  a  number  of  dense  meshes  for  damping  the 
entering  flow  disturbances  and  a  constant  level  tank.  The  test  channel 
made  of  stainless  steel  has  a  rectangular  2.8  x  5.6  sq.  cm  cross-section. 
Uniform  magnetic  field  was  directed  normal  to  the  longer  side  of  the 
channel  cross-section.  The  electromagnetic  pole  length  was  90  cm, 
and  magnetic  field  B  could  vary  up  to  1 .2  T.  A  fine  honeycomb  was 
placed  into  the  flow  upstream  of  the  test  section  in  order  to  eliminate 
penetration  of  any  turbulence  from  upstream  into  the  test  section.  We 
examined  the  behavior  of  turbulence  generated  streamdown  of  the 
honeycomb.  Local  velocity  measurements  have  been  performed  by 
means  of  a  conduction  anemometer.  Turbulence  intensity  and  spectra 


of  velocity  fluctuations  were  defined.  A  more  detailed  description  of 
the  experimental  facility  and  methods  is  given  in  [12]. 

Experiments  have  been  mainly  performed  at  mean  velocity  U0  35 

0.16  m/s  corresponding  to  Reynolds  number  Re  of  52  x  10J,  and 
some  of  the  experiments  -  at  U0  *  0.08  m/s.  Ha  number  varied  in  the 
range  of  60-1200,  and  interaction  parameter  N  -  in  the  range  of  0.1- 
30,  the  magnetic  Reynolds  number  being  Rem  =  pQa  U0L  «  1; 
here  L  is  the  length  scale,  and  p0  is  magnetic  permeability. 

Our  experiments  have  confirmed  that  turbulence  intensity 
decreases  under  a  comparatively  weak  magnetic  field  if  the 

parameter  103Ha/Re  increases  up  to  2.5.  Then  the  turbulence 
intensity  reveals  an  abrupt  2-3-fold  growth  in  the  intermediate  range 

of  2.5  <103  Ha/Re  <  5.  After  that  it  changes  slightly  in  the  range  of 

5  <  103Ha/Re  <  10.  We  have  obtained  one  more  specific  range  of  a 
significant  turbulence  amplification  -  that  of  the  parameter  increase 

in  the  range  of  13  <  103Ha/Re  <  25. 

Velocity  spectra  measured  have  shown  that  a  qualitative  change 
in  the  dependence  of  turbulence  intensity  on  Ha/Re  is  accompanied 
by  a  change  in  spectral  index.  Fig.  4  shows  velocity  spectra 
measured  at  N  -  0.2  and  0.7;  here  Eu  is  spectral  energy  density,  and 
f  -  frequency.  Turbulence  velocity  spectra  obtained  under  a  weak 
magnetic  field  (Fig.  4A)  are  characterized  by  the  spectral  slope 
close  to  a  well-known  Kolmogorov’s  index  -5/3  inherent  to 
turbulence  in  the  inertial  range.  Significant  changes  in  spectral 
index  become  evident  when  the  parameter  Ha/Re  is  increased.  The 
respective  spectrum  shown  in  Fig.  4B  differs  from  those  obtained  in 
the  previous  mode.  Particularly,  their  spectral  index  close  to  -7/3  in 
the  high  frequency  range  [12]. 

Turbulence  velocity  spectra  obtained  in  the  range  of  the 
interaction  parameter  N  >1.4  are  shown  in  Fig.  5.  Three  spectra 
(series  A)  with  very  close  values  were  obtained  in  the  range  of  1 .6  < 
N  <  9.  The  spectrum  C  corresponds  to  N  =15.6,  whereas  the 
spectrum  B  -  to  intermediate  conditions.  Their  high  frequency 
ranges  are  described  by  spectral  indices  close  to  -11/3  or  4.  A 
significant  amplification  of  spectral  density  is  observed  at  low- 
frequency  scales  ifN  >10. 

4.  Discussion  of  the  results 

We  have  revealed  four  modes  of  turbulent  motions  based  on 
turbulence  intensity  versus  Ha/Re  and  on  the  values  of  spectral 
indices,  as  well.  They  correspond  to  the  following  Ha/Re  and 
interaction  parameter  values,  as  shown  in  the  Table. 


Modes: 

1 

2 

3 

4 

103Ha/Re 

<2.5 

2.5-5 

5-13 

13-25 

N=Ha2/Re 

<0.3 

0.3-1. 4 

1.4-10 

10-30 

MHD  Turbulence  Modes 


The  first  mode  represents  a  transformation  of  Kolmogorov’s 
turbulence  with  spectral  index  -5/3  noted  at  rather  low  values  of  the 
parameters  Ha/Re  -  10"3  ;  N  ~  0. 1.  It  manifests  itself  in  turbulent 
intensity  decrease  with  growing  parameters.  The  second  mode 
represents  helical  turbulence  generation  accompanied  by  an  abrupt 
transition  from  the  spectral  index  of -5/3  to  that  close  to  -7/3.  This 
transition  is  an  important  fact  pointing  to  a  qualitative  change  in 
turbulence  mode.  In  Kolmogorov’s  turbulence,  the  only  and  the 
main  mechanism  of  the  generation  of  velocity  field  and,  hence,  of 
the  spectral  index  -5/3  in  the  inertial  scale  range  is  energy  transfer. 
The  crucial  parameter  is,  respectively,  energy  transfer  rate  e  =  du2/dt 
[13].  In  the  third  mode  helical  turbulence  qualitatively  changes 
becoming  intermittent.  Then,  in  the  fourth  mode,  the  intermittency 
is  developing,  and  turbulence  localization  regions  grow  in  number. 

In  helical  turbulence  having  spectral  slope  of -7/3,  the  crucial 
parameter  is  helicity  transfer  rate  rj  =  dH/dt,  where  H  =  <u  rot  u>  is 
helicity.  In  this  case,  a  respective  inertial  spectral  range  is  generated 
under  the  action  of  helicity  transfer.  This  drastically  changes  motion 
characteristics,  particularly,  leads  to  a  decrease  and  maybe  even  to  a 
negative  value  of  turbulent  viscosity  [14].  In  case  of  helical 
turbulence  characteristic  features  of  velocity  behavior  can  be 
described  by  the  model  equation  [  1 5] 

d<U>/dt  =  a  rot<U>  +  vA<U>  (9) 


380 


where  a  =  Ht,  t  being  the  correlation  time.  A  new  remarkable  quality 
of  the  equation  (10)  is  the  dissipative  “anti viscous”  force  resulting 
from  the  term  a  rot  U  ~  L'1  providing  for  the  feedback  between 
motions  along  different  axes.  This  force  decreases  more  slowly  than 
the  viscous  force  (~  L*2 )  with  increasing  characteristic  scale  L. 

Direct  computation  of  turbulent  viscosity  shows  that  mean  helicity 
and  its  fluctuations  decrease  its  value.  Indeed,  using  the  representation 
of  the  helicity  parameter  a  =  <a>  +  a',  where  <a'>  55  0,  and  letting 
<a'(t)  a'(t')>  =  2D5(t  -  t'),  we  average  the  equation  (9)  over  the 
helicity  fluctuations  and  obtain  the  same  equation  with  the 
substitutions  a  -»  «x>  and  v  ->  v  -  D  showing  the  turbulent  viscosity 
decrease.  Turbulent  viscosity  can  essentially  decrease  [3]  in  helical 
turbulence  with  finite  correlation  time  and  non-zero  mean  helicity. 
This  is  important  under  real  ocean  conditions,  where  there  is  neither 
homogeneity,  nor  isotropy.  Moreover,  even  under  isotropic  and 
homogeneous  conditions,  but  with  the  account  of  sufficiently  high 
correlation  times  of  turbulence  and  intense  helicity  fluctuations, 
turbulent  viscosity  may  reverse  its  sign.  The  condition  of  sign  reversal 
in  this  case  is  ti  >  t,  where  ii  is  the  characteristic  time  of  helicity 
fluctuations,  and  t  is  the  characteristic  correlation  time  of  small-scale 
turbulence,  supposing  that  the  amplitude  of  helicity  fluctuations  is 
close  to  the  average  level. 

Negative  viscosity  observed  in  the  experiments  on  the  analysis  of 
MHD  flows  [16]  is  well  explained  by  helical  turbulence  model. 
Turbulent  viscosity  decrease  described  by  helical  turbulence  model  is 
observed  in  experimental  studies  of  drag-reduced  flows.  Irrelevant  of 
the  nature  of  a  factor  causing  drag  reduction,  both  in  MHD  flows  and 
in  case  of  polymer  additives  a  decorrelation  between  u'  and  v' 
components  of  velocity  fluctuations  takes  place,  resulting  in  a 
decrease  in  Reynolds  stresses.  A  decrease  in  one-point  correlations  < 
u'  v'  >  making  the  principal  contribution  to  Reynolds  stresses  is 
presented  in  Fig.  6  for  a  MHD  flow  [17]  and  in  Fig.  7  -  for  drag 
reduction  by  polymer  additives  [18].  This  fact  testifies  to  a  profound 
similarity  of  turbulence  modes  at  drag  reduction  under  various  factors 
and  is  one  of  arguments  in  favor  of  our  approach. 

It  is  established  [19]  that  in  MHD  shear  flows  helicity  generation 
occurs  depending  on  the  interaction  parameter  N  value.  Helicity 
increase  makes  the  motion  more  regular  than  in  Kolmogorov’s 
turbulence.  The  principal  properties  of  energy  transfer  are  essentially 
changed  in  helical  turbulence  mode.  In  contrast  to  Kolmogorov’s 
turbulence,  where  energy  losses  occur  at  the  expense  of  energy 
transfer  from  the  source  scale  to  the  sink  small-scale  regions  with  high 
dissipation,  at  sufficiently  high  mean  helicity  the  usual  transfer  of 
turbulent  energy  into  the  viscous  sink  is  interrupted.  In  fact,  the  more 
oscillations  are  excited  in  the  system,  the  better  chaotization 
conditions.  Under  the  conditions  of  a  direct  energy  transfer,  the 
number  of  vortical  harmonics  grows  due  to  vortex  splitting,  and  the 
chaotization  process  is  accelerated.  However,  under  the  conditions  of 
an  inverse  energy  transfer  along  the  spectrum,  the  number  of  vortical 
harmonics  decreases  due  to  vortex  merging,  the  chaotization  process 
is  slowed  down,  and  quasi-laminarization  arises. 

Drag  coefficient  for  helical  turbulent  motions  in  channels  and  at  the 
overflow  of  bodies  under  the  mentioned  conditions  should  decrease. 
Indeed,  drag  reduction  observed  in  MHD  turbulent  flows  and 
interpreted  as  laminarization  has  been  obtained  in  flows  with  turbulent 
fluctuations.  We  have  revealed  in  our  experiment  that  helical 
turbulence  mode  with  the  spectral  index  -7/3  is  generated  at  the 
parameter  Ha/Re  value  where  drag  reduction  range  begins.  Fig.  7a 
shows  drag  coefficient  dependence  on  Ha/Re  parameter  obtained  in 
[20]  -for  a  broad  range  of  Re  numbers  in  a  mercury  flow  in  a  smooth 
channel  under  a  transverse  magnetic  field.  Fig.  7b  presents  a 
dependence  of  spectral  index  n  on  Ha/Re  parameter  obtained  in  [12]. 
Apparently,  at  n  values  close  to  -7/3  corresponding  to  the  appearance 
of  helical  turbulent  mode  drag  coefficient  becomes  close  to  its  laminar 
value  shown  in  Fig.  7a  as  Hartmann’s  solution. 

It  is  well-known  (see  [21]  and  references  therein),  a  motion  of 
helical  nature  is  generated  near  the  wall,  such  as,  say,  streamwise 
vortical  structures.  Their  evolution  is  the  key  point  in  boundary  layer 
formation  and  in  drag  reduction  problem.  The  approach  to  the 
problem  using  helical  turbulence  model  is  physically  grounded  and 
allows  us  to  interpret  data  obtained  at  drag  reduction  by  various  means 
from  a  single  point  of  view. 

5.  Conclusion 

A  significant  drag  reduction  in  turbulent  flows  is  achieved  by 
means  of  additives,  such  as  dilute  polymer  and  surfactants  solutions 
and  also  observed  in  magnetohydrodynamic  (MHD)  flows.  Despite 
different  physical  nature  of  the  action  on  the  flow,  this  phenomenon  is 


characterized  by  similar  turbulence  properties.  A  similar  behavior  of 
such  characteristics  of  turbulent  flows  as  drag  coefficients,  mean 
velocity  profiles,  Reynolds  stresses  fall-down  obtained  in  above 
experiments  is  an  argument  in  favor  of  a  universal  key  mechanism 
of  a  significant  drag  reduction  due  to  a  specific  turbulence  mode. 

Our  studies  of  MHD  turbulence  have  shown  that  its  mode 
changes  with  increasing  MHD  interaction  parameter.  The  spectral 
index  varies  from  -5/3  value  inherent  to  Kolmogorov’s  turbulence 
to  -7/3,  when  the  interaction  parameter  becomes  higher  than  a 
certain  value.  Our  studies  have  shown  that  a  spectrum  with  the 
index  -7/3  is  formed  due  to  the  transfer  of  helicity  generated  in  a 
shear  flow  under  the  action  of  a  magnetic  field.  The  comparison 
with  experimental  data  on  drag  reduction  in  MHD  flows  shows  that 
it  is  achieved  at  the  values  of  the  interaction  parameter  close  to  the 
appearance  of  helical  turbulence. 

We  have  shown  that  helical  turbulence  possesses  a  number  of 
features  favorable  for  the  formation  of  a  drag-reduced  flow,  such  as 
a  reduced  effective  viscosity,  low  dissipation,  inverse  energy 
transfer  from  small  scales  to  large  ones.  It  is  known  that  in  turbulent 
flows  near  walls  helical  vortices  are  developed.  These  vortices  lose 
their  stability  and  break  down  leading  to  kinetic  energy  production 
and  dissipation  near  a  wall.  Helical  movement  stabilization 
represents  an  adequate  universal  mechanism  of  the  influence  of  both 
body  forces  and  additives  on  the  motion  near  walls  leading  to  drag 
reduction.  The  application  of  this  approach  to  seawater  drag 
reduction  under  various  conditions  will  be  fruitful. 

Acknowledgment 

The  authors  are  grateful  to  Mrs.  N.  Goldbaum  for  her  inestimable 
assistance  in  the  paper  preparation. 

References 

1.  Toms,  B.A.  1949.  Some  observations  on  the  flow  of  linear 
polymer  solutions  through  straight  tubes  at  large  Reynolds  numbers. 
Proc.  of  the  1st  Intemat.  Rheology  Congress,  II,  Part  2  (North- 
Holland,  Netherlands),  135-142. 

2.  Branover,  H.,  Moiseev,  S.,  Eidelman,  A.  and  Nagorny,  M.  1994. 
Quasi-two-dimensional  helical  turbulence  in  MHD  and  geophysical 
flows.  Proc.  2nd  Intern.  Conf.  on  Energy  Transfer  in  MHD  Flows, 
Sept.  26-30, 1994,  Aussois,  France,  v.  2,  777-785. 

3.  Belyan,  A.V.,  Moiseev,  S.S.  and  Chkhetiani,  O.G.  1994.  On  eddy 
viscosity  in  helical  turbulence.  Physics  -  Dokl.,  v.  39,  No.  1, 13-15. 

4.  Golbraikh,  E.,  Chkhetiani,  O.,  Moiseev,  S.,  Eidelman,  A.  and 
Branover,  H.  1998.  On  the  character  of  turbulent  energy 
redistribution  in  helical  flows.  Ann.  Geophys.,  v.  16,  II. 

5.  Moffatt,  H.K.  1969.  The  degree  of  knottedness  of  tangled  vortex 
lines.  J.  Fluid  Mech.,  v.  35,  p.  1, 117-129. 

6.  Genin,  L.G.,  Zhilin,  V.G.  and  Petukhov,  B.S.  1967.  Experimental 
investigation  of  turbulent  flow  of  mercury  in  a  circular  tube  in  a 
longitudinal  magnetic  field.  High-Temperature  Sci.-Res.  Inst.,  v.  5, 
No.  2,  266-271. 

7.  Klebanoff,  P.S.  and  McMichael,  J.M.  1976.  On  MHD  pipe  flow. 
Proc.  Bat-Sheva  Intemat.  Seminar  on  MHD-FIows  and  Turbulence, 
Beer-Sheva.  J.  Wiley,  N.Y.,  p.  73. 

7a.  Levin,  B.V.  and  Chinenkov,  I. A.  1966.  Experimental  study  of 
turbulent  flow  of  a  conducting  fluid  in  a  pipe  in  the  presence  of  a 
longitudinal  magnetic  field.  Magnetohydrodynamics,  No.  4,  147. 

7b.  Kovner,  D.S.  and  Krasil’nikov,  E.Yu.  1965.  Experimental  study 
of  turbulent  pipe  flow  of  an  electrically  conducting  fluid  in  a 
parallel  magnetic  field.  Dokl.  Akad.  Nauk  SSSR,  No.  5,  1096. 

8.  Fraim,  F.W.  and  Heiser,  W.H.  1968.  The  effect  of  a  strong 
longitudinal  magnetic  field  on  the  flow  of  mercury  in  a  circular 
tube.  J.  Fluid  Mech.,  v.  33,  part  2, 397-413. 

9.  Virk,  P.S.  1975.  Drag  reduction  fundamentals.  AIChE  J.,  v.  21, 
No.  4,  625-656. 

10.  McComb,  W.D.  and  Rabie,  L.H.  1982.  Local  drag  reduction  due 
to  injection  of  polymer  solutions  into  turbulent  flow  in  a  pipe. 
AIChE  J.,v.  28,  547-565. 

1 1.  Branover,  H.  1978.  Magnetohydrodynamic  flow  in  ducts.  Wiley 
&  Sons,  N.Y.,  290  p. 

12.  Branover,  H.,  Eidelman,  A.,  Nagorny,  M.  and  Kireev,  M.  1994. 
MHD  simulation  of  quasi-two-dimensional  geophysical  turbulence. 
In:  Progress  in  Turbulence  Res.,  Eds.  H.  Branover  and  Y.  Unger.,  v. 
162,  64-79. 

13.  Monin,  A.S.,  Yaglom,  A.M.  1975.  Statistical  Fluid  Mechanics. 
Ed.Lumley,  J.  MIT  Press,  Cambridge,  Mass. 


381 


14.  S.  Moiseev,  H.  Branover,  O.  Chkhetiani,  A.  Eidelman  and  E. 
Golbraikh.  1998.  Role  of  helicity  and  chirality  in  drag  reduction  in 
turbulent  flows.  Proc.  Intern.  Symp.  Seawater  Drag  Reduction. 

15.  Moiseev,  S.S.  1990.  Helical  mechanism  of  large-scale  structure 
generation  in  continuous  media  Plasma  Physics,  v.  16,  No  8, 951-958. 

16.  Henoch,  C.,  Hoffert,  M.,  Branover,  H.  and  Sukoriansky,  S.  1993. 
Anisotropic  turbulence:  analogies  between  geophysical  and 
hydromagnetic  flows.  In:  Current  Trends  in  Turbulent  Research. 
Progr.  in  Astron.  and  Aeron.,  AIAA,  v.  149,  190-209. 

17.  Reed,  C.B.  and  Lykoudis,  P.S.  1978.  The  effect  of  a  transverse 
magnetic  field  on  shear  turbulence.  J.  Fluid  Mechanics,  v.  89,  No.  1, 
147-171. 

18.  Gampert,  B.  and  Yong,  CX  1990.  The  influence  of  polymer 
additives  on  the  coherent  structure  of  turbulent  channel  flow.  In: 
Structure  of  Turbulence  and  Drag  Reduction,  Ed.  A.  Gyr,  Springer- 
Verlag,  Berlin,  223-232. 

19.  Chkhetiani,  0.,  Moiseev,  S.,  Golbraikh,  E.  and  Eidelman,  A.  1997. 
On  the  helicity  generation  in  shear  flows  in  the  external  magnetic 
field.  Ann.  Geophys.,  v.  15,  II,  C607. 

20.  Brouillette,  E.C.  and  Lykoudis,  P.S.  1967.  Magneto-fluid- 
mechanic  channel  flow.  Phys.  Fluids,  v.  10,  No.  5,  995-1001. 

21.  Kline,  S.J.  and  Robinson,  S.K.  1990.  Turbulent  boundary  layer 
structure:  Progress,  status,  and  challenge.  In:  Structure  of  Turbulence 
and  Drag  Reduction,  IUTAM  Symp.,  Zurich,  Switzerland,  1989;  Ed. 
A.  Gyr,  Springer-Verlag,  3-22. 


Fig.  2.  Mean  velocity  profiles  streamdown  of  polymer 
(5  wppm)  injection  (McComb  &  Rabie,  1982):  I)  x/d 
=  8;  DR,%  =  -2.5;  2)  40;  26.5;  3)  76;  46;  4)  100;  57; 

5)  190;  65;  6)  214;  67;  7)  Virk’s  asymptote:  u+  = 

=  26.9  log  y+  - 1 7;  8)  u+  -  5.75  log  y+  +  5.5;  9)  u+  -  y+. 


Fig.  1.  Dependence  of  drag  coefficient  on  Reynolds 
number  and  Hartmann  number  (Klebanoff  & 
McMichael,  1976).  Comparison  with  other  sources:  1) 
Fraim  &  Heiser,  1968;  2)  Levin  &  Chinenkov,  1970; 
3)  Genin  et  al.,  1967;  4)  Kovner  &  Krasil’nikov,  1966; 
5)  Virk’s  asymptote:  X  -  2.32  Re"058;  6)  our 
approximation:  X  =  2.39  Re*°  S6;  7)  Blasius  formula: 
k  =  0.3146  Re*025. 


Fig.  3.  Mean  velocity  profiles  in  MHD  flow.  Re  x  104: 
a)  2.39;  b)  4.25;  Ha:  1)  0;  2)  279;  3)  390;  4)  502; 

5)  614;  6)  u+  =  5.75  log  y+  +  5.5;  7)  Virk’s  asymptote: 
u*  =  26.9  log  y+  -  1 7;  8)  parabolic  profile. 


382 


Ig  Ou,  cm2/s 


.<1.25  0.25  0-75  125  lgf 


Fig.  4.  Velocity  spectra  transformation  under  a 
magnetic  field:  A:  N  =  0.2;  B:  N  =  0.7.  The  spectrum 
B  is  shifted  downwards  by  two  orders. 


0  0-2  0-4  0-6  0-8  10 

y;d 


4  to  y +■  too  m 


Fig.  6.  Reynolds  stress  profiles  transformation  in 
flows  with  drag  reduction:  a)  MHD  flow,  Re  -  25000; 
103  Ha/Re:  1)  0;  2)  1.08;  3)  2.07;  4)  3.63  (Reed  & 
Lykoudis,  1978);  b)  polymer  solution  flow  (Gampert 
&Yong,  1990). 


Fig.  5.  Velocity  spectra  evolution  with  growing 
interaction  parameter  N.  A:  N  =  1.6;  B:  9.06;  C:  15.6. 


Re 


2  4  S  Ha/Rex  1000 


Fig.  7.  Drag  coefficient  A.  for  MHD  turbulent  flow  as 
compared  with  Hartmann’s  solution  for  laminar  flow 
(Brouillette  &  Lykoudis,  1967)  (a)  and  turbulent 
spectral  index  n  (Branover  et  al.,  1994)  (b)  versus  the 
parameter  Ha/Re. 


383 


DRAG  REDUCTION  BY  ELECTRO-MAGNETIC  FORCES 


Vladimir  I.  Merkulov 

Institute  of  Theoretical  and  Applied  Mechanic 
SB  of  the  Russian  Academy  of  Sciences,  Novosibirsk,  630090,  Russia 
merkulov@itam.nsc.ru 

Abstract -  We  present  a  newphysical  and  mathematical  formulation  of  a  problem  on  the  external  flow  of  an  electroconducting 
fluid  (sea  water)  under  the  action  of  the  body  motion  and  certain  bulk  control  force  (Lorentz  force).  For  the  slender  axisym- 
metric  bodies  we  find  within  the  framework  of  an  inviscid  model  the  boundary  values  of  electromagnetic  fields  depending  on 
the  body  shape,  which  ensure  the  absence  of  the  pressure  distur  bance  in  the  overall  flow  field  and, in  particular, ensure  a  wa¬ 
veless  motion  of  a  half- submersed  body.  The  second  example  concerns  the  problem  of  friction  drag  decrea  se  in  a  viscous  liqu- 
idby  way  of  displacement  of  the  flow  of  sliding  for  the  flow  with  roll  ing.In  the  conclusion  the  electromagnet  ic  providing  cont¬ 
inuous  flowingaround  sphere  for  the  large  numbers  of  Reynolds  is  calculated. 


I.  INTRODUCTION 

A  strong  magnetic  field  combined  with  a  weak  electric 
field  in  the  case  when  they  occupy  a  large  volume  enable  one 
to  create  a  force  being  sufficient  for  a  practical  goal  in  such 
a  widespread  medium  as  the  sea  water.  The  Japanese  re¬ 
searchers  from  the  Kobe  University  of  Mercantile  Marine  have 
made  use  of  this  possibility  [1].  However,  it  is  preferable  to  use 
such  a  fine  and  flexible  form  of  the  effect  on  the  fluid,  which  is 
represented  by  the  electromagnetic  field,  not  so  much  for  the 
thrust  production  as  for  the  control  of  external  fluid  flow.  For 
the  planar  flow  the  proposed  problem  formulation  has  been 
considered  in  the  author’s  work  [2]. 

II.  FORMULATION  OF  THE  PROBLEM 

Let  us  consider  a  fluid  flow  caused  by  the  longitudinal 
motion  of  a  slender  axisymmetric  body.  We  will  be  interested 
in  the  flow  character  outside  the  boundary  layer  the  presence  of 
which  can  be  taken  into  account  by  increasing  the  body  width. 
Assuming  the  inviscid  fluid  model  we  arrive  at  the  following 
equation  system  [3]. 

VH  +  wXu  =  F  (1) 

w  =  V  X  u;  Vu  =  0 
with  the  boundary  conditions 

un  -  0  (2) 

on  the  boundary, 

limu  =  U 

at  the  infinity.  Here  H  is  the  total  energy  of  the  fluid  parti¬ 
cles  including  its  potential  part,  F  is  the  non-potential  part  of 
the  bulk  forces.  Let  us  introduce  the  stream  function  of  the 
axisymmetric  flow,  the  Stokes  function,  by  the  relationships 
u  =  UV  X  (a'°^/r).  Here  a0  is  ort  the  cylindrical  coordinate 
system  r,a,z .  We  express  the  vectorF  also  in  terms  of  a  scalar 
function  A:  F  =  U2V  x  (a°A/r).  The  operation  V  applied 
to  equation  (1)  enables  us  to  eliminate  the  function  H  and  to 
obtain  for  the  axisymmetric  flow 

Uzduj/dz  +  urdtu/dr  =  (Vx  F)a  (3) 

Here  o;-is  azimuthal  nonzero  component  of  the  vorticity. 

For  slender  bodies  the  control  objectives  are  attainable 
with  the  aid  small  control  forces,  then  with  the  accuracy  up  to 
the  quantities  of  the  second  order  of  smallness  we  can  obtain 
from  [3]  a  linear  equation  with  constant  coefficients 

[(9/9z)V  x  V  x  (a°«/r)]Q  =  [V  x  V  x  (a°/l/r)]a  (4) 

^he  material  presented  here  was  first  reported  at  the  Inter¬ 
national  Conference  on  Marine  Electromagnetics  (MARELEC 
97)  on  23-26  June  1997,  London,  UK. 


The  integration  of  this  equation  leads  to  the  formula 

^  =  r2/2  +  ^+  /  A(r,  z)dz>  (5) 

J  —  oo 

where  4>-  is  the  Stokes  function  [3],  representing  the  stream 
function  of  the  potential  flow  in  the  absolute  coordinate  sys¬ 
tem,  in  which  the  fluid  is  at  rest  a  the  infinity,  and  the  body 
moves  at  the  speed  —U  in  the  direction  of  the  2  axis. 

Denote  by  r  =  ( (z )  the  equation  of  the  surface  of  the 
body  flowed  around.  For  slender  bodies  the  following  formulas 
are  valid:  un  =  ur  =  UC{z)  =  —  [1  /  r)(d^  /  d  z)  at  r  =  ((z). 
Substituting  here  the  representation  (5),  we  obtain 

d^/dz  =  -c'C  -  A 

at  r  =  C(z)-  Now  we  add  to  this  the  condition  at  the  infinity 
lim  dip/dz  —  0. 

To  complete  the  problem  formulation  let  us  write  down  the 
Bernoulli  integral.  For  the  case  of  a  slender  body  and  a  small 
force  we  can  write  with  the  accuracy  up  to  the  second  order 
quantities  the  following  expression  for  the  Bernoulli  integral 
on  the  surfaces  #  =  const  : 

H  =  f  Fz(z)dz  (6) 

J  — oo 


III.  DETERMINATION  OF  LORENTZ 
FORCES 

Taking  into  account  a  small  electric  conductivity  cr  of  the 
water  and  consequently  a  small  current  density  one  can  de¬ 
termine  the  force  F  within  the  framework  of  a  non-induction 
approximation.  This  enables  us  to  introduce  the  potentials 
of  the  electric  field  (f>e  and  of  the  magnetic  field  4>b  m  such  a 
way  that  E  =  V<£e,  B  =  V<^-  The  Lorentz  force  related  to 
the  density  is  equal  to  the  product  F  =  j  X  B/p.  And  since 
the  Ohm,s  law  for  the  electroconducting  medium  moving  at  a 
speed  u  has  the  form  [4] 

j  -  <r( V <j><*  +  u  X  V4>b). 

The  potentials  of  the  electric  and  of  the  magnetic  field 
should  be  solved  under  the  boundary  conditions 
d<f)e/dn  =  e,  d<f>b/dn  =  6  on  the  boundary, 
lim  V^>e  —  limV.^b  =  0  at  the  oo. 

All  the  arbitrariness  in  the  choice  of  the  control  function 
will  finally  reduce  to  the  choice  of  the  boundary  values  for  the 
electric  and  magnetic  fields.For  our  purposes  it  is  search  for 
the  boundary  conditions  of  the  form 
e  =  eo(^)  sin  ATcv,  b  =  bo(z)  sin  Na. 

Here  eo(z),bo(z)  are  slowly  varying  functions,  N  is  the 
number  of  pairs  of  the  poles  of  electromagnetic  fields.  For 
slender  bodies  the  velocity  field,  the  electromagnetic  field  and 
the  forces  created  by  the  latter  field  can  be  determined  in  each 
section  2  =  const,  under  the  assumption  of  their  independence 
of  z.  A  weak  dependence  of  2  is  taken  into  account  here  by  a 


385 


weak  alteration  of  the  radius  and  the  amplitude  values  of  the 
field  as  functions  of  a  parameter,  whereas  the  relative  values 
£/r  will  not  depend  on  With  regard  for  the  above  circum¬ 
stances  the  approximate  of  potentials  is  [5] 

4>e  =  [e0(z)C(*)/An(C/r)^sin7Va 
4>b  -  [M*K(*)/^(C/r)WsinMx, 

which  approximate  well  the  arbitrary  boundary  conditions. 
The  necessary  computations  enable  us  to  obtain  the  formula 

F  =  z0eo(2)6o(2)(C/r)2^+1)(<r/p)(l  -  C60/e0)  (7) 


We  can  see  that  the  boundary  values  chose  by  us  engender 
electric  and  magnetic  fields,  which  are  orthogonal  to  each  other 
and  which  produce  the  force  oriented  along  the  z  axis  and 
this  field  does  not  depend  on  the  azimuthal  coordinate.  The 
formula  last  we  have  that 


A 


eo(2)MzMCA)2(C/r)2iNr 
2  NU2p 


(1  —  Ubo/eo) 


(8) 


In  Concluding  this  section  we  wish  to  show  that  the  total 
work  of  the  control  force  is  equal  to  zero. 


N  = 


I  uF  dr—  I  \iX7Hdr-\-  /  u(w  X  u)dr 

J  r  J  T  J  T 


Here  r  is  the  disturbed  volume  of  the  fluid.  Since  u(u/  x  u)  = 
0,  we  have  that 


N 


=  /  u VHdr  =  (p  HundS  +  ®  HundS  =  0. 
J  T  J  Si  J  S2 


Here  un  =  0  on  the  hull  boundary  body  Si  and  H  =  const 
on  the  control  surface  S2  which  lies  outside  the  disturbance 
zone.  Thus  the  electromagnetic  system  works  in  the  nose  part 
(f;  >  0,Ubo  <  eo)  in  the  regime  of  pump  and  requires  the 
power  supply,  whereas  in  the  stern  part  (£;  <  0,  Ubo  >  eo) 
the  similar  system  should  work  in  the  regime  of  an  MHD- 
generator.  Their  powers  are  equal. 


IV.  NON-DISTURBANCE  MOTION 

Let  us  turn  the  representation  (5)  for  the  stream  function 
The  first  item  corresponds  to  the  nondisturbed  flow.  The 
second  item  describes  the  disturbances  caused  by  the  moving 
body.  The  third  item  describes  the  perturbations  from  the 
control  force.  Let  us  choose  the  value  of  the  control  force 
in  such  a  way  that  its  nonzero  a  component  of  the  vector- 
potential  a0 A  has  the  following  boundary  value: 

A  =  -<'<  (9) 

at  r  =  £(z)  In  this  case 

=  r2  / 2  +  /  Adz 
J  —  00 

.  The  longitudinal  component  of  velocity  for  such  the  function 
of  current  will  be  determined  by  formula 

u*  =  1  +  (1/r)  f  (dAjdr)dz—  1  +  f  Fzdz. 

J  —00  J  —00 


V.  PERIODIC  FLOW  IN  UPPER  HALF-PLAN 

As  is  known,  the  equations  governing  in  the  viscous  flow 
admit  in  the  upper  half-plane  only  the  solution  corresponding 
to  the  fluid  at  rest.  However,  the  incorporation  of  a  control 
force  removes  this  restristion.  Let  us  choose  the  spatial  and 
temporal  change  of  the  control  force  in  accordance  with  the 
progressive  wave  law  F(a:/  —  Ct,  y),  where  C  is  the  phase  speed 
of  the  progressive  wave.  In  the  co-moving  coordinate  system, 
which  moves  at  the  speed  C,the  control  force  takes  a  stationary 
for  x,  which  is  periodic  in  F(a?,y).  This  will  enable  us  to 
construct  an  x-  periodic  flow  of  a  viscous  fluid  in  the  upper 
half-plane.  By  using  the  stream  function  the  equations  may 
be  written  as  follows: 

=  Aw  +  A  A,  Aip  =  —u>.  (10) 

D(x,y) 

Here  z °A  is  vector-potential  of  the  force  F,  which  is  de¬ 
fined  as  follows:F  =  V  x  (z °A)/Re.  The  system  (10)  should 
be  solved  under  the  boundary  conditions 

ip  =  0,  d'lp/dy  —  —C  (11) 


Let  us  now  turn  to  the  Bernoulli  equation. 

u2z/2  -j-  ul/2  +  p/p  +  n  =  (p/p  +  n)oo  +  f  Fzdz 

J  —00 

The  substitution  of  expression  for  the  velocity  into  this  equa¬ 
tion  allows  on  to  get,  with  the  accuracy  assumed  above,  p  — 
const  on  the  equipotentials  of  the  gravitational  force.  Such 
the  movement  called  by  us  non-disturbance  near  the  surface 
is  not  accompanied  by  the  formation  of  gravitational  waves, 
the  body  does  not  undergo  the  wave  drag.  The  parameters 
of  boundary  values  of  the  electric  and  magnetic  fields  provid¬ 
ing  non-disturbed  movement  may  be  determined  by  the  body 
geometry.  The  a  component  of  the  vector-potential  a0  A  repre¬ 
sented  by  formula  (8)  will  satisfy  the  boundary  condition  (9), 
if  the  electromagnetic  parameters  eo(z),bo(z)  will  be  chosen 
from  the  condition 

o-eo(*),6o(2K2(z)(l  -  Ub0/e0)  =  2 NU2K'C 

Furthermore,  the  condition  for  the  symmetry  of  electro¬ 
magnetic  fields  and  for  the  axial  symmetry  of  the  flow  allow 
the  application  of  the  of  the  obtained  results  also  for  the  caise 
of  a  half-submersed  body  at  which  the  body  axis  lies  in  the 
free  surface  plane.  Not  that  the  control  force  is  present  only  in 
those  parts  of  the  hull  in  which  f ^  0,  that  is  in  the  nose  part 
and  in  the  stern  part,  and  it  is  absent  in  the  middle  cylindrical 
part.  It  is  easy  to  understand  that  it  is  possible  to  impose 
on  the  control  force  an  additional  function  of  developing  the 
thrust,  whereas  the  existing  MHD-propulsion  units,  which  are 
mounted  in  the  middle  part  of  a  ship,  cannot  realize  the  control 
function. 


at  y  —  0, 


d'lp/dy  =  1  —  C 


(12) 


at  y  oo. 

Let  us  represent  the  solution  of  the  problem  (10)  in  the 
form 

^  =  V(y)  +  ^i(y),  A  =  Ai(y)  +  A2(y)„ 
where  ^(y)  is  the  stream  function  of  the  plane-parallel 
flow,  which  may  be  found  by  solving  the  equation 


d4V  __  d?Ax 
dy 4  dy2 


(13) 


under  boundary  conditions  (11), (12).  The  small  function  'ipi 
satisfies  with  the  accuracy  up  to  the  quantities  of  the  second 
order  of  smallness  the  inhomogeneous  equation 


D  rd3V  d'tpl 
Re[dy*  dx 


dty  dAipi 


dy  dx 

•with  the  zero  boundary  conditions 


]  =  A2ipi  +  A  A2, 


(14) 


ip  i  =  d'lp/dy  =  0 


at  y  =  0  and  y  oo. 

Let  us  introduce  the  Orr-Sommerfeld  equation  of  the  hy¬ 
drodynamic  stability  theory  [6]: 


3A^0  ,  d3^  d'lpo  d<5f  dAipo  2 

Reo[ —  +  "  j;—  =  A  (15) 

Denote  by  ipo  the  eigenfunction  at  the  critical  point.  The 
eigenvales  of  the  same  problem  will  be  denoted  by  cvo ,  Re o ,  Cr ,  C{  — 
0.  We  will  search  for  the  stationary  solution  of  the  inhomo¬ 
geneous  problem  in  the  form  'ip i  =  qipo ,  where  q  is  a  constant 


386 


to  be  determined.  Let  us  substitute  this  representation  into 
equation  (14)  and  take  into  account  (15).  As  a  result  we  obtain 
the  relationship 

q(Re/Re0  -  1)A2^0  =  A A2. 

Since  Re  <  Reo  and  the  solution  ipo  is  stable  for  all  dis¬ 
turbances,  it  proves  to  be  possible  to  satisfy  the  relationship 
last  in  the  energy  measure. 


g(l  -  Re/Reo)  I  (ATpo)2da  ■ 


Vt/>0VA2  da 


This  equation  relates  the  amplitude  value  of  the  control 
function  to  the  amplitude  of  the  eigenform. 

Further  computations  require  the  specification  of  the  con¬ 
trol  function  form.  The  physical  realization  of  the  control  func¬ 
tion  may  ensure  the  following  laws: 

M  -  Ai(0)exp(-j5t/). 

A2  =  A2(0)exp(-py)cosax 

An  order  to  obtain  these  dependences  on  may  pay  atten¬ 
tion  to  chapter  (4).  The  limit  transition  r  -4  00,  N  — y  00 
allows  one  to  consider  axis-symmetrical  flow  instead  of  the 
plane  one. 

Let  us  turn  equation  (13)  ,  which  determines  the  main 
flow: 

U  =  d^/dy  =  [A  1  (0 )/(3]  exp (-(3y)  +  C\ . 

By  virtue  of  the  condition  at  the  infinity.  C 1  =  1  —  C,  where 
C  is  the  phase  speed  at  which  the  coordinate  system  chosen 
by  us  moves.  Consequently 
U  =  1  -  C  -  exp(-/3y.) 

The  coefficient  (3  is  related  to  the  displacement  width  S 
via  an  obvious  relationship.  If  the  displacement  width  is  cho¬ 
sen  as  a  reference  length,  then  (3  =  1  and  Re  =  US /is.  The 
exponential  profile  arising  in  the  process  of  the  suction  of  the 
boundary  layer  studied  in  detail  by  Schlichting  [6].  It  is,  in 
particular,  known  that  the  critical  Reynolds  number  for  the 
stationary  flow  equals  to  7104. 

Thus  if  the  control  force  along  the  total  length  of  the  body 
sustains  the  Reynolds  number  at  the  level  being  less  than  7104 
,  then  the  boundary  layer  will  preserve  the  laminar  regime  as 
in  the  case  of  the  suction.  As  is  known,  the  section  through  big 
orifices  only  destabilized  the  boundary  layer,  and  the  small  ori¬ 
fices  rapidly  become  dirty.  The  control  with  the  aid  of  a  force 
does  not  have  such  a  shortcoming.  For  the  periodic  flows  the 
drag  coefficient  is  equaled  to  zero.  It  is  achieved  by  the  work 
of  control  force  F  which  has  the  order  0(1 /Re).  The  work  of 
this  force  has  the  same  order.  The  addition  of  a  periodic  com¬ 
ponent  to  the  control  force  appears  to  ensure  a  stable  periodic 
flow  for  larger  Reynolds  numbers  than  7104. 

Let  us  now  turn  to  the  neutral  curve  for  the  exponential 
profile  [6]  .The  disturbances  with  the  wave  numbers  a  >  0.1 
decay  at  any  Reynolds  numbers.  The  subharmonic  wave  num¬ 
ber,  for  which  the  periodic  flow  in  the  consideration  without 
viscosity  is  unstable,  equals  to  a/2  =  0.05  [7].  However,  the 
viscous  force  ensure  the  stability  of  this  disturbance  for  the 
Reynolds  numbers  <  7I05. 

Note  that  for  the  periodic  flows  the  Reynolds  number  char¬ 
acterizes  the  local  properties  of  the  flow.  The  number  of  the 
periods  along  the  body  length  may  be  arbitrary. 


VI.  NON-SEPARATED  FLOW 

One  can  formulate  for  the  control  forces  an  objective  of 
ensuring  a  non-separation  flow  around  a  body  of  small  elonga¬ 
tion.  It  is  easy  to  see  that  for  the  prevention  of  a  separation 
of  the  dynamic  boundary  layer  it  will  be  required  from  the 
control  force  to  have  a  large  energy  density  sufficient  for  the 
compensation  of  the  momentum  loss  in  the  dynamic  bound¬ 
ary  layer.  A  small  electric  conductivity  of  the  sea  water  and 
the  limitations  for  the  magnetic  field  induction  do  not  enable 
one  to  reach  such  energy  densities.  Therefore,  it  is  reasonable 
to  aim  at  the  restoration  of  the  pressure  in  the  stern  at  the 


expense  of  forming  an  external  flow  by  withholding  the  sep¬ 
arated  boundary  layer  near  the  body  and  the  flow  axis.  In 
this  case  the  electromagnetic  forces  can  comprise  a  large  vol¬ 
ume  as  in  the  previous  problems,  and  no  big  density  will  be 
required  from  them,  and  the  flow  itself  will  be  weakly  vorti¬ 
cal  and  be  described  by  the  inviscid  fluid  model.  It  is  known 
that  the  flow  equations  admit  both  separated  and  attached 
solutions.  The  stability  condition  performs  a  physical  choice. 
Since  the  question  of  the  global  stability  defies  all  attempts 
of  the  theoretical  investigation,  we  have  carried  out  the  phys¬ 
ical  experiment  aimed  at  answering  the  above  question  [2].  A 
self-motion  of  a  sphere  in  the  fluid  was  investigated,  which 
was  ensured  by  the  supply  of  the  axial  momentum  in  a  narrow 
ring  in  the  middle  section  by  the  mechanical  means.  An  al¬ 
most  complete  restoration  of  the  pressure  was  registered  in  the 
stern  half-sphere,  so  that  the  pressure  on  the  wind-side  half¬ 
sphere  exceeded  the  pressure  on  the  lee  side  by  the  amount  of 
the  order  0(l/\/Re).  Since  the  fluid  dynamics  does  not  de¬ 
pend  on  the  origin  of  the  forces,  it  is  to  be  expected  that  the 
realization  of  the  bulk  control  forces  by  electromagnetic  means 
might  also  ensure  a  non-separated  flow  regime  and  maintain 
the  body  motion.  The  scale  for  the  control  force  is  determined 
from  the  condition  that  its  work  compensates  for  all  the  losses 
related  to  the  motion,  including  the  viscous  losses. 

Denote  by  P  the  hydrodynamic  drag  force.  Then  the  work 
of  this  force  will  be  equal  to  PU.  The  condition  for  the  body 
self-motion  requires  the  satisfaction  of  the  equation 


=  J  Fuodr, 


where  r  is  the  volume  occupied  by  the  fluid,  u°  is  the  fluid 
velocity  in  a  fixed  coordinate  system.  Since  we  consider  the 
regimes  with  a  small  control  effect,  then  we  can  assume  with 
an  accuracy  up  to  second  order  of  smallness  that  the  flow  is 
potential  outside  the  boundary  layer  and  consequently  the  ve¬ 
locity  is  representable  in  the  form  u°  =  V<^°. 

The  bulk  force  F  may  be  presented  by  the  expression 

F  =  o-[V0e  +  V0  x  V <£*>]. 

Here  (j)  is  the  velocity  potential  of  the  fluid  flow  in  a  moving 
coordinate  system  related  to  the  body.  The  potentials  which 
appear  in  this  formula  may  be  written  down  for  different  body 
shapes  coinciding  with  the  coordinate  surface  of  the  curvilinear 
coordinate  system  [5].  Let  us  consider,  for  example,  the  case 
of  a  flow  around  the  sphere  of  a  radius  a.  In  the  spherical 
coordinate  system  p,  9 ,  a  we  have  that 

4> 0  =  Up  cos  9[1  —  (a3/2p3)], 

<f>e  =  [-ea/(N  +  l)]<£(p0)  sin(Na),  (16) 

(f>b  =  [— ba/(N  +  l)]$(p0)  cos(Na). 

Here  $(p0)  =  (a/p)^+1  sin(NO).  This  representation  cor¬ 
responds  to  a  special  choice  of  the  boundary  conditions 
d(f>e/dn  =  e  sin^  Os\n(Na)  , 

84>b/dn  =  bsinN  6  cos(Na)  at  p  =  a. 

Here,  as  above,  N  is  the  number  of  the  pairs  of  the  poles 
located  along  the  azimuthal  coordinate  a.  The  superposition 
this  function  enables  us  to  approximate  the  boundary  condi¬ 
tions  of  a  more  general  form,  however,  the  biggest  energetic 
contribution  is  provided  by  the  first  item  written  down  by  us 
above. 

Using  this  representations  we  obtain  after  some  calcula¬ 
tions  the  mechanical  work  performed  by  the  Lorentz  forces: 

f ,  <77ra3TV2JV!!  ,  x 

iy„= x  (it) 


MeJ[l  —  3M 


4  AT3  +  15  N2  +  8N  +  3 


L  2N(2N  +  3){2N  +  7)  1 

Here  M  =  Ub/e  is  the  loading  coefficient.  In  the  particular 
cases  N  =  1,  M  <  1 

Wm  =  0. 167  e2  area3  M  (1  —  M). 


387 


For  TV  »  1,M  <  2/3 

9  ,V,} 

Wm  =  - '—--e2<nra3M(l  -  3M/2). 

m  N(2N  +  1)!!  '  ’ 

To  choose  an  optimal  value  of  the  loading  coefficient  it  is 
required  to  determine  the  electric  capacity  at  the  expense  of 
which  the  needed  mechanical  work  is  performed. 


We=a 


l 


(E  +  U  x  B)jdr  = 


(18) 


i 


[V(f>e  —  V(U  pc  os#)  X  V</>{,](V0e  +  V  0  x  V<j>b)dT. 


Carrying  out  the  necessary  calculations  similar  to  those  which 
have  been  required  for  the  determination  of  the  electric  capac¬ 
ity  we  find  that 


We  =  ana6  e' 


3  2 


27V!! 


(7V  +  l)2(27V  +  3)!! 


(19) 


[2(27V2  4  57V  4  3)  -  57V(27V  4  3)M  4  (67V2  4  67V  4  4.5)7U2]. 

The  efficiency  is  determined  by  the  relationship  77  =  Wm/We . 
In  the  particular  cas  TV  =  1,  M  <  lwe  have  that 


M(1  -  M) 

4(1  -  57VT/4  +  33A//2/40) 


(20) 


The  maximal  value  of  the  efficiency  is  equal  to  77  =  0.11  and 
is  achieved  at  M  =  0.55.  For  TV  >>  1 ,  M  <  2/3  77  — 

M/2(l  —  M). 

The  maximal  value  77  — y  1  is  achieved  at  M  — V  2/3. 


VII. SUMMARY 

The  perspectives  of  using  the  electromagnetic  forces  in 
ship  building  are  determined  by  the  degree  of  energetic  effi¬ 
ciency.  The  problems  of  control  for  a  flow  require  less  density 
of  energy  and,  hence,  they  are  performed  for  higher  electric  ef¬ 
ficiency.  Arising  with  this  possibility  of  increasing  the  velocity 
of  movement  decreases  to  a  larger  degree  the  part  of  Ohms’ 
losses. 


VIII.  REFERENCES 

1.  A.  Jwata,  E.  Tada  and  Y.  Saji,  ’’Experimental  and  the¬ 
oretical  study  of  superconducting  electromagnetic  ship  propul¬ 
sion”.  In  Proc.  5th  Lips  Propeller  Symposium  Drunen,  The 
Netherlands,  p.2,3,1983. 

2.  V.I.  Merkulov,  Fluid  Flow  Control  Novosibirsk:  Nauka 
1981  p.180. 

3.  G.K.  Batchelor,  An  Introduction  to  Fluid  Dynamics. 
Cambridge  at  the  University  Press,  1970. 

4.  W.  F.  Hughes  and  F.  J.  Young,  Electromagnetodynam¬ 
ics  of  Fluids,  New  York:J.  Wiley, 1966. 

5.  G.  A.  Korn  and  T.  M.  Korn,  Mathematical  Handbook 
for  Scientists  and  .Engineers, New  York:  McGrow-Hill  Book 
Company,  1968. 

6.  H.  Schlichting,  Grecuzschicht-Teorie  Karlsruhe:  Verlag 
G.  Braun,  1950,  p.  500. 

7.  R.  T.  Pierrehumbert  and  S.  E.  Widnall  ’’The  two- 
and  three-dimensional  instabilities  of  a  spatially  periodic  shear 
layer,”  JFM,  v.29,  part  3,1967,  pp. 417-440. 


388 


ELECTROMAGNETIC  EFFECTS  ON  LOW  SPEED  COHERENT  STRUCTURES 

EMBEDDED  IN  A  WALL  LAYER 


Jean-Paul  Thibault,  Valery  Botton  &  Lionel  Rossi 
PAMIR  Team,  LEGI, 

BP  53  X,  38041  GRENOBLE  Cedex,  France 
Jean-Paul.Thibault@hmg.inpg.fr 
Valery.Botton@hmg.inpg.fr 

Abstract  -  This  work  deals  with  ElectroMagnetic  Flow  Control  (EMFC)  and  the  basic  mechanisms  involved  in  turbulence  intensity  or  skin 
friction  reduction  by  the  use  of  EMFC.  Due  to  the  strong  complexity  of  the  problem,  our  analysis  is  based  on  an  idealised  and  simplified 
approach  of  the  wall  normal  configuration.  The  first  part  of  our  work  is  an  analytical  study  of  the  EM  forces  and  EM  vorticity  imposed  to  the 
boundary  layer.  Due  to  the  3D  configuration,  the  analytical  computation  is  very  interesting  but  limited  to  some  specific  regions  of  the  EM 
actuator.  Consequently  we  also  present  a  numerical  approach  to  the  electromagnetic  problem.  Our  results  clearly  demonstrate  that  the  EM 
vorticity  field  presents  a  maximum  spanwise  vorticity  above  the  magnet  poles  at  a  fixed  distance  from  the  wall,  a  maximum  streamwise 
vorticity  above  the  electrodes  and  a  null  vorticity  at  the  centre  of  the  EM  tile.  The  comparison  of  our  results  with  the  scales  (in  wall  units)  of 
a  canonical  boundary  layer  demonstrates  that  the  imposed  EM  vorticity  is  capable  of  completely  redistributing  the  vorticity  in  the  boundary 
layer.  The  second  part  of  our  work  deals  with  an  experimental  approach  of  the  concept  using  our  seawater  tunnel.  Our  contribution  is  based 
on  an  idealised  situation  ;  “a  synthetic  turbulent  boundary  layer”.  In  fact  we  use  a  laminar  boundary  layer  in  which  coherent  structures  are 
produced  by  a  wall  hemisphere  protuberance  and  maintained  within  the  boundary  layer.  Presently  we  demonstrate  that  we  are  able  to 
produce  and  visualise  the  coherent  structures.  An  EM  actuator  is  constructed  and  inserted  in  the  tunnel.  We  plan  to  visualise  soon  the 
behaviour  of  the  structures  when  submitted  to  the  EM  action. 


1  INTRODUCTION 


MagnetoHydroDynamics  (MHD)  makes  it  possible  to  apply 
Laplace-Lorentz  forces  directly  in  selected  domains  of  a  seawater 
flow.  In  particular,  one  can  act  directly  within  a  boundary  layer  by  the 
use  of  well  designed  permanent  magnets  and  wall  electrodes  [I]. 
Recent  experiments  ([2],  [3],  [4])  demonstrate  significant  drag 
reduction,  turbulence  intensity  reduction  and  boundary  layer 
separation  prevention.  Basically  two  configurations  (resp.  wall  normal 
and  axial)  can  be  identified  whether  the  direction  of  the  mean  Lorentz 
force  is  orthogonal  or  parallel  to  the  wall. 

The  main  feature  of  the  axial  configuration,  as  it  seems  to  us,  is 
the  local  creation  of  a  favourable  pressure  gradient  likely  to  prevent 
separation.  Though  it  can  also  lower  skin  friction  by  the  mean  of 
turbulence  intensity  reduction  (see  Henoch  &  Stace  [4}),  this 
configuration  doesn’t  seem  very  promising  as  far  as  energetic 
efficiency  is  concerned.  Significant  drag  reduction  has  however  been 
obtained  using  the  wall  normal  configuration  (see  [2],  [3])  in  which 
the  Lorentz  force  field  can  be  highly  rotational  and  may  be  seen  as  an 
artificial  injection  of  vorticity  within  the  boundary  layer. 

The  mechanism  which  effectively  allows  a  local  (in  space  and 
time)  EM  (electromagnetic)  force  and  EM  vorticity  to  strongly  change 
the  behaviour  of  a  turbulent  boundary  layer  is  not  clearly  understood. 
Our  theoretical  contribution  is  devoted  to  the  analysis  of  idealised 
and/or  asymptotic  situations,  which  intends  to  select  scales  and  non 
dimensional  parameters  in  order  to  pertinently  describe  the  EM  flow 
control.  Our  experimentaif  contribution  is  devoted  to  produce  well 
known  coherent  structures  and  to  make  them  interact  with  EM  forces 
and  EM  vorticity,  which  intends  to  identify  the  dominant  mechanisms 
implied  in  turbulence  modification.  The  present  paper  is  restricted  to 
uniform  conductivity  flows. 

In  the  wall  normal  configuration.  Electromagnetic  flow  control 
(EMFC)  makes  use  of  wall-flush  actuators  which  can  be  organised  in 
arrays  [5].  Our  approach  is  first  to  get  a  better  understanding  of  the 
action  of  a  single  so  called  “tile”  on  the  flow  and  then  to  study  the 
interactions  between  several  tiles  within  an  array. 


Figure  1:  wall  normal  EM  actuator 


2  SHAPE  OF  THE  IMPOSED  VORTICITY  ABOVE  AN 
EMFC  ACTUATOR 

Let  us  focus  on  the  wall  normal  control  in  a  steady  state  case. 
Figure  1  shows  a  typical  basic  element  of  EMFC  array.  It  is 
comprised  of  a  pair  of  sub-surface  magnet  poles  and  of  a  pair  of  wall- 
flush  electrodes.  The  electric  currents  density,  j  (A/m2),  and  the 
magnetic  field,  B  (T),  thus  created  in  the  flow  result  in  an  EM 
volumic  force  field  (  Laplace-Lorentz  force). 

2.1  GOVERNING  EQUATIONS 

Regarding  hydrodynamics  equations,  the  Navier-Stokes 
equation  includes  a  (jxB)  term  and  the  vorticity  (w=curl  u)  equation 
includes  a  (curl  (jxB))  term: 

du  _ 

p - 1-  \P+  pg  =  p  V  u  +  jxB 

dt  'mZ 

iorces 

P~~  ~  P  w*  Vu  +  //  V2w  +  Vx(jxB) 

MHD  vorticity 
Source 

When  dealing  with  permanent  magnets  and  low  conductivity 
electrolytes  (like  sea-water),  the  (jxB)  term  in  the  momentum 
equation  is  weak  compared  to  the  others.  However,  the  EM  force  field 
can  be  highly  rotational  and  can’t  be  neglected  when  calculating  the 
curl  of  this  equation  to  derive  the  vorticity  equation.  This  EM 
vorticity  field  appears  to  be  of  particular  interest  in  the  wall-normal 
configuration. 

Regarding  Electromagnetics  equations,  we  are  in  the  case  of  a 
weak  MHD  coupling  (Rm«l)  and  negligible  induced  currents 
(E/(uxB)  »  1).  Consequently  the  EM  unknowns  (magnetic  induction, 
electric  field,  electric  potential,  etc.)  are  obviously  independent  of  the 
flow.  The  induction  equation  and  the  Ohm’s  law  reduces  then  to: 

V2B  =  0  and  j  =  O  E 

with  o  (S/m)  the  apparent  electrical  conductivity  of  the  fluid  and 
E  the  imposed  electric  field  (V/m). 

In  addition,  conservation  equations  of  mass,  induction  and 
current  are  also  involved  in  the  following  development.  Notice  that,  as 
a  is  considered  uniform,  one  has  (div  j  =  0)  =>  (div  E  =  0). 

The  characteristic  scales  of  each  EM  unknown,  and  thus  of  the 
Lorentz  force  distribution,  are  closely  linked  with  the  tile’s 
dimensions.  Moreover  these  are  the  scales  to  be  compared  to  that  of 
the  flow  (location  of  the  action)  together  with  that  of  turbulence 
(phenomenological  point  of  view).  A  simple  analytical  approach 
together  with  3D  numerical  simulation  of  the  fields  are  able  to 
provide  such  information. 


389 


2.2  ANALYTICAL  APPRAOCH  OF  THE  EM 
VORTICITY  FIELD 


As  the  electric  and  magnetic  fields  are  independent  of  the  flow, 
the  MHD  terms  of  the  hydrodynamics  equations  can  be  assess  after 
some  simplification.  Let  us  consider  a  2D  distribution  for  the 
magnetic  induction  B,  which  is  fully  justified  in  the  case  of  very  long 
magnets,  as  in  the  Nosenchuck  experiment’s  array  [5].  Due  to  the 
necessarily  finite  extension  of  the  electrodes,  the  electric  currents  field 
is  3D.  Notice  that  the  mean  flow  can  have  some  direction  or  an  other. 

One  can  then  express  the  EM  force  and  vorticity  fields  as 
functions  of  the  electric  and  magnetic  fields: 


B 


0 


E 


z.ky.z) 

Er(x,y,z) 

Ez{?,y,z) 


JxB  =  <j 


y  z 

BA 

BA-BEy 


Vx(jxB)=<r 


'  d: 


v  dy 


in  which  the  electric  field  conservativity,  divE=0,  allowed  some 
simplifications. 


Vx(jxB)  =  cr 


only  the  x-component  of  the  EM  vorticity  is  non-zero,  and  it 
exhibits  a  maximum  at  the  wall,  since  both  Ey  and  0Bx/3y  are  maxi  at 
the  wall  and  decrease  with  y,  to  zero  at  infinity. 

zone  3  is  the  region  near  by  the  electrodes  median  plan,  above 
the  magnets; 


Vx(jxB)=  a 


only  the  z-component  is  non-zero  and  exhibits  a  maximum  at  a 
distance  8a  from  the  wall.  Indeed,  as  the  electric  field  derives  from  a 
potential,  it  is  curl-free,  thus  3Ez/3y  =5Ey/8z.  Moreover,  as  no 
electrical  current  can,  of  course,  be  provided  by  the  magnets,  one  has, 
at  their  surface,  Ey=0  and  3Ey/3z=0.  Now,  as  this  quantity,  dEz/dy,  is 
continuous,  null  both  at  the  wall  and  at  infinity  and  obviously  not  zero 
everywhere,  it  reaches  a  maximum  at  some  distance  from  the  wall.  On 
the  other  hand  By  is  maximum  at  the  magnet  surface  and  decreases 
with  y.  Subsequently,  the  EM  vorticity  is  maximum  at  some  distance 
5a  from  the  wall.  This  distance  entirely  depends  on  the  distribution  of 
E  and  B,  which  corroborates  the  impact  of  the  tile’s  geometry  on  the 
EM  action:  fringe  effects  on  the  electric  field  thus  monitor  the  3D  EM 
vorticity  distribution. 


B, 


0 

0 

<UL 

dy 


-E. 


''  dy 

0 

0 


Zone  2 


Zone  3 


Figure  2:  Schematics  of  the  simplification  domains 

Obviously,  the  EM  force  field  is  dominantly  directed  towards 
the  wall  (rather  than  wall  normal).  Moreover,  it  is  interesting  to 
analyse  the  imposed  vorticity  distribution  in  some  specific  regions 
above  the  EM  actuator.  Using  simplifications  based  on  the 
conservation  equations  in  a  uniformly  conducting  medium,  Thibault 
&  Rossi  [6]  obtained  the  following  expressions  of  the  imposed 
vorticity.  The  results  are  expressed  in  three  particular  zones,  as  shown 
in  figure  2. 

zone  1  is  the  central  region  of  the  tile  (intersection  of  the  2 
median  plans);  the  curl  of  the  EM  force  is  negligible  in  this  zone  : 


Vx(jxB)=  a 


B 


0 

0 

dEz 
d  x 


=  0 


zone  2  is  the  region  near  by  the  magnet  poles  median  plan, 
above  the  electrodes: 


Maximum  injected 
vorticity 


Figure  3:  Local  spanwise  (left)  and  streamwise  (right) 
EM  vorticity  maxima 

Finally,  the  topological  support  of  the  imposed  vorticity  can  be 
visualised  as  a  ring  standing  above  the  actuator.  As  the  flow  can  be 
aligned  optionally  with  the  x  or  the  z  direction,  let’s  illustrate  these 
expressions  in  the  case  of  a  streamwise  direction  along  the  x-axis.  The 
vorticity  imposed  to  the  flow  is  then  streamwise  in  the  neighbouring 
of  the  electrodes  and  spanwise  above  the  magnet  poles,  at  a  distance 
8a  depending  on  the  tile’s  geometry  (see  fig.  3).  An  evaluation  of  the 
EM  vorticity  in  terms  of  wall  units  (see  §3.2),  concerning  the 
Nosenchuck  experiment,  lead  Thibault  and  Rossi  [6]  to  the  conclusion 
that  the  imposed  vorticity  is  likely  to  dominate  the  dynamic  of  the 
buffer  layer.  The  vorticity  injected  into  this  region  of  the  flow  is 
indeed  much  stronger  than  that  of  a  canonical  wall  layer,  and  the 
excitation  streamwise  wavelength  can  be  adjusted  to  the  typical 
ejection  frequency. 


390 


2.3  NUMERICAL  APPROACH  OF  THE  EM  VORTICITY 
FIELD 


The  analytical  approach  presented  above  is  strictly  limited  to  the 
two  median  plans  of  the  EM  tile.  Anywhere  else  analytical 
computation  is  no  more  possible  and  numerical  modelling  is  needed. 
Let  us  first  of  all  describe  the  problem  and  its  governing  equations. 
Both  electric  and  magnetic  unknowns  are  independent  of  the  flow, 
moreover  the  magnetic  field  is  produced  by  permanent  magnets  and 
magnetic  permeability  as  well  as  electrical  conductivity  of  the  flow 
are  uniform.  Consequently  both  fields  are  irrotational  and 
conservative  which  means  they  can  be  formulated  as  deriving  of 
potentials  :  <|>  the  electric  potential  and  (p  the  magnetic  potential,  which 
both  obey  a  Laplace  equation  : 

A(J)  =  0  and  A(p  =  0 

Symmetry  plans  for  (|), 

Symmetry  "~7?Cv  7  antisymmetry  for  <p 

plan  for  <p  r 


Antisymmetry 
plans  for  <)) 


Figure  4:  EM  array  seen  from  above, 
symmetries  and  computational  domain 


The  problem  settled  in  the  present  paper  is  focused  on  the  wall 
normal  configuration  described  by  D.  Nosenchuck.  Figure  4,  drawn  in 
the  (x,z)  plan,  gives  a  top  view  of  the  array  of  electromagnetic  tiles 
which  is  almost  of  infinite  extend.  Our  computation  is  based  on  a 
steady  state  excitation  condition  which  is  not  strictly  proper  to  a 
pulsed  current  excitation  mode.  From  the  previous  analysis  it  is  clear 
that  the  imposed  vorticity  is  strongly  non  uniform  which  mainly 
depends  on  the  geometrical  dimensions  of  EM  tiles.  An  energetic  and 
dynamic  optimisation  of  the  concept  requires  the  knowledge  of  forces 
and  vorticity  distributions  in  a  domain  of  very  large  extend.  The  full 
computation  would  have  a  huge  size  or  would  have  to  be  based  on  a 
very  broad  meshing  of  the  domain  which  would  not  describe  properly 
the  imposed  vorticity  structures.  But  one  can  point  out  that  an  EM 
tiles  array  presents  some  periodical  arrangement  regarding  magnetic 
field  and  currents  distribution.  The  following  analysis  of  the  problem 
aims  at  identifying  the  smallest  sub-domain  on  which  detailed 
computation  can  be  done  and  then  extrapolated  to  the  entire  array 
using  observed  symmetries  and  anti -symmetries.  Finally  this  method 
allows  in  the  same  time  a  detailed  computation  and  a  very  large 
simulated  domain. 

On  figure  4,  the  electrodes  which  are  powered  at  the  time 
considered  are  coloured  in  black  and  dark  grey  (i.e.  +  &  -)  and 
magnetic  poles  (i.e.  N  &  S)  are  permanently  active.  The  electric 
problem  is  essentially  3D  but  one  can  identify  (x,y)  plans  parting  in 
the  middle  each  pair  of  active  electrodes  (see  figure  4)  which  are  anti¬ 
symmetry  plans  for  the  electric  potential  in  the  mean  time  (y,z)  plans 
parting  in  the  middle  electrodes  (see  figure  4)  are  symmetry  plans. 
The  magnetic  problem  is  almost  2D  (i.e.  independent  on  z)  one  can 
identify  (y,z)  plans  parting  in  the  middle  each  magnetic  pole  (see 
figure  4),  as  symmetry  plans  regarding  the  magnetic  potential.  The 
plans  (y,z)  parting  in  the  middle  each  electrode  are  anti-symmetry 
plans  for  magnetic  potential.  Consequently  the  smallest  computational 
domain  identified  corresponds  to  the  grey  coloured  zone  (see  figure 
4),  the  rest  of  the  array  can  be  extrapolated  using  the  symmetries  and 
anti-symmetries. 

Formulation  of  the  boundary  conditions  on  the  electric  potential 
is  shown  on  figure  5.  The  3D  computational  domain  comprises  a 


bottom  plan  corresponding  to  the  wall  (y  =  0)  where  the  potential  is 
fixed  on  the  electrode  surface  ((j>  =  cste),  the  rest  of  this  plan  as  well  as 
the  two  vertical  (y,z)  plans  are  of  Neumann  type  (3(|>/5n  =  0).  The 
topping  plan  as  well  as  the  two  vertical  (x,y)  plans  have  a  null  electric 
potential  (<f>  =  0). 

Formulation  of  the  boundary  conditions  for  the  magnetic 


(j)  =  0  8(j)/0n  =  0  <|>  =  0 


Figure  5:  Boundary  conditions  on  the  electric 
potential 

potential  which  is  almost  a  2D  problem  (i.e.  any  (x,y)  plan  in 
Neumann  type)  are  shown  on  figure  6.  The  bottoming  plan 
corresponds  to  the  upper  surface  of  the  iron  plate,  placed  here  to  drive 
the  magnetic  flux  directly  from  a  magnet  to  the  next  one.  Both  this 
plan  and  lateral  faces  of  the  magnets  are  of  Neumann  type  (3(p/5n  = 
0).  The  magnetic  pole  is  at  constant  magnetic  potential  (tp  =  cste)  and 
the  rest  of  the  boundary  have  a  null  magnetic  potential  (cp  =  0). 

The  solver  used  is  a  standard  3D  finite  elements  using  an  hexaedric 
meshing  .  At  present  the  computation  are  on  progress  and  are  going  to 
be  completed  soon.  After  computation  of  both  potential  in  the  3D 
domain  described  previously,  we  have  to  calculate  the  forces  and 
imposed  vorticity  distributions.  And  finally  to  extend  the  solution  to 
an  entire  array  of  EM  tiles. 


Cp  =  0 


Figure  6:  Boundary  conditions  on  the  magnetic 
potential 

The  perspective  of  our  computation  is  more  interesting  because 
it  concerns  flow  simulation.  The  problem  posed  is  the  behaviour  of  a 
turbulent  boundary  layer  submitted  to  the  EM  forces  distribution 
computed  with  the  EM  model  previously  described.  Hopefully  this 
distribution  is  independent  of  the  flow  itself  but  on  the  contrary  the 
proper  description  of  the  flow  seems  more  ambitious  in  the  sense  that 
the  forces  are  strongly  non  uniform  and  acting  very  close  to  the  wall. 
At  present  we  are  not  completely  fixed  on  the  model  adapted  but  it 
seems  that  a  DNS  simulation  has  to  be  envisaged  seriously.  We  want 
to  emphasise  the  fact  that  this  simulation  has  no  physical  sense  if  the 
first  step  electromagnetic  computation  is  not  properly  done. 

3  PRELIMINARY  EXPERIMENTAL  INVESTIGATION 
OF  ELECTROMAGNETIC  FLOW  CONTROL  (EMFC) 
The  great  complexity  of  a  fully  turbulent  Boundary  Layer  makes 
proper  experimental  investigation  of  local  phenomenon  somewhat 
tricky.  In  the  case  of  interest  here,  a  deep  analysis  would  be  all  the 
more  difficult  as  a  complex  3D  EM  vorticity  field  should  be 
superimposed  to  the  already  very  complex  structure  of  the  boundary 
layer.  The  idea  is  then  to  focus  on  the  simpler  case  of  artificial 
coherent  vortical  structures  conveyed  by  a  laminar  boundary  layer: 
this  case  allows  easier  (statistical)  quantification  through  the 
reproductibility  of  periodic  events. 

So  the  first  stage  is  to  produce  well  known  discrete  coherent 
structures  -  hairpin  vortices  -  in  a  laminar  boundary  layer  in  order  to 
create  a  well  organised  “synthetic  turbulent  boundary  layer”.  An 
extensive  description  of  this  type  of  flow  has  been  found  in  Acalar  & 
Smith  [7]:  the  process  involves  a  hemispheric  protuberance  (half¬ 
sphere  flush-mounted  to  the  wall)  entirely  contained  in  an  initially 


391 


laminar  boundary  layer  (see  fig.  7).  The  standing  vortex  forms  a 
stationary  horseshoe-shaped  structure  near  the  leading  edge  of  the 
hemisphere,  which  finally  develops  hairpin  vortices  created  by  the 
separation  of  the  flow  over  the  hemisphere. 

The  present  experiment  is  carried  out  in  the  PAMIR  team  sea- 


coated.  The  spanwise  permanent  rare-earth  magnet  is  equipped  with  a 
steel  magnetic  flux  backing  plate  in  order  to  concentrate  the  magnetic 
flux  lines.  The  whole  magnet  is  embedded  into  the  Perspex  body,  2 
mm  deep  under  the  surface  of  the  plate.  The  induction  at  the  wall  is 
about  0.3  T  above  the  magnet  poles. 


u«=8  cm/s 


water  tunnel  [8],  shown  in  fig.  8.  The  test  section  (4  cm  x  4  cm  x  1  m) 
is  made  with  Perspex,  thus  allowing  Laser  Anemometry  and  flow 
visualisation.  The  flow  velocity  is  adjustable  from  0  up  to  10  m/s.  A 
tranquillisation  chamber,  placed  upflow  the  channel,  renders  the  flow 
laminar  and  uniform.  The  electrolyte  usually  in  use  is  a  Sodium- 
chloride  solution  of  apparent  electrical  conductivity  about  4  S/m. 
Several  sizes  of  protuberance  are  also  available:  till  now,  3  radius  of 
hemi-sphere  have  been  tested  at  the  same  location  in  the  duct.  A 
compromise  has  to  be  found  between  a  fair  visualisation  (big  R)  and 
the  range  of  velocities  allowing  the  sphere  to  be  totally  sunk  within 
the  boundary  layer. 


Figure  8:  PAMIR-Team  Sea- Water  tunnel 


As  proposed  by  S.  Tardu  [10],  though  the  magnetic  and  electric 
fields  are  independent  of  the  flow,  it  is  certainly  meaningful  to 
evaluate  dimensions,  and  other  quantities  in  relation  to  the  EM  tile,  in 
terms  of  wall  units.  The  late  are  indeed  representative  of  the  typical 
length  scale  of  interest  from  an  hydrodynamics  point  of  view.  The  tile 
can  be  seen  as  a  square  of  side  Lt=32.10'3  m,  thus,  assuming  from  a 
numerical  simulation  presented  by  Nosenchuck  [5]  that  $,-0.06  Lt, 
the  height  of  action  is  5a«2. 10'3  m.  The  friction  velocity  at  the  location 
of  the  tile  is,  say,  4. 10'3  m/s  (equals  x\J20  with  u«,=8  cm/s,  typical 
velocity  of  our  experiment).  Consequently  the  undimensionnal  scales 
of  the  tile  are: 

•  a  distance,  Lt+,  of  128  wall  units  between  the  two  vorticity 
maxima,  above  the  magnet  poles, 

•  the  eight  of  these  maxima:  5a+=8  wall  units,  which 
corresponds  to  the  lower  part  of  the  buffer  layer. 

Notice  that  the  length  Lt+~130  is  comparable  with  the  size  of 
the  streaky  patterns  of  wall  layer  turbulence.  In  the  hypothesis  of 
section  2.2,  the  spanwise  EM  vorticity  intensity  can  be  assess  by 
wz~a.By.3Ez  Idy.  Assuming  an  electric  field  gradient  of  1000  V/m2 
(i.e.  25  V/m,  which  corresponds  to  100A/m2  currents,  over  15  mm), 
the  undimensionnal  vorticity  strength  w+  =  w.v/u*2  is  about  125, 
which  is  much  stronger  than  the  natural  vorticity  generated  by  shear 
stress  within  the  wall  layer  (of  the  order  of  1  wall  unit  [1]). 


3.1  PRODUCTION  AND  VISUALISATION  OF  HAIRPIN 

VORTICIES 

Thibault  &  Rossi  [6]  performed  a  preliminary  experiment  with 
the  aim  of  validating  the  possible  production  and  visualisation  of 
Hairpin  vortices  in  that  facility.  Hydrogen-bubbles  visualisation  gave 
them  access  to  the  structure  emission  frequency  and  velocity.  Results 
in  good  agreement  with  that  of  Acalar  &  Smith  [7]  have  been 
obtained:  figure  9  gives  the  evolution  of  the  structure  emission 
reduced  frequency,  P  -  f.v/u*2,  versus  the  Reynolds  number,  Rer, 
based  on  the  hemisphere  radius,  R.  The  first  plateau  (Rer<700) 
corresponds  to  a  frequency  that  linearly  increases  with  the  flow 
velocity.  The  right  hand  part  of  the  curve  (Rer>700)  corresponds  to  a 
constant  frequency,  which  is  probably  due  to  a  transition  to  turbulence 
in  the  vicinity  of  the  protuberance. 

Adding,  as  in  the  present  investigation,  an  EM  actuator  forbids 
hydrogen-bubbles  visualisation  techniques,  for  it  involves  electrolysis 
of  the  flowing  fluid.  Thus  the  electrodes  meant  for  producing 
visualisation  bubbles  may  interact  with  that  designed  to  act  on  the 
flow.  However,  “classical”  flow  visualisation  techniques  permit  a 
qualitative  approach  of  the  structures  feedback  to  the  action  of  a 
flush-mounted  EM  tile. 

3.2  PRESENT  ELECTROMAGNETIC  ACTUATOR 

A  single  EM  actuator  has  been  designed  and  dwelled  about  15R 
downflow  the  hemisphere.  This  experiment  being  preliminary,  the  tile 
width  (see  fig.  1 0)  has  been  fitted  to  that  of  the  test  duct.  Moreover  a 
square  shape  has  been  chosen  for  reasons  of  simplicity  and  for 
purpose  of  comparison  with  former  experiments.  The  streamwise 
electrodes  are  made  with  Titanium  and  their  upper  side  is  Platinum- 


L25r 


0. 

0 
0.1 5 
0.1 
O.Ofi: 


2r  4, 


XA 


Xao°  ^xxnnnn 
°  o 


^-Sphere 

radius 

°  R 

o 


o  6  mm 
□  8  mm 
a  4  mm 
X  6  mm 


o 


o 


0  '  . > . > . *-  '  ' 

200  400  600  800  1000  1200  1400 

ReR 


Figure  9:  Structure  emission  reduced  frequency  versus  hemisphere 
Reynolds  number 

Furthermore,  the  convective  speed  at  the  location  of  the 
maximal  injected  vorticity  (u+=y+=8)  is  about  3.2  cm/s,  namely  40% 
of  the  outer  velocity.  Consequently,  the  transit  time  of  a  fluid  particle 
over  the  tile  is  1  second  at  that  height,  whereas  it  is  0.4  seconds  in  the 
outer  flow.  This  can  be  compared  to  the  structure  emission 
frequency,  3Hz  at  8  cm/s  from  [6],  which  corresponds  to  a  2.7  cm 
long  gap  between  two  successive  hairpin  vortices,  i.e.  106  wall  units, 
see  fig.  7. 

Every  result  above  is  expressed  in  the  case  uOT=8  cm/s;  to  get 
the  tendencies  as  functions  of  the  outer  velocity,  one  can  assume  the 
Blasius  profile:  the  friction  velocity  is  then  given  by 
(u7u«)2=0.332.Rex"1/2.  Thus,  for  a  given  location,  one  gets: 

•  u*  u„3/4 

•  6;,+  (resp.  L/)  =  8a.u7v  °e  u  J14 


392 


•  w+  =  w.v/u*2  oc  u„-3/2,  since  the  (dimensionnal)  EM 
vorticity,  w,  is  independent  from  the  outer  velocity, 
Uc  ,(weak  coupling). 

•  f*  =  f.v/u*2  -  u„*1/2,  assuming  for  f,  emission 
frequency,  a  linear  dependence  to  the  outer  velocity, 
Uoo,  (from  [7]  and  as  long  as  Rer  <  700). 

A  better  quantification  of  the  mechanism  is  to  be  provided  by  a 
current  finite  elements  simulation  of  the  EM  force  field.  This  intends 
not  only  to  provide  such  quantitative  information  in  the  single  tiie 
case,  but  also  to  study  the  electrical  coupling  between  several  active 
tiles  of  the  same  array. 


4  CONCLUSION 

Attention  is  driven  on  wall  normal  EM  seawater  flow  control.  A 
simplified  analytical  approach  gives  access  to  the  shape  of  the  3D 
vorticity  ring  imposed  by  an  EM  actuator  within  the  boundary  layer. 
This  analysis,  based  on  a  2D  magnetic  induction  and  3D  electric  field 
model,  corroborates  the  description  previously  provided  by 
Nosenchuck  [9]:  the  imposed  vorticity  tends  to  zero  in  the  central 
region  of  the  tile,  is  spanwise  above  the  spanwise  magnet  poles  and 
streamwise  above  the  streamwise  electrodes.  The  maximum  spanwise 
vorticity  is  at  a  distance  from  the  wall  which  is  fixed  by  the  geometry, 
partly  through  end-effects  of  the  electric  field. 

Comparison  between  the  scales  of  this  EM  “vorticity  ring”, 
expressed  in  wall  units,  and  that  of  a  turbulent  flow  leads  to  the 
conclusion  that  it  strongly  acts  on  the  buffer  layer.  This 
electromagnetically  imposed  vorticity  is  obviously  able  to  reorganise 
the  flow  inner  structure,  since  it  is  much  stronger  than  the  natural 
vorticity  of  the  wall  boundary  layer. 

In  order  to  validate  this  conceptual  basic  understanding,  both 
experimental  investigation  and  numerical  force-field  simulation  are 
currently  carried  out.  Their  issue  is  the  understanding  of  the  action  of 
a  single  tile  together  with  that  of  interactions  between  several  active 
tiles  of  a  staggered  array. 

The  experimental  approach  implies  the  visualisation  of  discrete 
coherent  hairpin  vortices  embedded  in  a  laminar  wall  layer  and  locally 
submitted  to  the  action  of  an  EM  actuator.  The  idea  is  to  accede  to  the 
mechanism  of  action  of  an  EM  actuator  on  single  vortical  structures. 
These  are  indeed,  in  this  case,  well-known,  isolated  and  reproductible 
which  allows  proper  investigation  whereas  the  complexity  of  a  real 
turbulent  flow  would  forbid  it. 

The  3D  numerical  approach  is  devoted  to  investigating  the  EM 
vorticity  field  imposed  by  a  staggered  array  of  EM  actuators.  The 
model  uses  symmetries  and  anti -symmetries  of  the  fields  to  restrict 
the  computational  domain  to  the  smallest:  a  “cheap”  potential-type 
formulation  is  derived,  which  allows  detailed  simulation  of  the  EM 
vorticity  field  by  the  use  of  a  standard  finite  elements  code.  Still  on 
progress,  this  calculation  is  presented  as  the  compulsory  first  step  of 
(further)  proper  flow  calculation. 

Further  work  may  be  devoted  to  the  choice  of  pertinent  scales 
and  parameters  likely  to  describe  the  mechanisms  implied  in  drag 
reduction  by  electromagnetic  means:  both  deeper  experimental  study 
and  proper  flow  simulation  are  foreseen.  Axial  EM  control  is  also  to 
be  investigated,  as  devoted  to  the  prevention  of  boundary  layer 
separation  and  turbulence  intensity  reduction. 


References 

1.  J.C.S.  Meng,  “Wall  Layer  Microturbulence 
Phenomenology  and  a  Markov  Probability  Model  for 
Active  Electromagnetic  Control  of  Turbulent  Boundary 
Layers  in  an  Electrically  Conducting  Medium”,  NUWC 
Division -  Newport  Technical  Digest ,  June  1995 

2.  D.M.  Nosenchuck  and  G.L.  Brown,  “The  Direct  Control  of 
Wall  Shear-Stress  in  a  Turbulent  Boundary  Layer”, 
Proceedings  of  the  International  Conference  on  Near-Wall 
Turbulent  Flows,  Elsevier,  pp.  689-698,  1993 

3.  James  C.  S.  Meng  et  al.f  “Experimental  Study  of  the 
Spanwise  Vortex  Resonance  Hypothesis  for  Turbulent 
Drag  Reduction  over  a  Flat  Plate  in  Salt  Water”,  NUWC 
Division-  Newport  Technical  Digest ,  March  1997 

4.  C.  Henoch  and  J.  Stace,  “Experimental  Investigation  of  a 
Salt  Water  Turbulent  Boundary  Layer  Modified  by  an 
Applied  Streamwise  Magnetohydrodynamic  Body  Force”, 
Phys.  Fluids  7,(6) ,  pp.  1371-1383,  June  1995 

5.  Daniel, M.  Nosenchuck,  “Boundary  Layer  Control  Using 
the  Lorentz  Force”,  ASME  Fluids  Engineering  Meeting , 
San  Diego,  July  1996 

6.  J.-P.  Thibault  and  L.  Rossi,  “Seawater  MHD: 
Electromagnetic  Flow  Control”,  Third  International 
Conference  on  Transfer  Phenomena  in  Magneto  Hydro 
Dynamic  and  Electroconducting  Flows ,  vol.  1,  pp.  243- 
248,  Aussois,  France,  1997 

7.  M.S.  Acalar  and  C.R.  Smith,  “A  Study  of  Hairpin  Vortices 
in  a  Laminar  Boundary  Layer.  Part  1.  Hairpin  Vortices 
Generated  by  a  Hemisphere  Protuberance  ”,  J.  Fluid  Mech. 
Vol.  175,  pp.1-41,  1987 

8.  P.  Boissonneau,  “Propulsion  MHD  en  Eau  de  Mer:  Etude 
des  Couplages  Hydrodynamique-Electrochimie-Electro- 
magnetisme”,  These  de  Doctorat,  UJF  Grenoble,  May 
1997 

9.  Daniel  M.  Nosenchuck,  “Electromagnetic  Turbulence 
Control”,  EBLC  Workshop,  Dresden,  Germany,  July  1997 

10.  S.  Tardu,  Personal  communication,  1997 


393 


SOME  RESULTS  ON  ELECTROMAGNETIC  CONTROL  OF  FLOW  AROUND  BODIES 


Tom  Weier,  Gunter  Gerbeth, 
Gerd  Mutschke,  Uwe  Fey 
MHD  Dept.,  Forschungszentrum 
Rossendorf 

P.O.Box  510119,  D-01314 
Dresden 

T.Weier@  fz-rossendorf.de 


Oliver  Posdziech 
Inst.  Aerospace  Eng., 

TU  Dresden 
D-01062  Dresden 
posdzie@tfd.mw.tu-dresden.de 


Olgerts  Lielausis,  Ernest  Platacis 
Institute  of  Physics  Riga 
Salaspils-1,  LV-2169,  Latvia 
mbroka@tesla.sal.lv 


Abstract  -  The  flow  around  bodies  (cylinder,  plate)  can  be  controlled  by  applying  electromagnetic  forces  originating  from  electrodes  and 
permanent  magnets  suitably  placed  on  the  surface  of  the  body.  There  is  a  large  variety  for  applying  those  forces  with  respect  to  the  geometrical 
arrangement  and  the  electrical  current  feeding  the  electrodes.  The  goals  of  this  approach  are  flow  stabilization,  drag  reduction  or  manoeuvrability 
of  the  body  in  an  electrically  low-conducting  fluid  like  seawater.  We  present  experimental  and  numerical  results  for  a  low  Reynolds-number 
range  of  200  <  Re  <  4000.  Experiments  were  performed  using  a  copper  sulphate  electrolytic  solution  and  a  sodium  hydroxide  loop.  Flows  are 
considered  around  a  cylinder  and  over  a  plate,  with  Lorentz  forces  being  parallel  to  the  body  surface.  Experimental  results  will  be  presented  for 
the  body  drag  and  the  wake  flow  structures  depending  on  different  regimes  of  electromagnetic  forcing.  In  particular,  we  distinguish  between  the 
regimes  of  direct,  frequency-variable  sinusoidal  or  pulsed  electric  currents.  Numerical  results  confirm  the  physical  tendencies  at  least  for  lower 
Reynolds  numbers.  Parameter  ranges  will  be  given  for  an  optimal  electromagnetic  flow  control  in  terms  of  drag  reduction  and  flow 
laminarization.  The  energetic  balance  will  be  discussed. 


I.  INTRODUCTION 

Drag  reduction  is  a  main  design  issue  in  engineering  because  drag 
estimates  to  a  large  amount  the  running  costs  of  transport  of  or  in  fluids. 
If  the  fluid  is  electrically  conducting,  like  seawater,  apart  from 
conventional  methods  there  is  an  additional  possibility  of  control  by 
electromagnetic  body  forces,  i.e.  Lorentz  forces.  In  low-conducting 
liquids,  these  forces  may  be  generated  by  the  application  of  suitably 
chosen  magnetic  and  electric  fields.  This  idea  was  first  published  by 
Gailitis  and  Lielausis  in  1961  [1].  The  main  advantage  of  the  Lorentz 
force  is  that  it  acts  on  a  volume  of  the  flow  and  is  not  confined  to  the 
edges  of  the  fluid  stream.  Therefore,  electromagnetic  flow  control  has 
recently  attracted  the  attention  of  several  research  groups  [2,3].  Main 
issues  are  control  of  turbulent  boundary  layers  by  different  strategies, 
transition  delay  as  proposed  in  [1],  separation  control  and 
manoeuvrability. 

1.1  Turbulent  Boundary  Layer  Control 

Most  flows  relevant  for  practical  applications  are  turbulent,  simply 
due  to  the  large  length-scales  involved.  Turbulent  skin  friction  is  one  of 
the  main  sources  for  drag  on  airplanes  and  ships.  However,  the 
mechanism  leading  to  the  orders  of  magnitude  higher  skin  friction  of 
turbulent  compared  to  laminar  boundary  layers,  is  still  largely 
unrevealed.  The  kinematics  of  turbulent  boundary  layers  has  been 
intensively  studied  in  the  past  (e.g.  Klebanoff  [4]).  The  region  of  highest 
turbulence  production  is  the  buffer  layer  near  the  wall.  This  region 
controls  the  magnitude  of  the  wall  shear  stress  T.  Typical  flow  structures 
of  the  buffer  layer  are  low-  and  high-speed  streaks,  i.e.  spanwise 
modulations  of  the  streamwise  velocity,  and  streamwise  vortices.  There 
is  general  belief  that  controlling  these  structures  would  lead  to 
considerable  reduction  of  skin  friction. 

Wall-normal  Lorentz  forces  were  applied  by  Nosenchuck  and  co¬ 
workers  [5]  in  two  different  configurations.  First,  a  gradient  of  the 
conductivity  o  produced  by  injecting  an  extra  electrolyte  together  with 
uniform  current  density  and  magnetic  field  was  used  to  suppress  lift-off 
of  near  wall  vortices  and  therefore  Reynolds-stresses.  The  near-wall 
fluid  has  a  higher  conductivity  then  the  outer  flow,  between  both  is  a 
sharp  interface  with  respect  to  a.  If  a  flow  structure  deforms  this 
interface,  a  Lorentz  force  counteracting  this  deformation  is  generated. 
Experiments  in  a  turbulent  boundary  layer  with  1100<Ree  <1700 
showed  a  reduction  of  the  friction  drag  of  about  90%.  A  drawback  of 
this  method  is,  the  need  to  inject  additional  electrolyte  into  the  boundary 
layer  in  order  to  achieve  the  desired  Lorentz  force.  This  implies 
additional  manufacturing  and  running  costs  and  makes  the  design  more 
complicated. 

In  a  second  series  of  experiments,  Nosenchuck  and  co-workers 
designed  special  arrangements  of  single  actuators  (’’Tiles”)  to 
checkerboard  patterns  [6].  These  tiles  where  driven  in  a  certain  way  to 
obtain  a  global  modification  of  the  near  wall  flow  characteristics,  i.e.  a 
travelling  wave  structure  was  generated  in  the  boundary  layer,  hereby 
completely  replacing  the  natural  flow. 

Experiments  in  a  laminar  boundary  layer  with  resonant  operating 
tiles,  i.e.  downstream  tiles  are  amplifying  the  structures  created  by 


upstream  tiles,  showed  peak  reductions  of  the  friction  drag  up  to  90% 
and  50%  in  the  average.  It  should  be  noted,  that  the  actuator  introduces 
locally  spanwise  and  streamwise  vorticity,  but  the  total  amount  of  these 
components  integrated  over  the  wall  is  zero.  The  modified  laminar 
boundary  layer  is  thicker  than  the  Blasius  boundary  layer,  the  vorticity 
distribution  is  changed,  and  the  average  skin  friction  is  finally  smaller. 

In  a  turbulent  boundary  layer  with  0.5- 105  <  Re*  <  3.6*  105,  a 
reduction  of  the  skin  friction  by  55%  was  measured.  The  reason  is 
argued  to  be  the  same  as  in  the  laminar  case,  i.e.  a  restructuring  of  the 
near  wall  flow  with  a  changed  vorticity  distribution.  In  another  paper  [7], 
Nosenchuck  gave  a  coefficient  of  performance  Ct,=0.71  which  is  defined 
as  the  fraction  of  work  saved  due  to  a  lower  drag  and  the  total  input 
energy.  Experiments  performed  at  other  groups  to  confirm  these  results 
quantitatively  were  not  yet  successful. 

A  first  experiment  to  control  a  turbulent  boundary  layer  by 
streamwise  forcing  was  performed  by  Henoch  and  Stace  [8].  The 
Lorentz  force  is  generated  by  the  simple  strip-like  geometry  (SSG,  see 
Fig.  1)  of  alternating  electric  and  magnetic  poles  [1].  The  Reynolds 
numbers  in  their  experiments  were  in  the  range  of  510s  <  Re  <  3106.  At 
very  high  (7)  interaction  parameters,  an  increase  in  wall-shear  and  in 
turbulence  due  to  the  Lorentz  force  was  observed.  However,  the  increase 
in  friction  drag  is  compensated  by  the  thrust  due  to  the  force.  At 
moderate  interaction  parameters,  the  fluctuating  shear  stress  and 
streamwise  velocity  components  where  reduced  by  approximately  30%, 
while  the  mean  quantities  left  unchanged.  Henoch  and  Stace  explain  this 
effect  by  the  pumping  action  of  the  Lorentz  force.  By  the  acceleration  of 
the  near-wall  fluid,  the  lift-up  of  shear-generated  wall  vortices  is 
disrupted.  If  this  is  the  case,  the  force  would  act  similar  to  the  re- 
laminarizing  effect  of  a  favorable  pressure  gradient  [9].  The  inner  layer 
is  stabilized  by  the  addition  of  high  momentum  fluid,  thereby  the  process 
of  turbulence  production  and  dissipation  is  disrupted.  However,  in  the 
case  of  strong  interaction  parameter,  distinct  wall  jets  at  the  boundaries 
of  electrode  and  permanent  magnet  stripes  occur  due  to  a  spatially 
inhomogeneous  Lorentz  force. 

The  same  geometry  was  numerically  studied  by  Crawford  and 
Kamiadakis  [10].  By  means  of  a  spectral-element  method  a  channel  flow 
was  simulated  where  the  Lorentz  force  was  applied  at  one  side. 
Although  details  of  the  force  modelling  are  different  from  the 
experiment,  major  features  of  the  spanwise  inhomogeneous  distribution 
are  covered.  The  simulations  were  done  for  Reux=200  and  two 
interaction  parameters  N=0.1  and  N=0.4.  The  authors  report  a  friction 
drag  increase  at  the  controlled  wall  for  both  cases.  In  detail,  while  the 
streamwise  intensities  decrease,  as  measured  by  Henoch  and  Stace, 
spanwise  and  normal  fluctuations  increase  with  the  interaction 
parameter.  Also,  Reynolds  stress  increases  when  wall  shear  stress 
increases.  This  is  due  to  the  fact,  that  the  Lorentz  force  distribution  acts 
as  a  source  of  spanwise  and  normal  vorticity.  So  the  turbulent  motion  is 
influenced,  but  not  necessarily  towards  lower  drag.  In  the  opposite,  the 
streamwise  structures  in  the  boundary  layer  seem  to  be  amplified  (see 
Fig.  33  in  [10]). 

Widely  accepted,  streamwise  vortices  are  the  main  reason  for  the 
high  turbulent  wall  drag.  A  weakening  of  these  vortices  should  therefore 


395 


also  reduce  turbulent  skin  friction.  Several  successful  attempts  have  been 
done  to  shear  the  streamwise  vortices  with  oscillating  walls.  Choi  found 
a  maximum  reduction  of  skin  friction  by  50%  [11].  It  should  be  noted 
that  the  reduction  takes  place  at  that  point,  where  the  shear  due  to 
oscillation  is  acting.  Jimenez,  while  discussing  the  physical  effect  of 
spanwise  wall  oscillations  in  comparison  with  his  numerical  simulations, 
pointed  out  that  “...an  obvious  improvement  should  be  observed  by 
using,  e.g.  electromagnetic  oscillating  forces,  to  induce  the  same  effect 
over  volumes  of  the  order  of  the  wall  distance  given  above  (y+=30)” 
[12].  Kim  undertook  a  DNS  of  a  channel  flow  and  found  by  imposing 
oscillating  Lorentz  forces  in  spanwise  direction  a  skin  friction  drag 
reduction  of  30%.  These  calculations  were  done  for  a  Reynolds  number 
corresponding  to  a  boundary  layer  Rex=105.  At  this  Reynolds  number, 
the  efficiency  is  far  below  100%,  but  the  energy  which  has  to  be  spent 
for  the  Lorentz  force  should  decrease  proportional  to  Re2  [13],  therefore 
an  efficient  operation  of  this  control  could  be  possible  for  higher 
Reynolds  numbers.  An  experimental  verification  of  these  findings  is  not 
yet  known  to  the  authors,  but  appears  to  be  very  attractive. 

1.2.  Transition  Delay 

The  optimum  way  of  controlling  turbulence  is  to  prevent  its  arising 
because  laminar  skin  friction  is  orders  of  magnitude  smaller  than 
turbulent  one.  Therefore,  the  idea  is  to  achieve  transition  delay  which 
might  be  of  practical  importance  at  least  for  flows  around  smaller  objects 
(e.g.  hydrofoils). 

The  beginning  of  electromagnetic  boundary  layer  control  (EBLC) 
dates  back  to  the  sixties  when  in  Riga  it  was  firstly  formulated  the  idea 
of  achieving  transition  delay  by  introducing  an  appropriate 
electromagnetic  force  to  the  boundary  layer  [1].  The  motivation  was  to 
create  a  spanwise-homogeneous  and  in  wall-normal  direction 
exponentially-decreasing  Lorentz  force  [14]  which,  under  certain 
conditions,  asymptotically  leads  to  an  exponential  velocity  distribution 
in  the  boundary  layer.  The  key  point  is  that  such  exponential  velocity 
profiles  are  proven  to  have  much  better  stability  properties  than  ordinary 
Blasius  profiles  as  it  was  intensively  investigated  in  suction  experiments 
in  the  past  [15]. 

To  benefit  from  the  better  stability  properties  of  an  exponential 
velocity  profile,  one  has  to  find  an  appropriate  setup  of  electrodes  and 
magnets  in  order  to  create  that  body  force.  A  first  proposal  was  made  in 
the  sixties  in  Riga,  hereafter  referred  to  as  simple  strip-like  geometry 
(SSG)  and  shown  in  Fig.  1.  However,  already  at  that  time  Grinberg  [16] 
showed  by  an  analytical  modelling  of  the  field  distribution  that  the 
resulting  force  is  strongly  inhomogeneous  in  spanwise  direction, 
especially  in  regions  close  to  the  surface.  The  mathematical  reasons 
behind  are  simply  singularities  of  the  electric  and  magnetic  field  at  the 
comers  of  the  electrode  planes  and  the  rectangular  magnets,  respectively. 
This  leads  to  periodic  maxima  of  the  Lorentz  force  at  those  places. 

Any  variation  of  the  Lorentz  force  in  spanwise  direction  is  likely  to 
cause  3-D  instabilites  in  the  boundary  layer  which  certainly  will 
diminish  or  might  even  completely  destroy  the  desired  stabilizing 
influence  of  the  streamwise  forcing.  Although  this  has  not  yet  been 
checked  quantitatively,  one  goal  is  certainly  to  design  a  geometry  of 
electrodes  and  magnets  which  creates  a  perfectly  homogeneous  force. 
This  is  subject  of  current  work. 

1.3.  Separation  Prevention  and  Manoeuvrability 

Separation  prevention  reduces  form  drag  and  allows  higher  lift  at 
larger  angles  of  attack.  This  might  be  of  importance  for  flows  around 
hydrofoils  and  rudders  where  the  energetic  balance  is  not  the  main  goal. 
First  experiments  were  done  by  Nosenchuck,  directly  manoeuvering  the 
Buoyant  Test  Vehicle  by  a  Lorentz  force  applied  only  at  one  side  [7]. 


Figure  2:  Sketch  of  the  Cylindrical  Body 

II.  MODEL  EXPERIMENTS  ON  BLUFF  BODIES  AND  PLATES 

First  experiments  in  a  simple  rotating  annular  tank  (details  are 
described  in  [17])  were  performed  to  validate  the  force  effects  and  to 
visualize  flow  regimes  in  order  to  get  qualitative  results  on  the  spectrum 
of  possible  phenomena.  A  cylindrical  test  body  covered  with  electrodes 
and  magnets  to  create  a  wall-parallel  Lorentz  force  was  assembled.  Both 
half  sides  of  the  cylinder  might  be  powered  separately  (see  Fig.  2).  The 
main  focus  in  these  experiments  was  not  on  turbulent  boundary  layers, 
but  on  separation  control,  drag  reduction  and  modification  of  the  wake 
structure.  The  test  fluid  was  not  sea  water,  but  a  solution  of  10%  copper 
sulphate  and  5%  sulphuric  acid  in  water.  The  density  is  1120  kg/m3 ,  the 
electric  conductivity  is  16  S/m,  and  the  kinematic  viscosity  is  almost  that 
of  water.  Compared  to  sea  water,  besides  it’s  four  times  higher 
conductivity  the  solution  has  the  advantage  that  provided  a  critical 
current  density  is  not  exceeded,  no  electrolytic  bubbles  are  produced. 
Instead,  anode  material  is  degraded  and  galvanic  copper  deposition  takes 
place  at  the  cathode.  Growth  rates  are  only  in  the  order  of  micrometers 
per  hour.  The  range  of  Reynolds  numbers  covered  in  the  experiments  is 
500<Re<2000.  Static  forcing  as  well  as  sinusoidal  time-periodic  forcing 
was  investigated  in  detail.  The  results  were  obtained  by  flow 
visualization  with  colour-streaks  and  particles. 

To  extend  these  mainly  qualitative  results  and  to  investigate  certain 
phenomena  in  detail,  new  facilities  were  built  and  new  measurement 
technique  was  installed  at  Forschungszentrum  Rossendorf  (FZR).  .An 
open  electrolytic  channel  was  designed  to  perform  low-speed  mid-scale 
experiments.  The  covered  velocity  range  is  0.05  <  Uo  <  0.22  m/s  in  a  test 
section  of  0.2  x  0.2  x  1 .2  m.  The  maximum  volume  flow  rate  is  about 
32m3/h.  Honey  combs  and  screens  upstream  the  test  section  together 
with  a  2-D  contraction  of  3:1  ensure  at  0.22  m/s  only  0.5%  mean 
velocity  variations  and  a  turbulence  level  of  1.5%.  The  device  is  mainly 
made  of  plastics  and  can  be  used  for  seawater  as  well  as  for  e.g.  NaOH 
or  NaCl  based  electrolytes  without  corrosion  problems.  More  details  will 
be  presented  at  the  workshop. 

To  cover  larger  velocities  and  to  allow  for  “real-size”  experiments, 
a  closed  electrolytic  tunnel  is  currently  being  assembled  at  FZR.  The 
velocity  range  covered  is  0.5<U0<5  m/s  with  a  contraction  ratio  of  4:1 
ahead  a  test  section  of  0.3  x  0.4  x  1.2  m.  The  pump  engine  has  a  power 
of  15  kW.  The  material  used  is  mainly  stainless  steel,  as  electrolyte 
NaOH  is  planned.  Furthermore,  joint  experiments  at  the  Hamburg  Ship 
Model  Basin  HSVA  are  scheduled  to  be  performed  this  spring. 

In  all  these  facilities  experiments  are  currently  underway.  Test 
bodies  are  a  cylindrical  body  on  one  hand  as  described  above  but 
equipped  with  stronger  magnets  (0.28  T)  and  a  SSG  plate  of  1.5  x  50  x 
51  cm  size  where  both  sides  can  be  driven  separately.  Main  aims  are 
time-dependent  forcing  effects  for  the  cylinder  wake  and 
manoeuvrability  experiments  for  the  plate.  First  results  will  be  presented 
in  the  following.  More  results  of  currently  ongoing  experiments  will  be 
included  in  the  oral  presentation. 


396 


0  500  1000  1500  2000 

Re 

Figure  3:  Stability  diagram  for  steady  forcing 


m.  RESULTS 

The  flow  around  bluff  bodies  includes  phenomena,  which  can  not 
be  found  in  the  canonical  case  of  flat  plate  boundary  layer  under 
constant  pressure.  A  main  feature  here  is  the  occurrence  of  separation, 
resulting  in  an  complete  restructuring  of  the  flow  field.  Although  the 
boundary  layer  remains  laminar  in  the  cases  considered  here,  the  wake 
of  the  body  is  turbulent  even  for  small  Reynolds  numbers. 

With  increasing  Reynolds  number,  the  flow  changes  from  a 
creeping  flow  at  Re  <  1  to  an  asymmetric  flow  for  Re  <  5,  this  flow 
separates  for  larger  Re  and  the  wake  becomes  unstable  at  Re~45.  Further 
increase  of  the  Reynolds  number  leads  to  evolving  three-dimensional 
structures  at  Re»180  and  a  transition  of  the  wake  flow  into  turbulence. 
From  Re=1000  on  the  separating  shear  layers  are  subjected  to  Kelvin- 
Helmholtz  instabilities,  The  flow  picture  doesn’t  change  very  much  up  to 
Re=2105,  where  transition  of  the  boundary  layer  occurs.  The  now 
turbulent  boundary  layer  intensifies  the  momentum  transport  between 
boundary  layer  and  the  outer  flow.  Thereby  high  momentum  fluid  from 
the  outer  flow  increases  the  energy  of  the  boundary  layer,  and  boundary 
layer  separation  is  shifted  towards  the  rear  stagnation  point. 

Corresponding  to  these  changes  in  the  flow  pattern,  the  total  drag 
Cd  on  the  cylinder  changes  with  the  Reynolds  number.  The  friction  drag 
cf  could  be  obtained  from  integration  of  the  wall  shear  stress  along  the 
cylinder  surface,  the  pressure  drag  Cp  results  from  the  separated  flow  at 
the  rear  side  of  the  cylinder.  Due  to  this  separation,  pressure  at  the  rear 
stagnation  point  is  lower  than  at  the  front  stagnation  point.  The  friction 
drag  dominates  for  low  Reynolds  numbers,  while  for  Re>100  the 
pressure  drag  alone  determines  the  total  drag. 

3.1.  Static  forcing  -  Drag  reduction 

Separation  occurs  downstream  a  critical  point  where  the  normal 
derivative  of  the  streamwise  velocity  vanishes  (2-D,  steady  flow). 
Applying  a  streamwise  Lorentz  force  adds  momentum  to  the  near-wall 
flow  and  therefore  leads  in  general  to  a  delay  of  separation.  Sufficiently 
strong  forces  might  be  able  to  suppress  it  completely  in  certain  flow 
configurations. 

The  straightforward  application  of  the  SSG  (Fig.  1)  to  the  circular 
cylinder  is  sketched  in  Fig.  2.  The  Lorentz  force  is  directed  parallel  to 
the  cylinder  surface.  (One  could  imagine  two  plates  as  shown  in  Fig.  1 
each  wrapped  around  a  half  cylinder,  so  that  the  Lorentz  forces  on  both 
sides  of  the  cylinder  have  the  same  direction.  For  separation  suppression 
they  should  of  cause  point  downstream.)  The  stability  diagram  of  the 
flow,  obtained  from  flow  visualization,  is  shown  in  Fig.  3.  The  Reynolds 
number  Re  is  defined  with  the  cylinder  diameter  D  as  the  characteristic 
length.  As  the  interaction  parameter  N=(joB0D)/(pUo2)  is  defined  with 
the  imposed  magnetic  field  Bo  and  the  current  density  jo,  beside  the  fluid 
density  p  the  square  of  the  freestream  velocity  Uo  appears  in  the 
denominator.  Therefore,  an  parameter  S=N  Re2  is  introduced  as  a 
nondimensional  measure  of  the  applied  force  which  is  independent  of 
the  flow  velocity.  Above  the  drawn  critical  curve  in  fig.  3,  vortex- 
shedding  is  suppressed.  The  two  inserts  show  flow  snapshots  at  Re=760. 


Figure  4:  Streamlines  for  steady  forcing  at  Re=200 


No  Lorentz  force  is  acting  in  the  right  insert,  whereas  on  the  left  side  the 
flow  was  stabilized  due  to  a  Lorentz  force  of  S  =  1.47T06. 

A  strong  enough  downstream  forcing  results  in  a  jet  originating  at 
the  rear  stagnation  point.  This  jet  exerts  a  net  force  on  the  cylinder  in 
upstream  direction,  and  obviously,  the  total  drag  becomes  negative.  On 
the  other  hand,  a  force  directed  upstream  shifts  the  separation  towards 
the  front  stagnation  point,  and  a  vortex  street  with  larger  vortices  than  in 
the  unforced  case  forms.  In  this  situation,  an  increased  drag  has  to  be 
expected. 

These  experimental  observations  are  in  line  with  numerical 
simulations  of  the  flow.  They  were  done  using  a  finite  difference 
algorithm  in  a  vorticity  streamfunction  formulation,  for  details  of  the 
numerics  see  [18].  The  code  solves  the  two-dimensional  Navier-Stokes 
equation  of  an  incompressible  flow 

3v  1 

—  +  (v*V)v  =  -Vp  + —  Av  +  Nf,  (1) 

dt  Re 

V  ■  v  =  0,  (2) 

The  problem  is  formulated  in  cylindrical  coordinates,  the  mesh 
extends  over  121  points  in  radial  and  121  points  in  azimuthal  direction. 
The  grid  is  equidistant  in  azimuthal  direction  and  exponentially  spaced 
(r,~eTi)  in  radial  direction,  where  i  is  the  index  and  y  denotes  a  scaling 
factor.  The  grid  is  extended  to  50  cylinder  radii.  Due  to  the  exponential 
spacing  in  radial  direction  a  sufficient  resolution  of  the  boundary  layer 
for  the  chosen  Reynolds  number  of  200  is  obtained.  The  Lorentz  force  in 
Eq.  (1)  is  modeled  by  the  simple  relation 


397 


Figure  5:  LDA  measurements  of  the  streamwise  velocity  at  Re=4400 
and  x/d= 3 


11  5°  <  0  <  175° 

-1  185°  <£><  355°  (3) 

0  elsewhere, 

accounting  for  regions  at  the  front  and  rear  stagnation  point  where  no 
electrodes  are  present.  The  neglect  of  any  radial  force  component  and 
the  constant  radial  dependence  for  each  angle  0  represents,  obviously,  a 
simplification  of  the  real  experimental  situation.  The  parameter  a 
describes  the  electromagnetic  penetration  into  the  liquid  which  is  mainly 
defined  by  the  electrode  spacing,  modeled  in  correspondence  to  the 
experimental  situation  by  o=5te/4. 

Figs.  4  shows  calculations  of  the  flow  field  for  different  values  of 
the  force  amplitude  S.  The  isolines  of  the  streamfunction  have  equal 
levels  in  all  subfigures.  Only  a  small  part  of  the  region  covered  by  the 
mesh  is  shown,  the  flow  is  from  left  to  right.  In  the  top  part  of  Fig  4  the 
Karm&n  vortex  street  at  Re=200  without  the  action  of  the  Lorentz  force 
is  shown.  For  a  force  of  S  =  8-104,  corresponding  to  an  interaction 
parameter  of  N=2,  one  can  observe  that  although  the  wake  is  still 
unsteady,  separation  directly  at  the  wall  vanishes.  This  can  be  confirmed 
by  looking  at  the  vorticity  distribution  at  the  cylinder  surface.  Flow 
separation  is  instead  shifted  into  the  near-wall  region,  like  in  the  case  of 
a  moving  wall.  Behind  the  cylinder  a  region  with  two  relatively  stable 
recirculation  bubbles  forms,  wherein  the  fluid  motion  is  rather  slow. 
From  this  region  vortices  are  shed  with  approximately  the  Strouhal 
frequency  but  considerably  smaller  extension  compared  to  the  unforced 
case.  Further  increase  of  S  leads  to  complete  stabilization  of  the  flow. 
For  S=  2-105,  i.e.  N=5,  the  fluid  is  already  accelerated  by  the  force  as  can 
be  seen  by  the  narrowing  of  the  streamlines  even  upstream  of  the 


Figure  6:  Numerical  results  for  the  sum  of  cf  and  cp  versus  N  for  different 
Re 


cylinder.  At  a  very  high  force  of  S=  2-106  (N=50)  a  strong  jet  is 
produced.  Already  at  the  front  side  of  the  cylinder,  an  immense 
acceleration  of  the  fluid  takes  place.  The  fluid  leaves  the  cylinder  surface 
at  an  angle  of  approximately  135°  measured  from  the  front  stagnation 
point.  The  two  jets  merge  at  0.5  cylinder  diameter  downstream  the  rear 
stagnation  point,  enclosing  a  recirculation  region  with  several  small 
vortices. 

LDA  measurements  of  the  mean  streamwise  velocity  in  the  near 
wake  at  Re=4400  and  small  values  of  the  interaction  parameter  are 
shown  in  Fig  5.  With  increasing  interaction  parameter,  the  backflow 
vanishes  and  the  wake  depth  decreases.  These  measurements  were  done 
in  the  open  channel  with  a  mild  NaOH  solution  with  a  conductivity  of  4 
S/m,  e.g.  nearly  that  of  typical  sea  water. 

Fig.  6  shows  the  behavior  of  the  sum  of  both  friction  and  pressure 
drag  versus  the  interaction  parameter  at  two  different  values  of  the 
Reynolds  number.  Both  curves  have  a  minimum  at  an  interaction 
parameter  of  around  10  (Re=200)  respectively  5  (Re=500).  As  can  be 
seen  from  Fig  7,  pressure  drag  decreases  with  increasing  interaction 
parameter  because  of  separation  suppression.  For  sufficiently  strong 
forcing,  the  pressure  drag  reaches  even  negative  values.  On  the  other 
hand,  friction  drag  increases  with  stronger  forcing.  Since  the  boundary 
layer  is  laminar  and  the  force  accelerates  the  near-wall  fluid,  the  velocity 
gradient  at  the  wall  and  so  wall  shear  stress  is  increased  with  growing 
interaction  parameter.  This  effect  dominates  the  gain  in  pressure  drag  at 
large  values  of  the  interaction  parameter.  However,  one  has  to  take  into 
account  the  momentum  added  to  the  flow  by  means  of  the  Lorentz 
force.  So  even  at  low  interaction  parameter,  the  cylinder  experiences  a 
net  thrust. 

3.2.  Time  periodic  forcing 

Due  to  the  instantaneous  action  of  the  electromagnetic  field,  a  time 
dependent  Lorentz  force  can  be  easily  implemented  by  feeding  the 
electrodes  in  an  appropriate  manner. 

Using  time  dependent  currents  offers  the  possibility  to  avoid  the 
production  of  electrolytic  bubbles.  If  the  frequency  of  the  applied 
electric  field  is  high  enough,  a  specific  current  density  could  be 
established  by  charging  and  de-charging  the  electrolytic  double  layer 
around  the  electrodes.  This  would  inhibit  electrode  reactions  and  thus 
chlorine  production  in  sea  water  environments.  Above  all,  corrosion  at 
the  anodes  should  be  reduced  dramatically,  thereby  considerably 
simplifying  the  selection  of  electrode  materials.  Besides,  no  over-voltage 
of  the  electrode  reactions  has  to  be  overcome. 

From  fluid-dynamics  point  of  view,  usage  of  time  periodic  forces 
allows  to  interact  with  the  wake  structure  in  order  to  establish  flow 
regimes  with  desired  properties  as,  e.g.,  low  drag.  Examples  for  the 
control  of  flows  around  circular  cylinders  have  been  given  by  Taneda 
[19]  who  established  a  flow  regime  without  a  vortex  street  at  Re=300  by 
oscillatory  rotating  the  cylinder.  The  same  technique  was  used  by 
Tokumaru  and  Dimotakis  [20]  to  reduce  the  drag  of  a  cylinder  up  to  80% 
at  Re=1.5  104.  The  reason  of  the  dramatic  drag  reduction  is  the 
reorganization  of  the  vortex  street  which  becomes  narrow  under  the 
applied  control.  The  momentum  defect  in  the  wake  is  therefore  smaller 


Figure  7 :  Numerical  results  for  cp,  cf,  Cm  and  cd  versus  N  at  Re=200 


398 


Figure  8:  Suppression  of  the  vortex  street  by  antisymmetric  forcing, 
Re=540,  Se=1.5,  N=27 


and  so  the  drag.  These  result  were  recently  confirmed  by  Shiels,  Leonard 
and  Stagg  [21]  who  applied  a  vortex  method  to  investigate  numerically 
the  flow  at  Re=300  and  Re=1.5  104.  An  efficiency  of  the  control  was 
computed  defined  as  fraction  of  the  power  saved  by  drag  reduction  and 
the  power  spent  on  rotating  the  cylinder.  Although  the  method  was 
found  to  be  not  efficient  at  low  Reynolds  numbers,  it  was  argued  to 
reach  break  even  at  higher  Reynolds  numbers. 

Pack  and  Joslin  [22]  reported,  that  for  high  Reynolds  number  flow 
around  an  airfoil  with  a  flap,  oscillatory  blowing  is  two  orders  of 
magnitude  more  efficient  than  steady  blowing.  The  effect  used  here  is  to 
enhance  mixing  of  the  lower  momentum  fluid  at  the  wall  with  higher 
momentum  fluid  from  the  outer  flow,  thereby  increasing  the  near  wall 
fluids  momentum  and  making  the  boundary  layer  more  resistant  to 
separation. 

Up  to  now,  in  our  experiments  two  different  types  of  forcing  have 
been  investigated:  (i)  antisymmetric  forcing,  where  at  every  instant  the 
force  at  both  sides  of  the  cylinder  has  the  same  angular  direction,  and  (ii) 
symmetric  forcing,  where  the  force  direction  is  the  same  at  both  sides, 
i.e.  upstream  or  downstream  depending  on  time. 

For  sinusoidal  forcing  with  an  excitation  frequency  fe  a 
dimensionless  control  parameter  Se  =  D  fel  U0  can  be  introduced,  in  the 
following  referred  to  as  excitation  Strouhal  number.  The  time-periodic 
force  in  (1)  is  then  given  as 

f  =  cos(fflcf)e  l\(6)ee  (4) 

with  0)e  =  27tfe  and  t  denoting  time.  Interaction  parameter  N  and  force 
amplitude  S  are  computed  with  the  effective  current  density. 

For  anti-symmetric  forcing,  depending  on  forcing  frequency  and 
interaction  parameter,  flow  regimes  can  be  observed  which  are  similar  to 
the  ones  of  a  flow  around  an  oscillatory-rotating  cylinder  [20].  For 
forcing  frequencies  near  the  Strouhal  frequency  a  lock-in  of  the  flow 
occurs  even  for  small  interaction  parameters,  i.e.  the  frequency  of  the 


flow  is  determined  by  the  Lorentz  force  frequency.  If  the  forcing 
frequency  is  higher  than  the  Strouhal  frequency  and  the  interaction 
parameter  is  properly  chosen,  a  vortex  street  with  smaller  width  than  in 
the  unforced  case  forms.  Consequently,  a  smaller  drag  than  in  the 
unforced  case  is  expected.  Excitation  frequencies  smaller  than  the 
Strouhal  frequency  at  strong  interaction  parameter  lead  to  vortex  streets 
with  larger  vortices  and  broader  wakes  than  for  the  natural  flow,  here 
drag  should  be  increased.  At  large  values  of  the  interaction  parameter 
and  relatively  large  values  of  Se,  the  wake  can  even  be  stabilized  by  the 
unsteady  force  (similar  effects  were  observed  by  Taneda  for  an  rotating 
cylinder  [19].).  A  corresponding  flow  visualization  is  shown  in  Fig.  8. 
However,  the  interaction  parameter  necessary  to  reach  this  flow  regime, 
is  approximately  ten  times  larger  than  the  interaction  parameter 
necessary  to  stabilize  the  flow  by  steady  forcing. 

The  flow  visualizations  can  be  summarized  in  a  mode  selection 
diagram  shown  in  Fig.  9.  This  diagram  is  consistent  with  the  results  of 
Kamiadakis  and  Triantafyllou  [23]  who  investigated  the  globally-forced 
flow  around  a  circular  cylinder  numerically.  In  both  cases,  the  flow  is 
most  sensitive  to  forcing  at  frequencies  close  to  the  Strouhal  frequency. 

For  the  limiting  case  of  Se— >0  flow  structures  similar  to  the  ones  of 
a  flow  around  a  stationary-rotating  cylinder  are  expected,  i.e.  there 
should  also  exist  flow  regimes  without  vortex  shedding  but  non¬ 
vanishing  lift  due  to  the  Magnus  effect. 

The  flow  around  a  symmetrically  forced  cylinder  is  somewhat 
comparable  to  the  flow  around  a  cylinder  vibrating  in  line  with  the 
oncoming  flow,  a  case  studied  e.g.  by  Ongoren  and  Rockwell  [24]. 

Due  to  the  combination  of  symmetric  forcing  and  the 
antisymmetric  structure  of  the  natural  wake,  the  frequency  range  where 
lock-in  occurs  is  different  from  the  antisymmetric  case.  For 
antisymmetric  forcing,  lock-in  with  minimum  interaction  parameter 
occurs  when  the  flow  is  excited  with  the  Strouhal  frequency.  In  contrast, 
lock-in  at  symmetric  excitation  takes  place  first  for  frequencies  slightly 
larger  or  smaller  than  the  Strouhal  frequency. 

Symmetric  forcing  can  establish  symmetric  vortex  streets  of 
different  size  depending  on  interaction  parameter  and  forcing  frequency. 
Examples  of  flow  visualizations  and  numerical  calculations  are  given  in 
Fig.  10. 

IV.  OUTLOOK 

We  report  about  the  present  status  of  our  EBLC  programme.  This 
programme  is  aimed  to  take  benefit  of  the  main  property  of 
electromagnetic  boundary  layer  control:  its  flexibility  with  respect  to  the 
geometrical  arrangement  of  magnets/electrodes  and  the  electrical  feeding 
system.  For  the  future  we  see  the  following  most  interesting  scientific 
questions  and  applications  of  EBLC: 

■  Up  to  which  Re  a  flow  stabilization  can  be  reached  with  DC- 
currents  by  an  optimized  magnet/electrode  configuration? 


Figure  10:  Experimental  (left,  Re=1100,  N=3.3)  and  numerical  (right, 
Re=200,  N=5)  results  for  symmetric  forcing  at  different  excitation 
frequencies 


399 


■  Will  the  use  of  suitable  AC  currents  really  lead  to  an  energetic 
break-even  in  the  turbulent  region  at  higher  Re,  as  the  studies  on 
oscillating  cylinders  imply? 

■  Which  energetic  optimization  is  possible  by  means  of  some 
reactive  concept  based  on  some  feedback  control  strategy? 

■  What  is  the  practical  interest  in  terms  of  simple  and  cost-effective 
realizations  of  EBLC-actions  for  flow  manoevrability  or  lift 
production? 

Our  investigations  are  aimed  to  give  answers  to  these  questions. 

Y.  ACKNOWLEDGEMENT 

Financial  support  from  “Deutsche  Forschungsgemeinschaft”  under 
Grant  INK  1 8/A  1-1  is  gratefully  acknowledged. 

VI.  REFERENCES 

1.  A.  Gailitis  and  O.  Lielausis,  “On  a  possibility  to  reduce  the 
hydrodynamical  resistance  of  a  plate  in  an  electrolyte  ”,  Applied 
Magnetohydrodynamics.  Reports  of  the  Physics  Institute  12, 
(Prikladnaya  Magnitogidrodinamika.  Trudy  Instituta  Fiziki,  12),  Riga, 
pp.  143-146  (in  Russian),  1961. 

2.  Proc.  “International  Workshop  on  Electromagnetic  Boundary  Layer 
Control  (EBLC)  for  Saltwater  Rows”,  Dresden,  July  7-8,  1997 

3.  J.C.S.  Meng  “Seawater  Electromagnetics:  A  new  Frontier”, 
Magnetohydrodynamics  30  no.  4,  1994,  pp.  401-418. 

4.  P.S.  Klebanoff  “Characteristics  of  turbulence  in  a  boundary  layer  with 
zero  pressure  gradient”,  NACA-Report  1247,  1954. 

5.  D.M.  Nosenchuck  and  G.L.  Brown  “Discrete  Spatial  Control  of  Wall 
Shear  Stress  in  a  Turbulent  Boundary  Layer”,  in:  Near-Wall  Turbulent 
Rows,  R.M.C.  So,  C.G.  Speziale  and  B.E.  Launder  (Eds.),  Elsevier, 
1993,  p.  689-698. 

6.  D.M.  Nosenchuck,  G.L.  Brown,  H.C.  Culver,  T.I.  Eng  and  I.S:  Huang 
“Spatial  and  Temporal  Characteristics  of  Boundary  Layers  Controlled 
with  the  Lorentz  Force”,  12th  Australian  Ruid  Mechanics  Conference, 
Sydney,  1995. 

7.  D.M.  Nosenchuk  “Direct  Turbulent  Boundary  Layer  Control  on  an 
Axisymmetric  Body  using  the  Lorentz  force”,  4th  AIAA  Shear-Row 
Control  Conference,  1996. 

8.  C.  Henoch  and  J.  Stace,  “Experimental  investigation  of  a  salt  water 
turbulent  boundary  layer  modified  by  an  applied  streamwise 
magnetohydrodynamic  body  force”,  Phys.  Fluids,  Vol.  7,  No.  6, 
pp.  1 37 1-1383,  1995. 

9.  M.V.  Morkovin  “Panoramic  View  of  Changes  in  Vorticity 
Distribution  in  Transition  Instabilities  and  Turbulence”  1st  ASME  and 
JSME  Joint  Fluids  Eng.  Conf.  Portland  ,  OR,  June  23-27,  1991 

10.  C.  Crawford  and  G.E.  Kamiadakis  “Reynolds  stress  analysis  of 
EMHD-controlled  wall  turbulence.  Part  I  Streamwise  Forcing”,  Phys. 
Ruids  9  no.  3  pp.788-806,  1997. 

11.  K.S.  Choi,  P.E.  Roach,  J.R.  De  Bisschop  and  B.R.  Clayton  “Active 
Control  of  Turbulent  Boundary  Layer  by  Spanwise  Wall  Oscillations”, 
EUROMECH  Colloquium  261,  Berlin,  March  1997. 

12.  J.  Jimenez,  A.  Pinelli  “Wall  Turbulence:  How  it  works  and  how  to 
damp  it”,  AIAA  97-2112,  1997. 

13.  J.  Kim,  “Boundary  Layer  Control  for  Drag  Reduction:  Taming 
Turbulence”,  Proc.  “International  Workshop  on  Electromagnetic 
Boundary  Layer  Control  (EBLC)  for  Saltwater  Rows”,  Dresden,  July  7- 
8,  1997; 

14.  A..  Tsinober  and  A.G.  Shtem,  “On  the  possibility  to  increase  the 
stability  of  the  flow  in  the  boundary  layer  by  means  of  crossed  electric 


and  magnetic  fields”,  Magnitnaya  Gidrodinamica ,  No.2,  pp. 152-154  (in 
Russian)  1967. 

Nerets,  Y.  and  Shtem,  A.,  Experimental  investigation  of  a  possibility  to 
increase  the  stability  of  flow  in  the  boundary  layer,  6-th  Riga  MHD 
Conf.  Riga,  pp.  85-87  (in  Russian),  1968. 

15.  H.  Schlichting  and  K.  Gersten,  “Grenzschicht-Theorie”,  Springer,  9* 
edition,  Berlin  1997. 

16.  E.  Grinberg,  “On  determination  of  properties  of  some  potential 
fields ",  Applied  Magnetohydrodynamics.  Reports  of  the  Physics  Institute 
vol.  12,  (Prikladnaya  Magnitogidrodinamika.  Trudy  Instituta  Fiziki,  12), 
Riga,  pp.  147-1 54  (in  Russian),  1961. 

17.  T.  Weier,  G.  Gerbeth,  G.  Mutschke,  O.  Lielausis,  E.  Platacis, 
“Experiments  on  cylinder  wake  stabilization  in  an  electrolyte  solution 
by  means  of  electromagnetic  forces  localized  on  the  cylinder  surface”, 
”,  to  appear  in  Experimental  Thermal  and  Fluid  Science ,  1998. 

18.  G.  Mutschke,  G.  Gerbeth,  V.  Shatrov  and  A.  Tomboulides,  “Two- 
and  three-dimensional  instabilities  of  the  cylinder  wake  in  an  aligned 
magnetic  field”,  Phys.  Ruids  9  (1997)  p.31 14-31 16. 

19.  S.  Taneda  “Visual  Observations  of  the  Row  past  a  Circular  Cylinder 
Performing  a  Rotatory  Oscillation”  Journal  of  the  Physical  Society  of 
Japan  vol.45,  no.  3,  pp.  1038-1043, 1978. 

20.  P.T.  Tokumaru  and  P.E.  Dimotakis  “Rotary  oscillation  control  of  a 
cylinder  wake”  J.  Fluid  Mech.,  vol.  224,  pp.77-90, 1991. 

21.  D.  Shiels,  A.  Leonard  and  A.  Stagg  “Computational  Investigation  of 
drag  reduction  on  an  rotationally  oscillating  cylinder”  2nd  Int.  Workshop 
on  Vortex  Flows  and  related  numerical  Methods ,  Montreal,  Canada, 
August  20-24, 1995. 

22.  L.G.  Pack  and  R.D.  Joslin  “Overview  of  Active  Row  Control  at 
NASA  Langley  Research  Center”  SPIE’s  5th  Int.  Symp.  On  Smart 
Structures  and  Materials ,  San  Diego,  California,  March  1-5,  1998 

23.  G.Em.  Kamiadakis  and  G.S.  Triantafyllou  “Frequency  Selection  and 
asymptotic  states  in  laminar  wakes”  J.  Fluid  Mech.,  vol.  199,  pp.  441- 
469,  1989 

24.  A.  Ongoren  and  D.  Rockwell  “Row  structure  from  an  oscillating 
cylinder.  Part  2  Mode  competition  in  the  near  wake”  J.  Fluid  Mech.,  vol 
191,  pp.225-245 


400 


ANALYSIS  AND  FINITE  ELEMENT  SIMULATION  OF  MHD  FLOWS, 

WITH  AN  APPLICATION  TO  SEAWATER  DRAG  REDUCTION  1 

A.  J.  Meir  P.  G.  Schmidt 

Department  of  Mathematics  Department  of  Mathematics 

Auburn  University,  AL  36S49  Auburn  University,  AL  36849 

ajm@math.aubum.edu  pgs@math.aubum.edu 

Abstract  Much  research  effort  has  recently  been  devoted  to  the  electromagnetic  control  of  saltwater  flows,  exploiting  the  macroscopic  interaction 
of  saltwater  with  electric  currents  and  magnetic  fields.  This  interaction  is  governed  by  the  equations  of  viscous  incompressible  MHD,  essentially, 
the  Navier-Stokes  equations  coupled  to  Maxwell’s  equations.  A  major  problem  in  the  analysis  and  numerical  solution  of  these  equations  is  the 
fact  that  while  the  Navier-Stokes  equations  are  posed  in  the  fluid  domain,  Maxwell’s  equations  are  generally  posed  on  all  of  space.  Consequently, 
electric  and  magnetic  fields  do  not  satisfy  standard  boundary  conditions,  but  jump  or  continuity  relations  on  the  surface  of  the  fluid  domain  (and 
other  interfaces).  Frequently  the  resulting  difficulties  are  circumvented  by  prescribing  more  or  less  artificial  boundary  conditions. 

In  this  paper  we  present  a  novel  formulation  of  the  MHD  equations  that  avoids  some  inherent  difficulties  of  more  traditional  approaches  by 
employing  the  electric  current  density  rather  than  the  magnetic  field  as  the  primary  electromagnetic  variable.  This  formulation  leads  to  initial¬ 
boundary  value  problems  for  a  system  of  integro-differential  equations  in  the  fluid  domain  and  lends  itself  naturally  to  the  use  of  finite-element 
based  discretization  techniques.  As  a  first  application  we  describe  a  mixed  finite-element  method  for  the  numerical  solution  of  a  class  of  stationary 
MHD  flow  problems  and  report  on  the  computational  simulation  of  a  simple  drag  reduction  experiment. 


L  INTRODUCTION 

It  has  long  been  known  that  the  flow  of  an  electrically  conducting  fluid, 
such  as  seawater,  is  affected  by  Lorentz  forces,  induced  by  the  interaction 
of  electric  currents  and  magnetic  fields  in  the  fluid.  Only  recently  has  it 
been  demonstrated  that  such  Lorentz  forces  can  be  used  to  control  the  flow 
and  to  attain  specific  engineering  design  goals  such  as  flow  stabilization, 
suppression  or  delay  of  flow  separation,  reduction  of  near-wall  turbulence 
and  skin  friction,  drag  reduction  and  thrust  generation  (see,  for  example,  [4, 
9,  10]  and  the  references  cited  therein). 

The  theory  that  describes  the  macroscopic  interaction  of  an  electrically 
conducting  fluid  with  electric  currents  and  magnetic  fields  is  magnetohydro¬ 
dynamics  (or  MHD).  Assuming  the  fluid  to  be  viscous,  incompressible,  and 
finitely  conducting,  the  governing  equations  are  the  Navier-Stokes  and  pre- 
Maxwell  equations,  coupled  via  the  Lorentz  force  and  Ohm’s  law.  While  the 
Navier-Stokes  equations  are  posed  in  the  fluid  domain,  Maxwell’s  equations 
are  generally  posed  on  all  of  space,  and  typically  both  interior  and  exterior 
fields  must  be  determined.  Only  under  special  circumstances,  most  notably 
in  the  presence  of  perfectly  conducting  walls,  is  it  legitimate  to  confine 
attention  to  the  body  of  conducting  fluid  and  to  neglect  its  electromagnetic 
interaction  with  the  outside  world.  In  general  this  interaction  is  of  critical 
importance;  in  fact,  it  constitutes  what  mostly  distinguishes  MHD  from 
ordinary  hydrodynamics  and  is  a  source  of  challenging  mathematical  and 
computational  problems. 

Traditionally,  the  MHD  equations  are  formulated  as  a  system  of  evo¬ 
lution  equations  for  the  fluid  velocity  and  the  magnetic  field,  along  with  an 
auxiliary  equation  for  the  electric  field  outside  the  fluid  region.  The  fact 
that  the  magnetic  field  extends  to  all  of  space  and  may  exhibit  jump  discon¬ 
tinuities  across  interfaces  separating  media  with  different  electromagnetic 
properties  causes  analytical  as  well  as  computational  difficulties,  which 
are  frequently  circumvented  by  prescribing  more  or  less  artificial  boundary 
conditions.  In  [5-8]  and  [12]  we  developed  a  novel  approach  to  viscous 
incompressible  MHD  that  avoids  some  intrinsic  difficulties  of  the  traditional 
method  by  employing  fluid  velocity  and  electric  current  density  (rather  than 
fluid  velocity  and  magnetic  field)  as  the  primary  variables.  This  “velocity- 
current  formulation”  exploits  the  fact  that  while  magnetic  fields  may  extend 
throughout  space,  the  unknown  currents  inducing  those  fields  are  typically 
carried  by  conductors  of  finite  extent.  If  we  consider,  for  example,  a  single 
body  of  conducting  fluid  and  assume  all  external  field  sources  to  be  known, 
the  only  unknown  current  flows  in  the  fluid  region  itself.  In  this  case,  the 
velocity-current  formulation  allows  us  to  perform  all  computations  on  the 
fluid  domain  while  still  accounting  exactly  for  the  effects  of  the  universal 
electromagnetic  field.  In  general,  the  velocity-current  formulation  leads  to  a 
system  of  evolution  equations  for  the  fluid  velocity  and  the  unknown  current 
density  in  the  fluids  and  adjacent  solid  conductors,  along  with  an  auxiliary 
linear  div-curl  system,  which  can  usually  be  solved  analytically  in  terms  of 
singular  integrals. 


The  velocity-current  formulation  lends  itself  naturally  to  the  use  of 
finite-element  based  discretization  techniques  and  provides  a  theoretical 
framework  for  the  development  of  efficient  computational  tools  for  the 
simulation  of  a  wide  variety  of  MHD  flow  problems,  including  the  elec¬ 
tromagnetic  control  of  seawater  flow.  While  the  method  has  not  yet  been 
applied  on  an  industrial  scale,  it  has  been  shown  to  be  effective  in  the  analy¬ 
sis  and  numerical  solution  of  a  class  of  stationary  MHD  flow  problems  (see 
[8]).  In  the  following  we  describe  the  general  approach  (Section  II),  derive 
a  mixed  variational  formulation  for  the  stationary  case  (Section  III),  discuss 
a  finite-element  method  based  on  this  formulation  (Section  IV),  and  re¬ 
port  on  the  computational  simulation  of  a  simple  drag  reduction  experiment 
(Section  V).  Despite  the  academic  nature  of  this  simulation,  it  illustrates 
the  potential  usefulness  of  our  approach  in  solving  a  variety  of  MHD  flow 
control  and  design  problems. 

II.  THE  VELOCITY-CURRENT  FORMULATION 

We  are  concerned  with  the  flow  of  a  viscous,  incompressible,  electri¬ 
cally  conducting  fluid,  confined  to  abounded  region  of  space  and  interacting 
with  various  body  forces,  electric  currents,  and  electromagnetic  fields.  Un¬ 
der  the  assumptions  of  the  MHD  approximation,  the  flow  is  governed  by  the 
Navier-Stokes  equations,  posed  in  the  fluid  domain,  and  the  pre-Maxwell 
equations,  posed  on  all  of  space;  both  are  coupled  via  the  Lorentz  force 
and  Ohm’s  law.  As  discussed  in  the  introduction,  we  seek  to  formulate 
the  problem  as  a  system  of  evolution  equations  for  the  fluid  velocity  u  and 
the  electric  current  density  J  in  the  fluid;  both  are  solenoidal  vector  fields, 
depending  on  time  t  and  position  x. 

The  evolution  of  the  velocity  field  is  governed, by  the  Navier-Stokes 
equations,  that  is,  the  momentum  balance 

put  -  r}Au  +  p(u  *  V)u  +  Vp  -  J  x  B  =  Fext  (1) 

along  with  the  continuity  equation 

V  •  u  =  0 ,  (2) 

reflecting  the  incompressibility  of  the  fluid.  Here  p  and  tj  denote  the  (con¬ 
stant)  density  and  viscosity  of  the  fluid;  Fext  is  a  given  external  body  force; 
and  p  is  the  scalar  pressure,  an  auxiliary  unknown  that  plays  the  role  of  a 
Lagrange  multiplier  associated  with  the  divergence  constraint  (2).  Equa¬ 
tions  (1)  and  (2)  are  coupled  to  Maxwell’s  equations  through  the  Lorentz 
force,  J  x  B,  and  Ohm’s  law, 

J  =  cr(E  +  u  x  B) ,  (3) 

where  E  and  B  denote  the  (unknown)  electric  and  magnetic  fields;  a  is  the 
(constant)  electric  conductivity  of  the  fluid.  Additional  currents  Jext  may 


]This  material  is  based  upon  work  supported  by  the  National  Science  Foundation  under  Grants  DMS-9404440  and  DMS-9625096. 


401 


be  flowing  in  external  conductors,  possibly  connected  to  the  fluid  domain 
via  electrodes  on  the  surface.  The  total  current  distribution, 


Since  B  =  V  x  A  with  A  =  Aext  +  A(3),  it  follows  that  V  x  (E  +  At)  =  0 
and  thus,  E  +  A t  =  —  V0  for  some  scalar  potential  0.  But 


r  cr(E  +  uxB)  in  the  fluid, 

J  -  J  +  Jext  -  |  in  the  exterior, 

must  satisfy  the  continuity  equation 

V- 1  =  0, 


A t  —  Aext  i  ^  *4(J)t 

=  V  x  £(Bext,t)  *** M^(Jextii)  f^^iJt) 


and  thus, 


E  -  EgXt  —  pC(3t)  —  V0  , 


reflecting  the  conservation  of  charge. 

In  order  to  obtain  an  evolution  equation  for  the  current  density,  we  need 
to  represent  E  and  B  in  terms  of  J.  To  begin  with,  we  write  the  magnetic 
field  as 

B  =  Bext  +  6(3) , 

where  Bext  is  an  applied  field,  possibly  generated  by  permanent  or  electro¬ 
magnets  surrounding  the  fluid  domain,  while  13(3)  is  the  field  induced  by 
J  =  Jext  +  J.  Adopting  the  quasi-stationary  form  of  Maxwell’s  equations, 
as  is  the  custom  in  MHD,  we  obtain  BQ)  as  the  solution  of 


where 

Eext  =  x  £(®exti*)  ~  /^(Jext,*)  • 
Substituting  this  into  Ohm’s  law  (3),  we  obtain 


J  =  <j(Eext  -  pC(3t)  —  V0  +  u  x  B) 


or  equivalently, 


pC(3t)  +  <r  'j  +  V0  -  u  x  B  =  Egxt  ■ 


(5) 


(6) 


V  x  p~lB(3)  =  J  and  V  •  £( J)  =  0, 

where  p  denotes  the  magnetic  permeability.  For  simplicity  we  assume  the 
fluid  as  well  as  all  materials  outside  to  be  nonmagnetic  so  that  p  is  the 
permeability  of  the  vacuum. 

Next  we  introduce  vector  potentials  for  the  (solenoidal)  vector  fields 
Bext  and  B(3\  that  is,  vector  fields  Aext  and  A(3)  satisfying 

V  x  Aext  =  Bext  and  V  •  Aext  =  0 , 

V  x  A(3)  =  BQ)  and  V-.4(J)  =  0. 

Since  we  have  V  x  p~lB(3)  =  J  and  since  p  is  assumed  to  be  constant, 
.4(5)  satisfies 

V  x  V  x  .4(5)  =  p3  and  V  •  -4(1)  =  0 , 

or  equivalently, 

-A4(5)  =  p3 . 

Under  a  suitable  radiation  condition  at  infinity,  this  equation  has  a  unique 
solution, 

4(5)  =  pC(  J)  =  p£(Jext)  +  > 

where  (formally)  C  -  (—A)”1.'  Similarly, 

Aext  =  £(V  x  Bext)  —  V  x  £(Bext) . 

We  note  that  £  is  a  weakly  singular  integral  operator,  given  by 


This  is  the  desired  evolution  equation  for  the  current  density  J  in  the  fluid 
domain.  Analogous  to  the  pressure  p  in  the  Navier-Stokes  equations,  the 
scalar  potential  0  plays  the  role  of  a  Lagrange  multiplier  associated  with  the 
divergence  constraint 

V-J  =  0.  (7) 

Obviously  the  system  of  equations  (1)— (2)  and  (6)— (7),  with  B  and 
Eext  given  by  (4)  and  (5),  is  closed  only  if  the  external  current  distribution 
Jext  is  assumed  to  be  known.  If  this  is  not  the  case,  Equations  (6) — (7) 
must  be  solved  in  a  larger  region  of  space,  including  the  fluid  and  adjacent 
external  conductors  (with  u  =  0  outside  the  fluid,  of  course).  It  should  be 
noted,  however,  that  Jext  enters  the  equations  only  via  the  induced  magnetic 
field,  pV  X  £(Jext)-  1°  many  applications  the  effect  of  this  field  on  the  fluid 
motion  will  be  negligible.  In  fact,  the  applied  magnetic  field  Bext  is  typically 
much  stronger  than  any  induced  field,  so  that  it  may  well  be  reasonable  to 
neglect  induction  effects  altogether.  Formally,  this  amounts  to  setting  p  =  0 
in  (4)-(6),  in  which  case  Equation  (6)  becomes  quasi-stationary. 

The  system  of  equations  (l)-(2)  and  (6)-(7)  must  be  supplemented 
with  initial  conditions  for  u  and  J  and  suitable  boundary  conditions  for 
(u,p)  and  (J,  0).  Let  Q  denote  the  fluid  domain,  T  its  surface,  and  n  the 
outward  unit  normal  vector  field  on  H  The  simplest  physically  reasonable 
and  mathematically  feasible  boundary  conditions  are  u  =  0  and  J  •  n  =  0 
on  T.  Here  we  allow  for  both  mass  and  current  flux  across  T,  which 
leads  to  inhomogeneous  Dirichlet  or  Neumann  type  boundary  conditions. 
Specifically,  we  prescribe  the  velocity  u  on  an  open  subset  Tj  of  F  and  the 
stress  77(Vu+(Vu)t)  -n— pnonits  complement  F2  =  r\F| ;  we  prescribe 
the  current  flux  J  •  n  on  an  open  subset  F3  of  F  and  the  electric  potential  0 
on  its  complement  T4  =  T  \  r3: 


C(f)(x) 


=  —  f 

4?r  J R3 


%) 

\x  —  y\ 


dy , 


u  =  gi  on  Fj ,  7] (  Vu  +  (Vu)T)  •n-pn  =  g2  onF2, 

J -11  =  03  o nF3,  0  =  04  on  F4. 


for  any  sufficiently  regular  vector  field  f  with  sufficiently  fast  decay  at 
infinity,  and  that 

V  x  £(f)(x)  =  -  L  /  7  *  ~  X  f (v)dy . 

4lr  J R3  \x  -  Vi 

The  resulting  representation  of  the  magnetic  field, 

B  =  Bext  +  BQ)  =  Bext  -f  pV  x  £(Jext)  +  x  £(J)  >  (4) 

is  commonly  called  the  Biot-Savart  law. 

Turning  to  the  electric  field  E,  we  observe  that  according  to  Faraday’s 

law, 

V  x  E  =  -Bt . 


In  certain  cases,  the  boundary  data  g] ,  g2,  03,  04  must  satisfy  compatibility 
conditions.  For  example,  if  T2  =0,  then  gi  •  n  must  have  mean  zero  on  T 
(since  V  •  u  =  0  in  ft);  if  r4  =  0,  then  03  must  have  mean  zero  on  F  (since 
V  -  J  =  0  in  ft). 

Summarizing,  our  problem  is  the  following:  Given  the  fluid  domain  Q 
(abounded  region  of  space  with  sufficiently  regular  boundary  F  =  Fj  UT2  = 
F3  U  r4),  given  the  positive  parameters  p,  p,  p,  and  a,  given  the  external 
fields  FeX(,  JgXt,  BeXf,  and  Eext  =  —  V  x  £(Bext,t)  —  /^£(Jext>*)’  given 
compatible  boundary  data  gj,  g2,  03,  and  04,  and  given  initial  values  u{) 
and  Jo,  find  vector  fields  u  =  u(t ,  x),  J  =  3(t,  x )  and  scalar  fields  p  = 
p(t,  x),  0  =  0(t,  x)  such  that  the  following  equations  are  satisfied  with 
B  =  Bext  +  pV  x  £(Jext) +  M^7  x  £(J): 

put  —  rj Au  +  p(u  •  V)u  +  Vp  —  J  x  B  =  Fext  (t  >  0,  x  £  H), 


402 


V  •  u  =  0  (t  >  0,  x  £  Q), 

p£(Jt)  +  <j-iJ  +  V0-ux  B  =  Eext  (t  >  0,  x  £  £2), 

V  •  J  =  0  (t  >  0,  x  £  H), 


with  square-integrable  first-order  derivatives.  Both  L2(Q)  and  H[(Q)  are 
Hilbert  spaces  with  norms  given  by 

II/IIl2(q)  :=  (/ni/i2) / 


U  =  gi  (t  >  0,  X  €  n), 

t/(Vu  +  (Vu)t)  n-pn  =  g2  ((  >  0,  x  6  r2), 

J  ■  n  =  33  (t  >  0,  x  e  r3),  <t>  =  94  (t  >  0,  x  €  r4), 

u  =  U()  (t  =  0,  X  e  fi),  J  =  Jo  (t  -  0,  X  £  O). 

Under  mild  regularity  assumptions  on  the  data,  this  problem  has  a  weak 
solution  (u,  J,p,0),  defined  for  all  time  t  >  0.  If  the  boundary  data  are 
sufficiently  small  (or  if  the  viscosity  77  and  resistivity  cr_1  of  the  fluid  are 
sufficiently  large),  the  solution  remains  bounded  as  t  — >  00.  For  further 
details  and  a  rigorous  proof  (if  only  in  the  case  r2  =  r4  =  0),  the  reader  is 
referred  to  [12]. 

III.  A  VARIATIONAL  FORMULATION  FOR  THE  STATIONARY 
PROBLEM 

As  a  first  step  towards  the  numerical  analysis  and  finite-element  ap¬ 
proximation  of  the  full,  time-dependent  problem  described  in  Section  II,  we 
consider  the  steady-state  version  where  data  and  unknowns  are  independent 
of  time.  In  this  case  Equations  (l)-(2)  and  (6)-(7)  reduce  to 


~7) Au  +  p(u  •  V)u  +  Vp  -  J  x  B  =  Fext ,  (8) 

V  •  u  =  0 ,  (9) 

a"1  J  +  V0  —  u  x  B  =  Eext ,  (10) 

V-J  =  0,  (11) 


all  posed  in  the  fluid  domain  Q _and  s_upplemented  with  boundary  conditions 
on  the  surface  T  =  Tj  U  T2  =  T3  U  I4: 

u  =  gi  onTi,  7/(Vu  +  (Vu)T)  *  n  -  pn  =  g2  onr2,  (12) 

J  ■  n  =  <73  onT3,  0  =  04  on  r4.  (13) 


and 

II/IIh1^)  :=  {\\f\\2L2(Q)  +  HV^llL2(a)) 

Bold-face  type  is  used  for  the  corresponding  spaces  of  vector  functions. 

The  following  assumptions  on  the  data  guarantee  that  all  the  equations 
are  meaningful  (in  the  weak  sense): 


Fext  £  F2(Q),  Eext  G  L2(Q), 

Jext€L2(R3\a),  Bext  6  H'(£2), 

g2€H-'/2(r2), 

93  6  n-x'\ r3),  94  6  ff,/2(r4). 

The  space  Hlf2(Ti),  for  1  <  i  <  4,  consists  of  the  traces  (or  generalized 
boundary  values)  on  T*  of  functions  in  and  H~l/2(Vi)  is  the  dual 

of  Hl/2(Ti).  These  are  Hilbert  spaces  with  norms  derived  from  that  of 
iT^Q).  Again,  bold-face  type  is  used  for  the  corresponding  spaces  of 
vector  functions. 

To  derive  a  weak  or  variational  form  of  the  problem  at  hand,  we 
multiply  Equations  (8)  and  (10)  by  test  functions  v  G  Xi  and  K  6  X2, 
respectively,  and  Equations  (9)  and  (1 1)  by  test  functions  q  £  Mi  and  ip  £ 
M2,  respectively.  We  then  integrate  over  Q,  perform  several  integrations  by 
parts,  regroup  terms,  and  add  the  equations  obtained  from  (8)  and  (10)  and 
those  obtained  from  (9)  and  (11).  This  procedure  results  in  two  equations 
of  the  form 


ao  ((«,  J),  (v,  K))  +  a\  ((u,  J),  (u,  J),  (v,  K)) 

+  &((v,K),(p,0))  =4(v,K) 


(15) 


and 

&((u,J),(<mW)  (16) 

where  ao  (a  bilinear  form),  ai  (a  trilinear  form),  b  (a  bilinear  form),  ^0  and 
t\  (linear  forms)  are  given  by 


As  before,  the  magnetic  field  is  given  by 

B  =  Bext  +  pV  x  £(Jext)  +  pV  x  C{ J) .  (14) 

On  physical  grounds,  Eext  should  be  zero  in  the  stationary  case,  but  for 
reasons  of  symmetry  in  the  equations  we  allow  for  an  arbitrary  field  Eext. 
We  assume  that  Q  is  a  bounded  Lipschitz  domain  and  that  the  subsets 
of  the  surface  V  are  non-empty,  open  Lipschitz  surfaces  with  T 1  n  V2  =  0, 
U  T2  -  T  and  T3  n  T4  =  0,  T3  U  T4  =  T,  (The  subsequent  analysis  would 
remain  valid,  with  only  minor  modifications,  if  one  of  the  sets  T\ ,  Y2  and/or 
one  of  the  sets  T3,  T4  was  empty.) 

We  will  seek  weak  solutions  (u,  J,p,  <p)  of  Equations  (8)— (14)  with 

u  6  X,  :=  H'(£2),  J  e  X2  :=  L2(£2), 

p  €  Mi  :=  L2(Q),  4>  e  Mi  := 

In  addition  to  the  above,  we  will  need  the  subspaces 


«o((vi,Ki),(v2,K2)) 

■=lj  (Vvi  +(Vv2>T)  :  (Vv2  +  (Vv2)-r)  +  <7_1  J  K|  •  K2 
+  J  ((k2xB„)  -v,  -  (K,  x  Bo)  v2)  , 

where  B0  :=Bext+pV  x  £(Jext),  for  (vi  }Kj),  (v2,  K2)  G  Xj  x  X2, 

“1  ((Vl,Kl)J(V2,K2)l(V3,K3)) 

:=jJ  (((vi  •  V)v2)  •  v3  -  ((v,  •  V)v3)  •  v2  j 

+  fi J  ({■ K3  x  (V  x  £(Ki)))  ■  v2  -  (k2  x  (V  x  £(K,»)  •  v3)  , 


for  (v, ,  K, ),  (v2,  K2),  (v3,  K3)  £  X,  x  X2, 


X,  :=  {v  6  X,  |  v  =  0  on  T| } 


6((v,K),(?,^))  :=-  /  (V  •  y)q  +  /  K  • 
Jci  Jci 


(V0), 


and 


M2  :=  {ip  G  M2  I  ip  =  0  on  r^}. 

Here  and  in  the  sequel,  L2(Q)  denotes  the  space  of  square-integrable  scalar 
functions  on  Q,  and  Hx  (Q)  is  the  subspace  of  L2(Q)  comprised  of  functions 


for  (v,  K)  G  Xi  x  X2,  ( q ,  ip)  £  Mi  x  M2, 


4(v,K):=  /Fexrv+  /  Eext  •  K  +  /  g2-v5 

J  Cl  J  Cl  J  V2 


403 


for  (v,  K)  £  Xi  x  X2,  and 


for  (q,  ip)  £  M\  x  A^2- 

Routine  arguments  show  that  finding  a  weak  solution  (u,  J,p,0)  of 
Equations  (8)— (14)  is  equivalent  to  solving  the  following  variational  prob¬ 
lem. 

Problem  ( P ).  Find  u  £  X|  with  u  =  gi  on  T),  J  £  X2,  p  £  M\,  and 
(j>  £  M2  with  0  =  <?4  on  r4  such  that  Equations  (15)  and  (16)  are  satisfied 
for  all  (v,  K)  £  Xj  x  X2  and  (q,ip)  £  M\  x  M2,  respectively. 

After  homogenization  of  the  essential  boundary  conditions  for  u  and 
0,  Problem  (P)  reduces  to  a  mixed  variational  problem  in  the  sense  of 
the  Ladyzhenskaya-Babuska-Brezzi  theory  (see,  for  example,  [2,  Chap¬ 
ter  IV.  1]).  This  allows  us  to  prove  the  well-posedness  of  Problem  (P),  at 
least  under  a  small-data  assumption. 

Theorem  1.  If  the  data  FeX(,  Eext,  Jext>  Bext  311(1  8i»  82.  9i,  94  are 
sufficiently  small  (or  if  the  viscosity  7?  and  resistivity  a-1  are  sufficiently 
large),  then  Problem  (P)  has  a  unique  solution  (u,  J ,p,0),  which  depends 
continuously  on  the  data  and  parameters  of  the  problem. 

Roughly  speaking,  Theorem  1  guarantees  the  existence,  uniqueness, 
and  stability  of  a  steady  solution  to  the  MHD  equations  in  the  case  of 
low  Reynolds  and  magnetic  Reynolds  numbers.  For  a  much  more  precise 
statement  of  the  theorem,  including  specific  bounds  on  the  allowable  size  of 
the  data  (relative  to  the  parameters  of  the  problem),  we  refer  to  [8]. 

IV.  FINITE-ELEMENT  DISCRETIZATION  AND  ERROR 
ESTIMATES 

In  order  to  discretize  Problem  (P),  we  choose  finite-dimensional 
approximations  Xf,  x£,  M|\  and  of  the  spaces  X\  :=  H'(Q), 
X2  :=L 2(Q),Mi  :=  L2(Q),  and  M2  :=  Furthermore,  we  set  X*1  := 

{vh  £  Xf  |  =  OonTi)  and  :=  bPh  €  M%  \  tjjh  =  Oonr4} 

and  choose  approximate  essential  boundary  data  gj1  £  {v^1  |r2  |  C  Xj1 } 
and  gh  €  {iph\yA  |  iph  £  M^}.  Here  h  is  a  discretization  parameter, 
for  example,  the  meshsize  of  a  triangulation  of  the  domain  Q.  We  assume 
that  the  spaces  X^  and  M*?  approximate  X*  and  Mi  in  the  sense  that  the 
error  of  best  approximation  of  a  function  in  Xi  or  Mi  by  elements  of  X b 
or  M^  tends  to  0  as  h  — >  0;  of  course,  we  also  assume  that  gj1  — »  gi  and 
9 b  — »  g4  (in  the  respective  trace  spaces).  We  then  consider  the  following 
finite-dimensional  approximation  of  Problem  (P). 

Problem  ( Ph ).  Find  uh  6  Xf  with  nh  =  g f  on  Jh  £  Xf ,  ph  £  M*. 
and  4>h  £  with  <ph  -  gb  on  T4  such  that  the  equations 

00  ((u\  Jh),  (yh,Khj)  +  a,  ((uh ,  3h), (uh ,  Jh), (v\ K'1)) 

\  /  \  (17) 

+  b((vh,Kh),(ph,<l>h))  =4(vft,Kh) 

and 

6((u\jfc),(g\V>fc))  (18) 

are  satisfied  for  all  (v\Kh)  6  Xf  x  X£  and  (9\^ft)  €  Aff1  X  M£, 
respectively. 

Under  certain  technical  conditions  on  the  finite-dimensional  spaces  X^ 
and  M^1,  an  analog  of  Theorem  1  holds  for  Problem  ( Ph ),  and  we  obtain 
an  optimal-order  estimate  for  the  discretization  error  (see  [8]  for  details). 

Theorem  2.  If  the  data  Fext,  Eext,  Jext,  Bext  and  gi,  g2,  93 ,  94  are 
sufficiently  small  (or  if  the  viscosity  77  and  resistivity  a~]  of  the  fluid  are 
sufficiently  large)  and  if  h  is  sufficiently  small,  then  both  Problem  (P) 
and  Problem  (Ph )  have  unique  solutions  (u,  J ,p,0)  and  (u\  J hyph,4>b), 
respectively.  Moreover,  the  discretization  error  (that  is,  the  distance  between 
(u,  J  ,p,(f>)  and  ( uh ,  Jh }  ph }  0^)  in  the  norm  of  the  product  space  Xj  x  X2  x 
Mi  x  M2)  is  of  the  same  order  as  the  sum  of  the  error  of  best  approximation 


of  (u,  J,p,0)  by  elements  of  Xi  x  X2  X  M\  x  M2  plus  the  error  in  the 
approximate  boundary  data,  ||gi  -  gf  IIh1/2^)  +  H^4  ~  9a\\h1/2{T4y  In 
particular,  (uh ,  J71 ,  ph ,  (f>h )  — >  (u,  J5p,0)  as  h  — >  0. 

Theorem  2  and  general  results  of  finite-element  theory  suggest  that 
Problem  ( Ph )  will  be  a  A:-th  order  approximation  of  Problem  (P)  (for  some 
positive  integer  k )  if  we  use  appropriate  piecewise  polynomial  approxima¬ 
tions  of  degree  k  for  the  velocity  and  electric  potential  and  of  degree  k  —  1  for 
the  pressure  and  current  density.  Assuming,  for  simplicity,  that  thedomain  Q. 
is  a  polyhedron  and  that  we  are  given  a  regular  decomposition  of  Q  into  sim- 
plicial  or  rectangular  elements,  we  may  approximate  and  L2(Q)  by 

the  spaces  pb  and  Pf1  of  continuous  piecewise  quadratics  (or  triquadratics) 
and  continuous  piecewise  linears  (or  trilinears)  on  tetrahedra  (or  rectangular 
parallelepipeds),  respectively,  and  then  set  Xj1  :=  Vj  x  pb  x  P £  and 

:=  P^ .  These  so-called  Taylor-Hood  type  velocity-pressure  pairs  are 
widely  used  in  computational  fluid  dynamics  and  well  understood  (see,  for 
example,  [1,  Chapter  VI.6]  or  [3,  Chapter  3]);  in  particular,  they  satisfy  all 
the  technical  conditions  needed  to  prove  Theorem  2,  the  most  important  of 
which  is  the  so-called  LBB-condition. 

In  view  of  the  above  choices  of  velocity-pressure  pairs,  it  is  natural 
to  set  Mb  :=  V%.  In  order  to  satisfy  the  LBB-condition,  the  space  X£ 
should  then  contain  the  gradients  of  all  continuous  piecewise  quadratics  (on 
tetrahedra)  or  triquadratics  (on  rectangular  parallelepipeds).  Thus,  in  the 
case  of  a  simplicial  triangulation,  we  choose  for  X^  the  subspace  of  L2(Q) 
comprised  of  all  vector  functions  on  Q  whose  components  are  (generally 
discontinuous)  piecewise  linears.  When  using  rectangular  elements,  we 
let  Xj  Xj  j  x  Xj2  X  X^3  and  choose  for  x£.  the  tensor  product  of 
the  space  of  (generally  discontinuous)  piecewise  linears  in  the  z-th  variable 
and  the  space  of  continuous  piecewise  biquadratics  in  the  remaining  two 
variables.  Note  that  in  any  case,  X^  contains  Pf1  X  P^  x  P [*.  Pairs  of 
spaces  like  X2  and  M^  are  commonly  used  in  connection  with  so-called 
primal  mixed  methods  (see,  for  example,  [11,  Section  12]). 

With  the  above  choices  of  finite-element  spaces,  the  error  of  best 
approximation  of  the  exact  solution  of  Problem  (P)  will  be  of  order  h2 
provided  that  the  exact  solution  is  sufficiently  regular  (that  is,  if  u  £  H2(Q), 
J  £  H1^),  p  £  0  £  H2(Q.)).  Approximate  essential  boundary 

data  can  be  chosen  in  such  a  way  that  the  error  in  those  is  of  the  same  order. 
For  example,  if  gi  and  94  are  sufficiently  smooth,  one  can  take  for  g b  and 
gb  the  Lagrange  interpolants  of  gj  and  g4  in  the  respective  trace  spaces  of 
Xb  and  M^.  In  general,  independent  of  the  smoothness  of  gf  and  g4,  one 
can  utilize  generalized  interpolants  of  Scott-Zhang  type  (see  [13,  Section  5]. 
In  any  case,  Theorem  2  then  guarantees  that  the  solution  of  Problem  ( Ph ) 
will  approximate  the  exact  solution  of  Problem  (P)  with  an  error  of  order 
h2. 

Several  methods  suggest  themselves  naturally  for  solving  the  discrete 
problem  (Ph).  Most  straightforward  is  a  simple  linearization -iteration 
scheme  where  one  lags  the  first  argument  (u^,  J h)  of  the  trilinear  form 
a\.  In  the  situation  of  Theorem  2,  this  scheme  converges  globally,  that 
is,  for  every  initial  guess  (uj,  J(^).  Despite  the  presence  of  the  nonlocal 
operator  £,  the  resulting  linear  systems  are  sparse  and  can  be  solved  either 
directly  or  iteratively.  Intermediate  computations  of  the  induced  magnetic 
field  /zV  x  £(J)  are  expensive,  but  can  be  handled  efficiently,  for  example, 
with  fast  multi-pole  methods. 

Further  speed-up  may  be  achieved  through  the  use  of  multi-level  meth¬ 
ods.  In  [5],  for  example,  we  describe  a  simple  two-level  algorithm,  which 
yields  optimal-order  approximations  by  first  solving  the  nonlinear  problem 
(Ph)  on  a  rather  coarse  grid  (with  h  ~  H,  say)  and  then  solving  a  lin¬ 
earization  of  (Ph)  on  a  much  finer  grid  (with  h  ~  H2).  Finally,  parts  of 
the  method  are  inherently  parallelizable  —  a  feature  that  will  have  to  be 
exploited  in  order  to  deal  with  industrial -strength  applications. 

V.  NUMERICAL  EXPERIMENT 

We  implemented  the  method,  as  described,  to  simulate  MHD  flow 
around  a  circular  cylinder  in  a  channel  with  square  cross  section  (see  Fig¬ 
ure  1).  The  flow  domain  was  discretized  by  first  mapping  it  to  a  rectangular 
channel  with  a  rectangular  cavity  and  then  decomposing  the  latter  into  cubes 
of  equal  size  (see  Figures  2  and  3).  In  view  of  the  remarks  about  suitable 
finite-element  spaces  in  Section  IV,  we  used  standard  triquadratic  Lagrange 


404 


elements  for  the  velocity  and  electric  potential,  standard  trilinear  Lagrange 
elements  for  the  pressure.  For  the  z-th  component  of  the  current  density, 
we  chose  Hermite  elements  with  nine  nodes,  namely,  those  nodes  of  the 
principal  lattice  of  degree  two  (on  the  reference  cube)  that  are  not  on  faces 
perpendicular  to  the  z-th  coordinate  axis;  two  degrees  of  freedom  were  as¬ 
sociated  with  each  such  node  a,  namely,  /  »-*■  f(a)  and  /  i-+  dif(a).  This 
choice  is  convenient  in  constructing  a  basis  for  the  somewhat  nonstandard 
space  Xj  We  used  Lagrange  interpolation  to  approximate  the  essen¬ 
tial  boundary  data  and  employed  the  simple  iteration  scheme  described  in 
Section  IV  to  solve  Problem  (Ph). 

We  prescribed  a  parabolic  inflow  velocity  profile  at  the  left  end  of  the 
channel,  zero  velocity  on  the  channel  walls  and  on  the  cylinder  surface, 
and  zero  stress  on  the  outflow  boundary  (the  right  end  of  the  channel).  A 
permanent  magnet,  generating  a  dipole  field  BeXf,  was  positioned  along 
the  cylinder  axis  (north  pole  facing  the  front),  and  a  pair  of  electrodes  was 
located  on  the  down-stream  part  of  the  cylinder  surface,  one  near  the  top,  the 
other  near  the  bottom.  On  the  electrodes  we  specified  the  electric  potential 
(negative  on  the  upper,  positive  on  the  lower  one);  on  all  other  boundaries 
we  required  zero  current  flux.  No  external  body  forces,  external  currents, 
or  external  electric  fields  were  accounted  for. 

Since  the  experiment  was  anyway  of  an  academic  nature,  we  set  all 
parameters  equal  to  one.  Moreover,  all  non-zero  data  (inflow  velocity, 
applied  magnetic  field,  and  boundary  values  of  the  electric  potential)  were 
roughly  of  order  one.  We  first  solved  the  problem  without  magnetism  and 
electricity;  Figure  4  shows  the  resulting  (purely  hydrodynamic)  velocity 
field.  We  then  repeated  the  computation  with  magnetism  and  electricity 
switched  on.  The  resulting  velocity  field,  depicted  in  Figure  5,  reveals  a 
significant  change  in  the  flow  pattern  in  the  wake  of  the  cylinder.  In  both 
cases,  we  also  computed  the  total  force  acting  on  the  cylinder,  that  is,  the 
integral  of  the  stress  over  the  cylinder  surface.  In  both  cases,  this  force  is 
parallel  to  the  channel  axis,  but  its  direction  is  reversed  when  magnetism 
and  electricity  are  switched  on.  The  numerical  values  obtained  were  +230 
versus  —148.  Most  of  the  change  in  the  total  force  is  due  to  a  reversal  of 
the  pressure  gradient  near  the  cylinder.  Computing  only  the  skin  friction 
component,  we  found  a  drag  reduction  from  56  to  17. 


Fig.  1 .  The  channel  and  cylinder. 


X 

Fig.  3.  Logical  grid. 


X 

Fig.  5.  Velocity  field  with  MHD. 


VI.  CONCLUDING  REMARKS 

A  novel  formulation  of  the  equations  of  viscous  incompressible  MHD 
was  presented  that  allows  for  realistic  boundary  and  interface  conditions 
and  accounts  for  the  electromagnetic  interaction  of  the  fluid  with  the  outside 
world  while  restricting  computations  to  the  region  occupied  by  the  fluid 
(and  possibly,  adjacent  solid  conductors).  A  mixed  variational  method  was 
developed  for  the  corresponding  steady-state  problem,  which  lends  itself 
naturally  to  a  finite-element  discretization.  The  method  was  successfully 
implemented  and  tested  by  simulating  a  simple  drag  reduction  experiment. 
The  method  can  be  used  to  solve  a  variety  of  MHD  flow  control  and  design 
problems,  where  the  controls  are  applied  magnetic  fields,  electric  currents, 
and  electric  potentials.  In  its  present  implementation,  the  method  is  limited 
to  the  simulation  of  steady,  laminar  flows  in  the  case  of  low  Reynolds  and 
magnetic  Reynolds  numbers,  but  the  approach  is  potentially  applicable  to 
the  simulation  of  unsteady  and  turbulent  flows  as  well. 


X 

Fig.  2.  Physical  grid. 


405 


VII.  REFERENCES 

1.  F.  Brezzi  and  M.  Fortin,  Mixed  and  Hybrid  Finite  Element  Methods, 
Springer,  New  York,  1991. 

2.  V.  Girault  and  P.-A.  Raviart,  Finite  Element  Methods  for  Navier-Stokes 
Equations,  Theory  and  Algorithms,  Springer,  New  York,  1986. 

3.  M.  D.  Gunzburger,  Finite  Element  Methods  for  Viscous  Incompress¬ 
ible  Flows,  Academic  Press,  Boston,  1989. 

4.  C.  Henoch  and  J.  Stace,  Experimental  investigation  of  a  salt  water 
turbulent  boundary  layer  modified  by  an  applied  streamwise  magneto¬ 
hydrodynamic  body  force,  Physics  of  Fluids,  Vol.  7  (1995),  pp.  1371— 
1383. 

5.  W.  J.  Layton,  A.  J.  Meir,  and  P.  G.  Schmidt,  A  two-level  discretization 
method  for  the  stationary  MHD  equations.  Electronic  Transactions  on 
Numerical  Analysis,  Vol.  6  (1997),  pp.  198-210. 

6.  A.  J.  Meir  and  P.  G.  Schmidt,  A  velocity-current  formulation  for 
stationary  MHD  flow,  Applied  Mathematics  and  Computation,  Vol.  65 
(1994),  pp.  95-109. 

7.  A.  J.  Meir  and  P.  G.  Schmidt,  Variational  methods  for  stationary  MHD 
flow  under  natural  interface  conditions,  Nonlinear  Analysis,  Theory, 


Methods  and  Applications,  Vol.  26  (1996),  pp.  659-689. 

8.  A.  J.  Meir  and  P.  G.  Schmidt,  Analysis  and  numerical  approximation 
of  a  stationary  MHD  flow  problem  with  nonideal  boundary,  SIAM 
Journal  on  Numerical  Analysis,  to  appear. 

9.  J.  C.  S.  Meng,  P.  J.  Hendricks,  and  J.  D.  Hrubes,  Superconducting 
electromagnetic  thrusters,  Sea  Technology,  Vol.  33  (1992),  pp.  29-39. 

10.  J.  C.  S.  Meng,  C.  W.  Henoch,  and  J.  D.  Hrubes,  Seawater  electromag¬ 
netohydrodynamics:  A  new  frontier,  Magnetohydrodynamics,  Vol.  30 
(1994),  pp.  401-418. 

11.  J.  E.  Roberts  and  J.-M.  Thomas,  Mixed  and  hybrid  methods,  in:  Hand¬ 
book  of  Numerical  Analysis,  Vol.  II,  Finite  Element  Methods  (Part  1), 
P.  G.  Ciarlet  and  J.  L.  Lions,  Eds.,  North-Holland,  Amsterdam,  1991, 
pp.  523-639. 

12.  P.  G.  Schmidt,  A  Galerkin  method  for  time-dependent  MHD  flow  with 
nonideal  boundaries.  Communications  in  Applied  Analysis,  to  appear. 

13.  L.  R.  Scott  and  S.  Zhang,  Finite  element  interpolation  of  nonsmooth 
functions  satisfying  boundary  conditions.  Mathematics  of  Computa¬ 
tion,  Vol.  54  (1990),  483-493. 


406 


LORENTZ  FQRCE  MODELING  IN  EMHD  TURBULENCE  CONTROL: 

DNS  STUDIES 

Y,  Du,  C.  H.  Crawford,  G.  E.  Karniadakis 
Center  for  Fluid  Mechanics 
Division  of  Applied  Mathematics 
Brown  University 

email:  (Y.  Du  -  ydu@cfm.brown.edu);  (G.  Karniadakis  -  gk@cfm.brown.edu) 

Abstract.  -  In  this  work  we  analyze  high-resolution  numerical  data  bases  for  a  turbulent  channel  how  of  a  weakly 
conducting  fluid  and  one  channel  wall  covered  with  electro-magnetic  tiles.  First,  we  investigate  different  approaches 
of  modeling  the  Lorentz  force  produced  by  the  tiles,  and  address  the  question  of  effective  force  penetration.  We  then 
present  results  from  different  simulations  corresponding  to  various  ways  of  force  pulsing  by  turning  on- and- off  the 
electrodes.  A  single  case  of  5%  drag  reduction  was  found  but  most  of  the  other  cases  considered  resulted  in  drag 
increase.  Structures  associated  with  drag  reduction  and  drag  increase  were  also  visualized. 


I.  INTRODUCTION 

In  classical  MHD  turbulence  a  magnetic  field  present  in 
the  flow  can  suppress  turbulence  fluctuations  leading  even  to  flow 
re-laminarization  and  significant  drag  reduction  ([13],  [14]).  The 
exact  result  depends  on  the  direction  of  the  magnetic  field  and 

the  interaction  parameter  I  =  ■  where  B0}UyL  are  scales  for 
the  magnetic  field,  the  velocity  field,  and  the  length,  and  a,  p  are 
the  electrical  conductivity  and  density  of  the  fluid,  respectively. 
However,  in  MHD  flows  with  a  weakly  conducting  fluid  (e.g.  sea 
water  or  ionized  gas)  the  induced  magnetic  and  electric  fields  are 
negligible.  Therefore  in  order  to  affect  the  flow  an  externally 
imposed  electric  field  is  necessary,  and  this  is  the  case  of  Electro- 
Magneto- Hydro- Dynamics  or  EMHD  that  we  study  in  this  paper. 
Unlike  MHD,  however,  where  the  Lorentz  force  is  a  body  force, 
in  EMHD  the  Lorentz  force  is  effectively  a  surface  force  and  the 
greater  it  penetrates  into  the  fluid  the  greater  its  effect.  This  is 
a  fundamental  and  crucial  difference  between  MHD  and  EMHD 
turbulence  control. 

In  EMHD  flows  the  magnetic  Reynolds  number  = 
ap,0UL  is  low,  of  the  order  of  10“5  or  smaller  for  seawater,  and 
the  only  non-negligible  Lorentz  force  is  due  to  the  current,  i.e. 
F L  oc  <jEB.  The  corresponding  interaction  parameter  is  then 
la  =  <md  for  typical  parameters  in  EMHD  control  Ia  <  1. 

It  is  thus  obvious  that  in  EMHD  the  magnetic  and  electric  fields 
are  not  affect  ed  by  the  flow  and  can  be  computed  using  the  equa¬ 
tions  of  electrostatics.  The  Lorentz  force  can  be  pre-computed 
and  then  introduced  in  the  Navier-Stokes  equations  at  every  time 
step  or  appropriately  corrected  for  time- dependent  behavior  in 
cases  the  electrodes  are  turned  on-and-off.  A  crucial  aspect  of 
modeling  the  Lorentz  force  in  EMHD  is  boundary  conditions  on 
the  magnetic  and  electric  fields  on  the  magnets  and  electrodes 
and  the  rest  of  the  surfaces.  The  size  of  the  substrates  of  mag¬ 
nets  is  important,  edge  effects  are  important  but  also  the  simple 
question  as  to  exactly  what  is  to  be  specified  at  the  surface  a 
potential  value  or  its  flux  cannot  be  readily  answered. 

In  this  work  we  present  results  from  a  simulation  study 
that  started  five  years  ago  [10]  in  numerical  modeling  of  EMHD 
turbulence  control  for  different  electro-magnetic  tile  configura¬ 
tions.  The  numerical  results  seem  to  be  in  disagreement  with  ex¬ 
perimental  results  reported  in  [6]  and  [7]  and  at  least  one  source 
for  those  differences  should  perhaps  be  attributed  to  inadequate 
models  for  the  Lorentz  force  used  in  the  simulations.  Specifi¬ 
cally,  we  address  the  question  of  force  penetration  as  a  function 
of  the  size  and  spacing  of  the  tiles  and  we  consider  other  impor¬ 
tant  effects.  We  then  present  results  from  spectral  element  DNS 
corresponding  to  tiles  and  conditions  matching  the  experimen¬ 
tal  configuration  of  [6]  where  a  nominally  normal  to  the  surface 
Lorentz  force  is  produced  if  a  pair  of  electrodes  is  placed  in  a 


direction  perpendicular  to  a  pair  of  magnets  to  form  the  basic 
electromagnetic  tile.  An  array  of  such  tiles  are  then  used  on  the 
controlled  surface  with  some  or  all  of  the  tiles  activated. 

II.  FORCE  MODELING 

In  order  to  address  the  question  of  the  effectiveness  of  the 
Lorentz  force  on  flow  modification  we  examine  the  effective  pen¬ 
etration  of  the  force  from  the  surface  into  the  fluid.  To  this  end, 
we  first  consider  a  simple  configuration  consisted  of  alternating 
strips  of  electrodes  and  magnets  in  the  streamwise  direction.  We 
then  consider  a  different  configuration  consisted  of  electrodes  and 
magnets  placed  perpendicular  to  each  other.  We  want  to  exam¬ 
ine  how  different  modeling  assumptions  employed  to  compute  the 
electro-magnetic  fields  as  well  as  different  configurations  affect  the 
force  penetration. 

Force  Penetration 

The  afore  mentioned  first  configuration  was  proposed  in 
[1]  and  was  tested  experimentally  in  [3]  and  numerically  in  [11], 
However,  in  [2]  an  ideal  case  was  considered  where  the  electrodes 
and  magnets  overlapped.  Specifically,  the  potential  equations  for 
the  E  and  B  fields  were  employed 


v2$,  =  0 

(la) 

=  0 

(lb) 

with  Neumann  boundary  conditions  on  the  electrodes  and 

mag- 

nets  of  the  form 

8$, 

dy 

jy\y~0 

(2a) 

= 

jocos(^x) 

(2b) 

d$B  _ 
dy 

-By  |y  =  Q 

(2c) 

= 

Bosin(^x) 

(2d) 

$j,$B 

— ►  0  as  y  — ►  oo 

(2e) 

where  a  is  the  width  of  electrode/magnet  and  also  the  distance 
between  electrodes  and  magnets  of  opposite  polarization  (see  Fig¬ 
ure  1).  The  exact  solution  is 

$  = - joe~2Zycos(-^-  r)  (3a) 

7T  2a  v  ' 

$jg  =  — Boe~^y  sin(^-x)  (3b) 

7T  2a  7  v  7 

The  only  component  of  Lorentz  force  is  in  the  streamwise  direc¬ 
tion,  i.e. 

Fx  =  JzBy  -  jyBz  =  $j,z$B,y  ~ 

=  — j0P0e“?y  W 


407 


A 

Dirichlet 

Neumann 

DN 

Mixed 

Simulation 

1/4 

1/2 

1/8 

1/8 

Exact  B 

1/8 

1/2 

1/8 

Table  I:  Force  penetration  length  for  alternating  strips  of  elec¬ 
trodes/magnets. 

which  obviously  penetrates  into  the  fluid  a  distance  a,  half  of  the 
distance  that  both  the  electric  and  magnetic  fields  penetrate. 

In  practice,  however,  such  a  configuration  is  not  possi¬ 
ble  and  instead  discrete  tiles  of  magnets  and  electrodes  are  used 
which  correspond  to  approximately  constant  fields  at  the  surface 
(see  Figure  1). 


where  S  is  the  surface  of  magnets,  n  the  unit  normal  to  5,  and 
M  the  permanent  magnetization.  For  the  calculation  in  table  I, 
we  take  the  height  of  the  magnet  to  be  3  times  the  length  of  the 
magnet. 

Edge  Effects 

The  functions  one  specifies  on  the  boundary  could  also 
play  an  important  role  in  the  final  force  distribution.  For  ex¬ 
ample,  even  if  we  specify  constant  values  of  the  potential  or  its 
flux  on  the  magnets  or  electrodes  it  is  important  to  account  for 
edge  effects  associated  with  the  finite  size  of  the  electrodes  and 
magnets.  To  obtain  an  approximate  measure  of  such  an  effect 
we  calculated  the  Lorentz  force  using  three  different  functions  on 
the  boundary.  The  first  one  is  constant,  the  second  one  is  a  4th 
order  polynomial  which  is  zero  at  the  edges,  and  the  third  one  is 
a  function  with  50%  value  increase  near  the  edges  (see  Figure  2). 


Figure  1 :  Boundary  functions  used  to  describe  the  fields  on  the 
surface  of  electrodes /magnets.  Ideal  case  is  shown  by  sin  and  cos 
functions,  and  realistic  case  is  shown  by  piecewise  constants. 


Solving  the  same  potential  equations  and  using  also  Neu¬ 
mann  boundary  conditions  in  a  finite  domain  of  height  2h  we 


obtain 


= 


„  r  &h±lh 
£*=0^  20 

+  h^(2h_y)]^s 

+e-ip-C2h-^)sin 


12£±1W 


(2fc+l)7T 


(5) 


where 


Ck  = 


Dk  = 


gJ°°  (-i)L 

ir2  (2fc+l)2 

x _ 1 _ 

A  (2k  +  l)nh 
e  a  - 

8Bna  (-D* 

7T2  (2fc+l)2 

v  1 

X  HEME 


(2fc+l]7r 


,(2h±l)z 


(6) 


1  —e  a 

Both  the  electric  and  magnetic  fields  decay  exponentially  as  be¬ 
fore  in  the  idealized  case,  however  it  is  difficult  from  the  expres¬ 
sions  above  to  infer  force  decay  and  thus  the  effective  force  pen¬ 
etration. 

To  measure  the  penetration  length  we  match  the  force 
profile  from  the  edge  between  an  electrode  and  a  magnet  to  the 
exponential  curve  e—  oX^,  where  a  is  the  length  of  a  single  elec¬ 
trode  or  magnet,  and  A  the  force  penetration  factor;  for  the 
idealized  case  we  have  A  =  1 .  We  then  numerically  compute  the 
fields  and  the  corresponding  Lorentz  force  and  measure  A  from 
different  simulations  corresponding  to  different  boundary  condi¬ 
tions.  The  electric  and  magnetic  fields  we  obtained  numerically 
match  the  analytical  expressions  above  within  machine  accuracy 


but  it  is  easier  to  compute  the  force  numerically. 

The  results  of  some  of  the  cases  we  considered  are  shown  in 
Table  I.  Here  “Dirichlet”  corresponds  to  using  Dirichlet  boundary 
conditions  for  the  potentials,  “Neumann”  to  Neumann  boundary 
conditions,  “DN”  to  Dirichlet  boundary  conditions  for  $e  and 
Neumann  boundary  conditions  for  $£?,  and  “Mixed”  means  that 
for  both  $£!  and  Dirichlet  boundary  conditions  are  specified 
over  electrodes/magnets,  and  Neumann  boundary  conditions  are 
specified  in  other  regions.  Case  “Exact  B”  corresponds  to  calcu¬ 
lating  the  potential  for  magnetic  B  field  as: 


471-  J  s  \x-x!} 


(7) 


Figure  2:  LEFT:  Functions  used  for  boundary  conditions; 
RIGHT:  Lorentz  force  profiles  corresponding  to  three  different 
boundary  functions. 

We  see  in  Figure  2  that  the  force  profile  (taken  at  an 
electrode/magnet  edge)  is  quite  different  for  the  three  cases  and 
that  the  corresponding  penetration  length  is  also  very  different. 

Substrate  Effects 

From  equation  (7)  we  see  that  the  exact  dimensions  of  the 
magnets  could  also  influence  the  force  penetration.  For  the  sim¬ 
plification  of  a  two-dimensional  magnet  that  we  consider  we  can 
vary  the  cross-section  of  the  magnet  corresponding  to  different 
aspect  ratios  or  =  hei3ht.  and  use  different  a  values  in  equation 

(7). 


Figure  3l  Force  contour  and  1%  contour  line  for  streamwise 
tiles  with  a  =  0.5. 

In  Figure  3  we  see  that  for  different  values  of  or  the  force  distri- 


408 


bution  and  the  shape  of  1%  contour  line  (defining  an  approximate 
penetration  length)  can  vary  substantially. 

General  Tile  Configurations 

The  results  presented  so  far  are  for  tiles  of  alternating  elec¬ 
trodes  and  magnets  all  in  the  same  direction  and  suggest  that  the 
maximum  force  penetration  length  is  a,  i.e.  the  size  of  the  elec¬ 
trodes,  and  such  penetration  can  hardly  be  achieved  for  realistic 
conditions.  We  examine  next  general  electromagnetic  tiles  where 
the  electric  and  magnetic  fields  are  “nominally”  perpendicular  to 
each  other.  Such  tiles  have  been  used  in  experimental  studies 
reported  in  [6],  [8],  [9])  and  [5]. 

The  first  computational  work  was  reported  in  [10]  for  the 
tiles  shown  in  Figure  4.  With  such  configurations,  the  Lorentz 


N 

- 

S 

N 

s 

N 

+ 

s 

** 

s 

S 

S 

- 

+ 

N 

N 

N 

Figure  4:  LEFT:  Tile  1;  RIGHT:  Tile  2.  We  assume  that  the 
flow  is  in  the  x\  direction. 


Figure  5:  Force  contours  for  Tile  1.  Dirichlet  boundary  condi¬ 
tions  are  used  in  computing  the  electric  and  magnetic  fields. 

force  field  generated  is  strongly  three-dimensional  as  shown  in 
Figure  5.  It  is  interesting  to  note  that  the  maximum  magnitude  of 
the  normal  force  F2  is  approximately  one  order  smaller  than  the 
larger  horizontal  force  component.  This  distribution  corresponds 
to  prescribing  Dirichlet  conditions  for  the  magnetic  and  electric 
potentials.  However,  if  we  instead  prescribe  Neumann  conditions 
we  obtain  a  force  distribution  with  magnitudes  approximately  the 
same  for  all  three  components.  We  will  discuss  this  comparison 
in  some  more  detail  later. 

For  these  general  tiles,  we  have  more  than  one  length 
scales  to  consider  such  as  the  spacing  of  electrodes  and  magnets 
as  well  as  their  sizes.  We  consider  next  some  other  configurations 
with  the  objective  to  investigate  the  effect  of  such  parameters 
on  the  overaU  force  penetration.  Figure  6  shows  the  footprint 
of  normal  Lorentz  force  component  on  the  bottom  wall.  The 
upper  left  plot  corresponds  to  Tile  2;  the  upper  right  plot  shows 
a  case  in  which  the  two  electrodes  are  much  closer  together;  the 
lower  left  plot  shows  a  case  using  two-dimensional  magnets;  and 
the  lower  right  plot  shows  a  tile  configuration  designed  at  Naval 
Underwater  Warfare  Center  [4].  The  results  for  the  four  cases  are 
obtained  by  solving  the  Laplacian  equation  for  $e  and  using 
Neumann  boundary  conditions.  We  see  that  the  force  distribution 
is  different  for  different  cases  but  it  is  directed  towards  the  surface 


Figure  6:  Footprints  of  normal  Lorentz  force  component. 


A 

D 

N 

DN 

Mixed 

Simulation 

1 

1 

1 

2 

2D  magnets 

1 

1 

1 

2 

Close  electrodes 

1 

1 

1 

1 

NUWC 

1 

1 

1 

1 

Table  II:  Force  penetration  parameter  for  general  tiles  corre¬ 
sponding  to  different  boundary  conditions.  The  larger  the  pa¬ 
rameter  A  the  larger  the  force  penetration. 


at  the  center  of  each  tile.  The  1%  iso-surface  of  Fnorrnai  resembles 
a  dome  over  the  center  of  the  tile.  We  have  summarized  the 
results  in  terms  of  the  penetration  parameter  A  by  matching  the 
decay  of  Fnorrnai  to  e~^y,  where  a  is  the  maximum  of  the 
distance  between  the  edges  of  two  electrodes  and  that  between 
edges  of  two  magnets. 

III.  DIRECT  NUMERICAL  SIMULATIONS 

We  have  performed  spectral  element  simulations  of  a  channel 
turbulent  flow  with  one  wall  (the  lower)  covered  with  electromag¬ 
netic  tiles  as  shown  in  Figure  7.  Details  of  the  simulation  as  well 
as  extensive  validation  with  standard  benchmarks  can  be  found 
in  [10].  Here  we  summarize  some  representative  results  (see  table 

in). 


Figure  7:  Streamwise  component  of  Lorentz  force  for  LEFT: 
Tile  1;  RIGHT:  Tile  2 

Static  Control 

We  first  performed  simulations  with  all  tiles  permanently 
activated;  the  initial  conditions  corresponded  to  a  fully-developed 
turbulent  flow  when  the  Lorentz  force  was  turned  on.  In  Figure 


409 


esssss 


Case 

I applied 

E 

B 

Rer(l) 

ReT(u) 

no  control 

none 

none 

none 

145.7 

143.7 

Tile  1 

1.1 

100V/m 

0.2T 

162 

148.4 

Tile  2 

1.1 

100V/m 

0.2T 

152 

146.1 

Table  III:  Summary  of  the  cases  studied  using  electro-magnetic 
tiles  on  the  lower  wall  of  a  canonical  channel. 


8  we  present  the  drag  force  on  the  controlled  wall  as  a  function 
of  time  for  both  types  of  tiles  we  discussed  earlier  and  compare 
them  with  the  uncontrolled  case.  We  see  that  the  averaged  drag 
value  is  higher  for  the  Tile  1  configuration  than  for  the  Tile  2. 
When  we  plot  the  instantaneous  streamwise  vorticity  field  (Fig¬ 
ure  9,  we  see  that  the  value  of  ljx  is  larger  for  Tile  1  than  for 
Tile  2  corresponding  to  larger  source  of  vorticity  (V  X  F3)  and 
consequently  larger  drag  force. 


Figure  8:  Drag  history  for  Tile  1  and  Tile  2. 


Figure  10:  Temporal  pulsing  pattern  used  for  the  time- 
dependent  force  case.  Shown  is  the  interaction  parameter  Iapplied 
versus  non-dimensional  time. 


Lime 


Figure  11:  Drag  history  for  Tile  2  with  Dirichlet  force:  LEFT 
-  drag  history;  RIGHT  -  drag  pdf,  normalized  with  averaged 
no-control  value. 


Figure  9:  Streamwise  vorticity  for  run  using  LEFT:  Tile  1; 
RIGHT:  Tile2. 


time 


Simultaneous  Pulsing  Control 

Next  we  investigated  the  drag  history  for  conditions  corre¬ 
sponding  to  turning  the  electrodes  on- and- off.  The  pulsing  signal 
is  as  shown  in  Figure  10.  To  evaluate  the  effect  that  the  boundary 
conditions  for  the  electric  and  magnetic  fields  have  on  the  Lorentz 
force  distribution  and  consequently  on  turbulence  modification, 
we  performed  simulations  first  using  Dirichlet  boundary  condi¬ 
tions,  and  then  using  Neumann  boundary  conditions  for  and 
In  Figure  11  and  Figure  12  we  present  the  corresponding 
drag  force  histories.  The  simulation  using  Neumann  boundary 
conditions  predicts  a  lower  averaged  drag  than  the  corresponding 
case  with  Dirichlet  conditions.  In  fact,  the  Neumann  case  gives 
about  5%  drag  reduction  while  the  Dirichlet  case  gives  about  2% 
drag  increase. 

Four-Phase  Pulsing  Control 

We  have  also  investigated  different  pulsing  patterns  in¬ 
cluding  four-phase  and  polarized- four-phase  pulsing  (see  Figure 
13).  In  the  four- phase  case,  the  tiles  marked  “1”  are  first  acti¬ 
vated  followed  by  those  marked  “2” ,  “3”  and  “4” .  Then  the  pat¬ 
tern  repeats  back  to  “1”,  etc.  In  the  polari zed-four-phase  case, 
the  only  difference  is  that  those  tiles  marked  by  negative  integers 
are  pulsed  with  —  F. 


Figure  12:  Drag  for  Tile  2  run  with  Neumann  force:  LEFT 
-  drag  history;  RIGHT  -  drag  pdf,  normalized  with  averaged 
no- control  value. 


4 

2 

4 

2 

4 

2 

4 

2 

3 

1 

3 

1 

3 

1 

3 

1 

2 

4 

2 

4 

2 

4 

2 

4 

1 

3 

1 

3 

1 

3 

1 

3 

4phase 


4 

-2 

4 

-2 

4 

-2 

4 

-2 

3 

-1 

3 

-1 

3 

-1 

3 

-1 

2 

-4 

2 

-4 

2 

-4 

2 

-4 

1 

-3 

1 

-3 

1 

.3 

1 

^3 

4phase.pola 


Figure  13:  Pulsing  pattern:  LEFT  -  four-phase;  RIGHT  - 
polari  zed- four-phase.  Tiles  with  the  same  (or  opposite  number) 
are  on  or  off  at  the  same  time  instance. 


410 


The  drag  history  over  the  controlled  wall  is  shown  in  Fig¬ 
ure  14  for  the  four-phase  case  and  in  Figure  15  for  the  polarized- 
four-phase  case.  Neither  case  exhibits  any  net  drag  reduction. 


lime 


Figure  14:  Four-phase:  LEFT  -  drag  history;  RIGHT-  drag 
pdf.  Both  are  normalized  with  averaged  value  of  no-control  case. 


Figure  15:  Polarized-four-phase:  LEFT  -  drag  history; 
RIGHT-  drag  pdf.  Both  are  normalized  with  averaged  value 
of  no-control  case. 


Structures  and  Mechanisms 

Figure  16  shows  the  averaged  shear  stress  over  a  single  tile 
in  the  four-phase  case.  In  particular,  the  upper  left  plot  shows 


Figure  16:  Averaged  shear  stress  over  a  single  tile  normalized 
with  the  averaged  value  of  no-control  case. 

shear  stress  averaged  over  the  entire  duration  of  the  simulation, 
the  upper  right  plot  shows  shear  stress  averaged  over  the  first  50 
time  units  which  corresponds  to  higher  averaged  drag,  and  the 
lower  left  plot  shows  shear  stress  averaged  over  the  time  period 
from  250  to  300.  It  is  evident  that  there  are  strong  pockets  of  very 


large  shear  almost  twice  the  averaged  value  as  well  as  pockets  of 
very  small  shear  reduced  by  as  much  as  97%  or  even  becoming 
negative  during  periods  of  lower  than  the  average  drag.  The 
distribution  of  instantaneous  shear  stress  is  shown  in  Figure  17 
and  it  is  very  similar  with  an  apparent  spatial  periodicity.  The 
shear  stress  value  is  normalized  by  the  average  value  of  the  no¬ 
control  case.  Again,  we  can  see  that  there  are  pockets  of  higher 


Figure  17 :  Instantaneous  shear  stress  on  the  controlled  wall. 

shear  and  pockets  of  lower  shear  over  the  region  where  the  tiles 
are,  but  most  of  the  region  outside  tiles  shows  values  like  the 
average  shear  of  the  non-controlled  case. 

To  identify  flow  structures  associated  with  such  regions  of 
high  and  low  shear  we  examine  velocity  distribution  at  a  stream- 
wise  plane  that  cuts  through  a  pair  of  low-high  shear  regions.  In 
Figure  18,  we  have  isolated  such  a  region  and  magnified  the  scale 
to  more  clearly  see  such  structures.  It  is  clear  that  drag  reduction 
corresponds  to  regions  of  reverse  flow,  which  however  are  followed 
by  regions  of  high-speed  fluid  impinging  on  the  wall  (sweep  -  Q4 
events)  that  induce  high  shear. 


Figure  18:  Blowup  of  previous  figure:  LEFT  -  burst;  RIGHT 
-  sweep. 


Figure  19:  Instantaneous  vorticity  field:  LEFT  -  contour; 
RIGHT  -  blowup. 


411 


IV.  DISCUSSION 

The  results  of  the  present  work  suggest,  that  there  is  sig¬ 
nificant  variation  in  the  distribution  of  the  Lorentz  force  due  to 
electro-magnetic  tiles  that  form  the  controlling  surface.  The  issue 
is  primarily  the  choice  of  boundary  conditions,  especially  for  the 
current  (or  electric  field)  on  the  electrode  surface.  We  have  seen 
that  prescribing  the  value  of  the  electric  potential  on  the  electrode 
surface  results  in  a  force  penetration  length  quite  different  than 
prescribing  the  normal  derivative  of  the  potential,  i.e.  the  normal 
component  of  the  electric  field.  Typically,  we  approximate  these 
surface  distributions  as  constants  but  that  assumption  seems  to 
be  in  contrast  with  recent  experimental  results.  For  weakly  ion¬ 
ized  gases  we  can  perhaps  incorporate  Poisson- Boltzmann  equa¬ 
tions  to  model  the  charge  and  corresponding  current  distribu¬ 
tion  around  the  electrodes  but  for  sea  water  it  is  not  clear  what 
assumptions  to  make  regarding  the  current  distribution  in  the 
immediate  vicinity  and  surfaces  of  electrodes. 

The  Lorentz  force  distribution  and  the  controlling  puls¬ 
ing  pattern  are  key  elements  in  suppressing  effectively  turbulence 
in  EMHD  applications.  We  have  performed  here,  via  spectral  di¬ 
rect  numerical  simulations,  several  simulations  of  turbulent  chan¬ 
nel  flow  with  one  of  the  walls  covered  by  electro-magnetic  tiles. 
From  the  various  configurations  we  examined  we  found  that  if 
all  tiles  are  permanently  and  simultaneously  activated  a  drag  in¬ 
crease  occurs  which  is  higher  if  the  current  is  in  the  spanwise 
direction  (TILE  1).  This  is  consistent  with  the  force  distribution 
and  associated  streamwise  vorticity,  which  is  higher  in  TILE  1 . 
Introducing  a  pulsing  scheme  may  or  may  not  result  in  drag  re¬ 
duction  and  we  have  presented  a  case  for  which  a  net  5%  drag 
reduction  occurs  but  most  cases  simulated  resulted  in  net  drag 
increase. 

Finally,  we  analyzed  flow  structures  associated  with  in¬ 
stances  of  drag  decrease  and  drag  increase  and  found  that  pockets 
of  instantaneous  flow  reversal  are  responsible  for  the  former  while 
sweep  events  are  responsible  for  the  latter.  What  has  been  spec¬ 
ulated  as  two-dimensional  “rollers”  corresponding  to  spanwise 
vorticity  ([15],  [16],  [6],  [7])  are  in  fact  local  three-dimensional 
structures.  Our  current  data  suggest  that  attention  should  be 
paid  to  the  relative  size  of  structures  corresponding  to  the  afore¬ 
mentioned  pockets  of  flow  reversal  which  seem  to  be  of  the  order 
of  5  to  10  wall  units.  That  size,  however,  depends  critically  on 
the  Lorentz  force  penetration  length. 

References 

[1]  Tsinober  A.  Turbulent  drag  reduction  versus  structure  of 
turbulence.  Proceedings  of  the  2nd  IUTAM  symposium 
on  Structure  of  Turbulence  and  Drag  Reduction.  Zurich, 
Switzerland,  1989. 

[2]  Tsinober  A.  MHD  flow  drag  reduction.  Viscous  Drag  Re¬ 
duction  In  Boundary  Layers ,  Progress  in  Astronautics  and 
aeronautics,  Vol.  123,  edited  by  D.  M.  Bushnell  and  L.  N. 
Heiner. 

[3]  Henoch  C.  and  Stace  J.  Experimental  investigation  of  a 
salt  water  turbulent  boundary  layer  modified  by  an  applied 
streamwise  magnetohydrodynamic  body  force.  Pkys.  Fluids 
l(7):1371,  1995. 

[4]  Henoch  C.  Private  correspondence. 

[5]  Bandyopadhyay  P.  R.  and  Castano  J.  M.  Micro- tiles  for 
electromagnetic  turbulence  control  in  saltwater-preliminary 
investigations.  Symposium  on  Turbulence  Modification  and 
Drag  Reduction ,  ASME  Summer  Meeting,  1996.  Invited  pa¬ 
per. 

[6]  Nosenchuck  D.  M.  and  Brown  G.  L.  Discrete  spatial  control 
of  wall  shear  stress  in  a  turbulent  boundary  layer.  Inter¬ 
national  Conference  on  Near-  Wall  Turbulent  Flows,  Tempt 
Arizona,  edited  by  C.  G.  Spezialeand  B.  E.  Launder  (1993). 

[7]  Nosenchuck  D.  M.  Boundary  layer  control  using  the  Lorentz 
force,  http://connector.bsl.prc.com/emtc/ emtc.htm. 

[8]  Eng  T.  I.  A  laminar  boundary  layer  response  to  an  elec¬ 
tromagnetic  forcing.  Master’s  thesis,  Princeton  University, 
May  1995. 


[9]  Culver  H.  C.  M.  An  experimental  investigation  of  a  laminar 
boundary  layer  subject  to  an  applied  Lorentz  force.  Master’s 
thesis,  Princeton  University,  January  1996. 

[10]  Crawford  C.  H.  Direct  numerical  simulation  of  near- wall  tur¬ 
bulence:  passive  and  active  control.  Ph  D’s  thesis,  Princeton 
University,  May  1996. 

[11]  Crawford  C.  H.  and  Karniadakis  G.  E.  Reynolds  stress  anal¬ 
ysis  of  EMHD-controlled  wall  turbulence. Part  I.  Streamwise 
forcing.  Phys.  Fluids ,  l(9):788,  1997. 

[12]  Jackson  J.  D.  Classical  electrodynamics.  John  Wiley  &;  Sons, 
1975. 

[13]  Reed  C.  B.  and  Lykoudis  P.  S.  The  effect  of  a  transverse 
magnetic  field  on  shear  turbulence.  Journal  of  Fluid  Me¬ 
chanics ,  89:147,  1987. 

[14]  Gardner  R.  A.  and  Lykoudis  P.  S.  Magneto-fluid-mechanic 
pipe  flow  in  a  transverse  magnetic  field.  Part  I.  Isothermal 
flow.  Journal  of  Fluid  Mechanics,  47:737. 

[15]  Donovan  J.  F.,  Krai  L.  D.  and  Cary  A.  W.  Characteriza¬ 
tion  of  a  Lorentz  force  actuator.  28th  AIAA  Fluid  Dynam¬ 
ics  Conference,  dth  AIAA  Shear  Flow  Control  Conference. 
June  29  -  July  2,  1997,  Snowmass  Village,  CO. 

[16]  Krai  L.  D.  and  Donovan  J.  F.  Numerical  simulation  of  tur¬ 
bulence  control  using  electromagnetic  forces.  Proceedings 
of  the  1996  ASME  Fluids  Engineering  Conference  Forum 
on  Control  of  Transitional  and  Turbulent  Flows.  July  7-11, 
1996,  San  Deigo,  CA. 


412 


Fundamental  Studies  on  Active  Control  of  Large  Scale  Coherent  Structures  in  Channel 

Turbulence. 


Peter  L.  O’Sullivan  and  Sedat  Biringen, 
Department  of  Aerospace  Engineering, 
University  of  Colorado  at  Boulder, 
Boulder,  CO  80309-0429. 


Abstract 

The  current  work  focuses  on  the  spatio-temporal  evolution  of  large  scale  coherent  structures  in  the  turbulent  boundary  layer  of 
a  plane  channel  both  with  and  without  EMHD  control.  The  control  actuator  design  we  have  used  is  closely  based  on  designs 
developed  by  Bandyopadhyay  The  aim  of  this  study  is  to  learn  more  about  the  correlation  of  wall  shear  stress  with  the  passage 
of  large-scale  quasi-streamwise  vortices  which  are  widely  believed  to  be  the  key  flow  structures  responsible  for  strong  turbulent 
ejection  events.  The  heuristic  concept  behind  the  microtile  designs  that  we  have  simulated  apparently  does  not  yield  a  successful 
drag  reduction  strategy  (for  the  passive  case)  and  hence  we  must  determine  how  the  applied  Lorentz  forces  are  interacting  with 
advecting  flow  structures  (e.g.,  hairpin  vortices).  We  performed  an  active  control  simulation  conditioned  on  the  passage  of  a 
strong  ejection  event  but  obtained  no  reduction  in  skin  friction.  Based  on  some  short-time  simulations  we  found  that  the  flow 
structures  undergo  merely  a  spatial  phase-shift  when  advecting  above  a  single  control  actuator.  During  this  interaction  of  the 
applied  Lorentz  force  with  the  flow,  the  Reynolds  stress  is  unchanged.  It  appears  that  the  applied  Lorentz  force  interacts  linearly 
with  near-wall  structures  and  that  the  structures  are  simply  decelerated  or  accelerated  with  little  change  in  their  topology. 


I.  INTRODUCTION 

In  this  paper  we  are  concerned  with  the  problem  of  control¬ 
ling  turbulent  flows.  Primarily  we  are  interested  in  achieving  vis¬ 
cous  drag  reduction  although  numerous  other  control  objectives 
may  be  tackled  by  a  similar  approach  to  the  one  discussed  here. 
The  background  for  the  current  work  lies  in  prior  attempts  by  us 
to  realize  skin  friction  reduction  via  passive  control  using  electro- 
magneto-hydro-dynamic  (EMHD)  forces  in  turbulent  channel  flows 
of  saltwater  [1,  2],  Using  passive  control  with  both  static  and  tem¬ 
porally  pulsed  Lorentz  forces  based  upon  experimental  microtile 
configurations  developed  by  Bandyopadhyay  and  co-workers  [3]  we 
obtained  0(1%)  net  skin  friction  reductions.  However,  we  also  ob¬ 
tained  O(±10%)  localized  deviations  in  time- averaged  skin  friction 
in  the  vicinity  of  the  EMHD  microtile  actuators.  These  findings 
indicate  firstly  that  passive  control  performs  very  poorly  at  low 
Reynolds  numbers  (using  the  designs  that  we  studied).  Secondly, 
the  results  indicate  that  an  active  control  scheme  may  succeed  in 
reducing  skin  friction  given  the  capability  of  the  microtile  actua¬ 
tors  to  effect  significant  localized  control.  In  the  following  sections 
we  briefly  summarize  the  model  and  numerics  for  the  EMHD  con¬ 
trol  simulations  and  refer  the  reader  to  [2]  for  greater  detail  and 
information  on  our  prior  work. 

For  electrically  conducting  fluids  it  is  possible  to  mediate  a 
controlling  force  within  the  fluid  medium.  This  can  be  accom¬ 
plished  by  imposing  external  electric  and  magnetic  fields  in  such  a 
way  that  their  cross  product  (that  is  the  Lorentz  force)  acts  in  a 
prescribed  manner.  Saltwater  (e.g.,  seawater)  is  an  example  of  a 
weakly  conducting  fluid  (the  conductivity  is  approximately  5-6 
Si/m  (or  H^/m)  in  SI  units).  Nevertheless,  the  Lorentz  force 
which  can  be  generated  with  electric  and  magnetic  fields  of  rea¬ 
sonable  magnitude  is  large  enough  that  a  viable  controlling  force 
may  be  obtained.  One  advantage  of  such  a  control  strategy  for 
saltwater  flows  is  that  it  may  be  possible  to  “tune”  the  force  to 
act  only  in  certain  regions  of  the  flow.  The  main  drawback  on  the 
other  hand  is  that  the  electrical  power  consumption  requirements 
may  be  prohibitively  large  and  ultimately  offset  any  fluid  dynamic 
gains  (e.g.,  drag  reduction). 

A  number  of  recent  research  efforts  have  been  made  into 
EMHD  turbulence  control.  Nosenchuck  and  Brown  [4]  performed 
experiments  by  injecting  an  electrolyte  into  a  non-conducting  pure 
water  turbulent  boundary  layer.  They  employed  a  “tile”  design 
and  reported  a  dramatic  (almost  complete)  reduction  in  turbulence 
intensity  and  equally  dramatic  reduction  in  skin  friction.  Their  re¬ 
sults  have  as  yet  to  be  widely  reproduced  in  general  saltwater  flows. 
Bandyopadhyay  and  Castano  [3]  modified  the  tile  design  by  reduc¬ 
ing  the  physical  dimensions  (to  0(1)  mm)  and  flush-mounting  the 


surface  with  more  “microtiles”  per  unit  area.  Once  again  it 
has  been  difficult  experimentally  to  produce  reliable,  reproducible 
data  [5].  Henoch  and  Stace  [6]  performed  experiments  using  a 
longitudinal  strip  design  with  a  single  component  (streamwise) 
Lorentz  force.  At  low  Reynolds  numbers  they  obtained  an  increase 
in  drag  although  at  high  Re  they  did  obtain  slight  reductions  in 
skin  friction.  Crawford  and  Karniadakis  [7]  performed  numerical 
simulation  analogs  of  the  Henoch  and  Stace  experiments  and  cor¬ 
roborated  the  slight  net  increases  in  skin  friction  at  low  Re. 

Bandyopadhyay  [3]  has  developed  a  number  of  Lorentz  force 
actuators  based  on  silicon  microfabrication  which  are  similar  to  the 
design  of  Nosenchuck  and  Brown  [4].  The  electrodes  and  magnets 
in  these  “microtiles”  have  dimensions  of  0(1)  mm.  This  new  de¬ 
sign  has  a  resultant  Lorentz  force  which  is  three-dimensional  (or 
possibly  quasi-two-dimensional).  The  magnets  and  electrodes  were 
rectangular  and  square  respectively  in  his  original  design,  i.e.,  they 
are  finite  in  extent  and  occupy  a  small  fraction  of  the  area  of  the 
controlled  surface  (as  opposed  to  the  streamwise  strips  design). 
There  is  a  twofold  benefit  to  this  type  of  design.  Firstly,  the  power 
consumption  is  reduced  compared  to  that  of  longitudinal  strips. 
Secondly,  the  vertical  extent  of  the  force,  or  penetration  depth, 
can  be  tuned  by  adjusting  the  separation  between  the  electrodes. 
In  this  way,  the  length  scales  of  the  actuator  force  can  be  matched 
to  those  of  a  fully  developed  turbulent  flow.  Also,  the  orienta¬ 
tion  of  the  microtiles  can  be  altered  to  produce  dissimilar  control 
schemes  based  on  the  differing  circulation  patterns  set  up  by  the 
re-oriented  Lorentz  force.  Finally,  the  microtiles  can  be  pulsed  in 
time  (and/or  phase- sequenced  in  space).  Pulsing  has  three  ben¬ 
efits:  reduced  power,  reduced  corrosion  of  electrode  surfaces  and 
the  possible  favorable  resonance  with  turbulent  flow  structures. 

In  a  preliminary  computational  investigation  of  the  effect  of 
these  microtiles  on  a  laminar  channel  flow,  Hatay  et  al.  [1]  found 
that  the  microtile  design  can  generate  a  secondary  vortical  flow 
with  feasible  input  power  requirements.  At  low  to  moderate  electric 
and  magnetic  field  strengths  secondary  flows  of  significant  strength 
were  presented.  The  microtile  engendered  a  flow  structure  consist¬ 
ing  of  counter-rotating  streamwise  vortices  above  the  wall.  The 
induced  velocity  at  the  “center”  of  the  actuator  was  wall-wards 
which  is  consistent  with  the  original  guiding  ideas  behind  the  de¬ 
sign.  Hatay  et  al.  [1]  also  showed  computationally  that  when  puls¬ 
ing  the  Lorentz  force,  the  flow  showed  a  fast  response  time. 

In  our  earlier  work  [2]  we  took  the  original  microtile  design  of 
Bandyopadhyay  and  Castano  [3]  and  performed  direct  numerical 
simulations  of  fully  developed  turbulence  in  a  canonical  channel 
flow.  We  studied  the  effects  of  EMHD  control  for  this  case  and 
for  a  number  of  pulsing  frequencies  in  order  to  investigate  Bandy- 


413 


opadhyay’s  hypothesis  of  a  resonance  mechanism  for  the  EMHD 
control  based  on  the  length  and  time  scales  of  the  resultant  Stokes’ 
layer  created  by  the  Lorentz  force.  We  experimented  with  the  elec¬ 
trode  spacing  to  focus  and  amplify  the  Lorentz  force  and  we  also 
performed  simulations  with  a  90°-rotated  version  of  the  microtile. 
This  last  numerical  experiment  was  in  the  spirit  of  recent  experi¬ 
ments  by  Jung  et  al.  [8]  and  Laadhari  et  al.  [9]  which  have  shown 
that  an  oscillatory  spanwise  wall  motion  can  lead  to  dramatic  re¬ 
ductions  in  skin  friction.  We  note  however  that  these  wall  oscilla¬ 
tions  have  no  streamwise  dependence  whereas  our  simulations  do 
have  a  sinusoidal  dependence  on  the  streamwise  direction  -  i.e., 
the  analogy  is  strictly  in  a  localized  sense.  Finally  we  studied  the 
effect  of  increasing  the  magnitude  of  the  Lorentz  force. 

The  outcome  of  our  earlier  work  was  that  passive  EMHD 
control  was  ineffective  (for  the  designs  that  we  used  at  low  Re). 
However,  the  reasonably  strong  localized  deviations  in  skin  fric¬ 
tion  gave  us  cause  for  more  in-depth  study  of  the  spatio-temporal 
behavior/interaction  of  the  applied  Lorentz  force  with  advecting 
large-scale  turbulent  flow  structures  in  the  boundary  layer.  The 
heuristic  concept  behind  the  microtile  actuator  design  is  that  the 
wall-normal  component  of  Lorentz  force  inhibits  the  uplifting  mo¬ 
tion  of  typical  second  quadrant  ejection  events  which  characterize 
turbulent  “bursts”.  It  is  clear  that  this  argument,  while  appealing, 
does  not  work  satisfactorily  because  it  ignores  the  three  dimen¬ 
sionality  of  the  Lorentz  force  and  its  (possibly)  adverse  effects.  We 
note  here  that,  as  yet,  it  is  unknown  whether  or  not  the  microtile 
Lorentz  force  does  in  fact  inhibit  ejections  of  low  momentum  fluid 
particles. 

The  first  simulation  we  report  on  is  a  long-time  active  control 
simulation  based  on  the  ttv-quadrant  detection  scheme  developed 
by  Alfredsson  and  Johansson  [10].  This  simulation  serves  as  an 
extension  of  our  earlier  work.  In  order  to  gain  insight  into  the 
EMHD  turbulence  control  problem  we  have  also  performed  two 
short-duration  numerical  simulations  (A £+  «  32)  of  fully  devel¬ 
oped  channel  turbulence  using  identical  initial  conditions.  The  first 
objective  is  to  perform  flow  visualizations  on  the  uncontrolled  case 
to  determine  the  validity  of  the  hairpin  vortex  structure  as  the  un¬ 
derlying  predominant  turbulence  structure.  By  this  we  mean  that 
there  is  evidence  to  support  a  somewhat  more  complex  picture  of 
the  vortex  dynamics  rather  than  a  picture  which  contains  only  iso¬ 
lated,  independent  hairpins.  Secondly,  we  want  to  illuminate  the 
instantaneous  flow  response  to  the  applied  EMHD  control  by  ob¬ 
serving  the  modification  of  advecting  coherent  structures  in  the 
vicinity  of  the  EMHD  actuators. 


Lz 


Figure  2:  Schematic  of  flow  geometry  and  co-ordinate  system. 


whose  time-dependence  is  taken  as  steady  or  instantaneous.  From 
Maxwell’s  equations  we  find 

V2V  =  V2Bj,  =  0 

which  are  solved  with  prescribed  Dirichlet  data  for  the  microtile 
distribution  of  V  and  By .  The  surface  electric  and  magnetic  dis¬ 
tributions  for  V  and  By,  respectively,  are  modelled  as  smoothed 
hyperbolic  tangent  step  functions.  The  remaining  components  of 
B  are  computed  algebraically  from  Maxwell’s  equations.  Details 
of  the  Lorentz  force  computation  can  be  found  elsewhere  [1,  2]. 
The  Lorentz  force  is  computed  in  a  pre-processing  step  assuming 
periodicity  in  x  and  z  and  then  incorporated  as  a  body  force  in  the 
momentum  equations.  Note  that  due  to  the  symmetry  (in  both  x 
and  z)  of  both  the  electrodes  and  magnets  in  each  actuator  con¬ 
figuration  there  is  zero  net  volumetric  body  force  in  the  x  and  z 
directions.  That  is,  the  Lorentz  force  does  not  induce  any  spatial 
mean  motion  in  (x,z). 

In  Fig.  (3)  we  present  a  schematic  diagram  of  the  microtile 
design  used  in  this  work.  A  vector  plot  of  the  Lorentz  force  for  this 
tile  design  is  shown  in  Fig.  (4).  The  plot  is  taken  at  a  ^-location 
half-way  between  the  magnets  of  a  single  actuator.  The  force  field 
is  predominantly  wall-ward  over  the  “inner”  region  of  the  actuator, 
i.e.,  the  region  between  each  pair  of  electrodes.  However,  one  can 
also  clearly  see  the  upward  force  outside  this  region  especially  at 
the  fore  and  aft  edges  of  the  electrodes  where  the  direction  of  E  is 
reversed. 


II.  COMPUTATIONAL  MODEL 

The  channel  geometry  is  depicted  in  Fig.  (2).  The  Navier- 
Stokes  equations  (plus  Lorentz  body  force)  are  non-dimensionalized 
by  the  channel  half-height,  h,  the  kinematic  viscosity,  z/,  and  the 
bulk  velocity,  uB-  Periodic  boundary  conditions  are  assumed  in 
the  horizontal,  (x,  z)-,  directions  and  no  slip  at  the  upper  and  lower 
channel  walls.  The  “box  size”  is  Lx  x  Lz.  The  microtile  design 
that  we  have  used  is  shown  in  Fig.  (3).  Notice  from  this  figure  that 
a  single  tile  comprises  a  diagonally  situated  pair  of  Lorentz  force 
actuators. 

The  Lorentz  force  is  given  by 

F  =  JxB 

where  J  is  the  current  density  (measured  in  Amps/m2)  and  B  is 
the  magnetic  induction  (measured  in  Tesla).  All  induced  electric 
and  magnetic  fields  are  neglected  from  the  outset  but  have  been 
verified  a  posteriori  to  be  dynamically  inconsequential.  In  this  case 
we  find  from  elementary  EM  theory  J  in  turn  is  given  by 

J  =  crExB  =  -crWxB 

where  er  is  the  electrical  conductivity  of  the  fluid  measured  in 
Siemen  per  meter  (Si  =  Ohm-1),  E  is  the  applied  electric  field 
and  V  is  the  electric  potential. 

We  have  invoked  the  static  MHD  approximation  in  which  the 
EM  fields  are  completely  decoupled  from  the  fluid  velocity  and 


III.  NUMERICAL  METHODS 

The  surface  V  and  B  fields  are  non-dimensionalized  by  a  ref¬ 
erence  voltage,  Vo,  and  magnetic  induction,  Bo-  The  resulting 
non-dimensional  incompressible  Navier-Stokes  equations  are  then 
given  by 

V  •  u  =  0 

and 

dtu  +  V  •  uu  =  F(t)5n  —  Vp  +  1  V2u  +  NB  (E  x  B) 

Res 

where  Res  =  uBh/is,  F(t)  represents  the  force  required  to  main¬ 
tain  a  constant  mass  flux  throughout  the  flow  domain  and  the 
interaction  parameter,  Nb ,  is  given  by 


NB=z 


aVoBg 

PUB 


The  corresponding  interaction  parameter  scaled  on  inner  variables 
we  denote  by  NT  with 


Nr 


(tVqBq 

pul 


Nb(ub/ut)2  . 


Our  code  employs  a  de-aliased  Fourier  Galerkin  method  in 
(re,  z)  and  fourth  order  accurate  finite  differences  in  y  (on  a  cosine- 
stretched  grid).  The  code  also  uses  a  staggered  mesh  in  y  in  order  to 


414 


Figure  3:  Schematic  of  microtile  dimensions  (millimeters)  for 
EMHD  control  case  (not  to  scale).  A  single  tile  consists  of  a  pair 
of  diagonally  situated  actuators. 


keep  divergence  errors  to  less  than  lO"10  within  each  cell.  The  spa¬ 
tial  resolution  was  64x80x96  points  in  the  streamwise,  wall-normal 
and  spanwise  directions,  respectively,  The  solution  was  advanced 
in  time  using  the  second  order  accurate  Adams-Bashforth/Crank- 
Nicolson  scheme  with  At  =  0.0025 h/uB- 

The  microtile  dimensions  and  channel  height  are  based  closely 
on  typical  experimental  specifications  except  that  the  electrode 
spacing  has  been  reduced  in  order  to  amplify  the  Lorentz  force. 
The  dimensions  Lx  and  Lz  were  then  chosen  so  that  the  non- 
dimensional  box  lengths  would  be  close  to  2n  x  7r  which  was 
found  to  be  sufficiently  large  for  spatial  de-correlation.  These  di¬ 
mensions  lead  to  the  non-dimensional  box  size  of  approximately 
(6.09  x  2  x  3.13).  The  Reynolds  number  was  set  to  Res  =  3, 140 
(constant  mass  flux)  with  resultant  Rer  ft*  196.6  and  Re<g  ft*  3,689. 
In  terms  of  wall  unit  scaling,  y+  —  yuT/v ,  the  dimensions  of  the 
domain  are  (1197  x  393  x  598 )y+.  The  horizontal  grid  resolution  is 
(Ax+,Az+)  m  (19,6)  and  (Ay+in,  (Ay+ax)  w  (0.15,7.72).  The 
simulations  we  report  on  were  initialized  with  a  fully  developed 
turbulent  flow  field  in  each  case. 


IV.  EVENT  DETECTION 

Alfredsson  and  Johansson  [10]  developed  an  experimental 
technique  for  reliably  and  robustly  detecting  turbulent  “events” 
in  which  the  uv-quadrant  analysis  is  performed  on  single  point  X- 
wire  data.  We  have  performed  a  similar  analysis  but  rather  using 
instantaneous  spatial  data.  Their  uv-quadrant  analysis  detects  an 
event  whenever 

-«V  >  HUrmsVrms 

where  H  is  a  positive  constant  threshold  and  u',vf  are  the  stream- 
wise  and  wall-normal  fluctuating  velocities.  Alfredsson  and  Jo¬ 
hansson  performed  this  test  at  a  height  of  y+  ft*  50  above  the  wall. 
This  detection  scheme  isolates  strong  second  (Q2)  and  fourth  quad¬ 
rant  (Q4)  turbulent  signals.  In  the  current  study  we  have  found 
H  =  5  (compared  with  H  =  4  of  Alfredsson  and  Johansson)  to  be  a 
good  cut-off  for  “strong”  events  and  we  also  located  our  detection 
“probe”  at  y+  ft*  30.  Note  that  the  values  for  urms,vrms  were 
obtained  in  prior  fully  turbulent  steady  state  simulations. 

In  Fig.  (5)  we  have  plotted  the  spatial  distribution  of  the  top 
ten  events  detected  using  this  scheme.  The  rank  of  each  event  is 
shown  alphabetically  with  A  denoting  the  strongest  event.  Event  I 


x 


Figure  4:  Vector  plot  of  the  non-dimensional  Lorentz  force  for  the 
UV  cases  along  the  centerline  of  a  single  actuator.  The  ^-location 
of  this  view  is  half-way  between  the  magnets.  The  x-coordinate 
is  measured  in  millimeters  while  the  vertical  coordinate  is  in  wall 
units.  Nb  =  0.0894. 


is  the  only  Q4  event  among  these  ten.  The  striking  feature  of  this 
figure  is  that  six  of  the  events  are  closely  aligned  in  the  spanwise 
direction. 


Figure  5:  Turbulent  events  detected  with  the  uu-quadrant  scheme 
for  an  instantaneous  flow  realization  at  Res  —  3,140.  The  letter 
beneath  each  symbol  denotes  the  ranking  of  each  event  with  A 
being  the  strongest.  Note  that  event  I  is  a  Q4  event  and  that  H  is 
shown  twice  because  of  periodicity.  The  dotted  line  indicates  the 
spanwise  period  of  the  computational  domain. 

In  ranking  the  detected  events  we  recursively  searched  the 
flow  field  for  the  maximum  Reynolds  stress  and  then  excluded  a 
control  volume  centered  around  this  point  from  subsequent  event 
detection  searches.  We  chose  the  dimensions  of  the  control  volume 
based  on  the  length  scales  of  typical  bursts  obtained  by  Alfreddson 
and  Johansson.  At  Rer  ft*  197  this  gives  a  control  volume  with 
dimensions  206  X  53  x  154 in  x,y,2.  The  individual  control 
volumes  for  detected  events  are  permitted  to  overlap.  From  Fig.  (5) 
we  see  that  with  this  detection  scheme,  e.g.,  events  A,  C  and  D  are 
separated  by  approximately  0.8  units  in  x  which  is  approximately 
160 y+.  We  have  measured  the  advection  speed  of  these  events 
to  be  around  9.5uT  which  leads  to  a  temporal  separation  of  17 1+ 
(£+  =  tu^fu).  Alfredsson  and  Johansson  found  the  duration  of 
uv  peaks  to  be  approximately  2  —  4£+  although  this  time  scaled 
neither  with  inner  nor  outer  variables.  The  low  Reynolds  number 
in  the  current  DNS  also  does  not  permit  us  to  conclusively  say 
that  events  A,  C  and  D  are  distinct  based  on  just  the  uv  peak 
separations. 


415 


V.  VORTEX  GROUPS 

In  Fig.  (6)  we  have  plotted  three  side  views  of  the  perturba¬ 
tion  vorticity  magnitude  at  the  same  instant  as  that  of  Fig.  (5). 
The  middle  view  is  aligned  at  the  same  spanwise  location  as  the 
strongest  Q2  event,  denoted  by  A  in  Fig.  (5).  The  streamwise  ex¬ 
tent  in  the  figures  is  the  total  computational  domain  size,  Lx.  The 
vertical  extent  is  2.5 <  y  <  5 %+  -  we  have  excluded  the  wall 
vorticity  from  the  images  for  clarity.  The  vertical  direction  has  also 
been  stretched  by  a  factor  of  3  in  order  to  see  the  structures  more 
easily.  In  the  middle  image  ( z+  =  0)  we  can  see  three  closely  situ¬ 
ated  inclined  vortices  near  x+  =  0  (by  vortices,  in  this  context,  we 
merely  mean  regions  of  high  vorticity  magnitude  which  might  be, 
and  probably  are,  vortices  in  the  more  accurate  sense  of  the  word). 
The  approximate  distance  between  these  structures  in  this  image 
is  125 y+.  The  two  close  spanwise  neighbors  of  this  middle  view 
are  presented  to  give  some  idea  of  the  spatial  structure  of  these 
vortices.  The  lowest  image  (at  z+  =  +13)  demonstrates  even  more 
convincingly  that  these  inclined  vortices  are  advecting  as  a  group. 
This  bottom  image  in  particular  shows  that' these  inclined  vortices 
can  in  fact  lie  above  one  another  (e.g.,  the  two  structures  at  the  left 
of  the  bottom  image).  In  this  case,  the  mutual  vortex  induction 
will  be  strong  enough  to  link  the  two  structures. 


Figure  6:  Three  side  views  of  perturbation  vorticity  magnitude 
during  a  characteristic  burst  event.  The  middle  view  is  at  the 
spanwise  location  of  maximal  ejection  strength;  the  streamwise  lo¬ 
cation  is  in  the  center  of  the  figure.  The  top  and  bottom  plots  are 
equivalent  side  views  at  spanwise  locations  of  z  —  ±13y+  from  the 
center  plot,  respectively. 

If  two  hairpin  vortices  occur  in  close  streamwise  proximity  at 
the  same  spanwise  location  then  the  mutual  induction  will  likely 
lead  to  the  classic  leap-frogging  interaction.  If  three  or  more  hair¬ 
pins  are  aligned  in  the  streamwise  direction  then  the  “sandwiched” 
vortices  will  be  largely  in  equilibrium  due  to  the  equal  and  opposite 
vortex  induction  of  the  leading  and  trailing  hairpins.  The  leading 
hairpin  will  be  spatially  compressed  and  retarded  while  the  trailing 


hairpin  will  be  spatially  enlarged  and  accelerated  just  as  in  leap¬ 
frogging.  In  addition  to  the  Biot-Savart  induction  the  mean  flow 
itself  will  add  to  this  effect  by  simple  differential  advection  in  the 
wall-normal  direction.  There  is  visual  evidence  in  the  bottom  im¬ 
age  of  Fig.  (6)  for  this  scenario:  the  three  inclined  structures  at  the 
left  are  such  that  the  trailing  vortex  is  “taller”  than  the  leading 
vortex.  In  summary,  we  infer  that  a  turbulent  burst  is  related  to 
the  passage  of  a  group  of  vortices  which  act  in  concert  rather  than 
as  separate  structures.  A  more  quantitative  measure  of  this  asser¬ 
tion  would  be  given  by  computing  the  two  point  correlations  for  a 
large  number  of  similar  bursts.  This  calculation  is  left  for  future 
work  for  now.  If  indeed  hairpins  advect  in  groups  then  this  more 
complex  structural  arrangement  will  have  ramifications  for  turbu¬ 
lence  control.  In  particular,  actuators  designed  with  the  aim  of 
introducing  equal  and  opposite  vorticity  at  the  wall  (via  EMHD  or 
any  other  means)  will  need  to  address  the  issue  of  complex  near¬ 
wall  quasi-st reamwise  vortices  (involving  overlaid,  intertwined  or 
braided  streamwise  vortices  from  the  legs  of  a  group  of  hairpin 
vortices). 


V.  ACTIVE  CONTROL 

Using  the  event  detection  scheme  described  in  section  we 
performed  a  long  time  integration  employing  an  (artificial)  active 
control  scheme.  That  is,  we  activated  a  single  EMHD  actuator  if 
and  when  a  strong  Q2  event  was  detected  at  some  distance  up¬ 
stream.  The  EMHD  actuators  are  those  shown  in  Fig.  (3)  and 
the  interaction  parameter  was  set  at  Nb  =  0.089,  Nr  =  22.04 
(a  =  6,  Vo  =  0,  Bo  =  0.6)  just  as  in  previous  passive  control  sim¬ 
ulations  [2].  Whenever  a  Q2  event  was  detected  (sampling  every 
4 £+  approximately),  the  nearest  downstream  actuator  was  turned 
on  while  all  other  actuators  were  turned  off.  The  purpose  of  this 
simulation  was  to  see  if  an  active  control  scheme  would  yield  any 
improvements  over  the  previous  passive  case.  In  Fig.  (7)  we  have 
plotted  the  running  time  average  velocity  gradient  at  the  lower 
controlled  wall.  The  angled  brackets  denote  an  average  over  the 
x  and  z  directions  and  the  previous  770 f+.  The  total  duration  of 
this  run  was  approximately  9, 700i+  but  we  have  omitted  the  early 
transient  data  from  the  figure. 


Figure  7:  Running  time  average  velocity  gradient  at  lower  (con¬ 
trolled)  wall  with  active  control  scheme. 

From  this  figure  we  can  see  clearly  that  there  is  no  reduction 
in  mean  wall  shear  and  possibly  in  fact  a  slight  increase.  This 
result  is  surprising  given  our  earlier  findings  of  small  but  consistent 
skin  friction  reductions  using  passive  control  with  similar  EMHD 
actuator  designs.  In  the  following  sections  we  explore  in  more 
depth  the  flow  response  to  the  applied  control  in  order  to  better 
understand  why  the  control  is  not  achieving  drag  reduction. 


416 


0.4 


VI.  INSTANTANEOUS  FLOW  RESPONSE 

Given  the  outcome  of  the  active  control  simulation  described 
above  we  performed  a  short-duration  simulation  with  EMHD  con¬ 
trol  turned  on  statically  while  again  performing  the  spatial  event 
detection  scheme.  The  x,  z- locations  of  detected  events  with  con¬ 
trol  ON  turned  out  to  be  extremely  similar  to  those  with  control 
OFF.  However,  a  certain  number  of  the  detected  Q2  events  did 
undergo  a  significant  alteration  when  control  was  applied.  In  Fig. 
(8)  we  have  plotted  the  x-location  of  the  strongest  Q2  event  versus 
time  with  control  both  ON  and  OFF.  For  the  uncontrolled  case 
we  see  a  characteristic  linear  advection  but  in  the  controlled  case 
we  observe  a  short  deceleration/acceleration  of  the  peak  Reynolds 
stress  location.  Subsequently  the  two  event  locations  coincide  al¬ 
most  identically. 


Figure  8:  Streamwise  location  of  strongest  Q2  event  vs.  time  for 
short-duration  simulations.  Solid  curve  is  for  control  OFF;  dotted 
curve  is  for  control  ON  (static  force). 


For  this  pair  of  (comparable)  events  we  also  saved  records  (in 
time)  of  the  instantaneous  fluctuation  velocity  which  is  shown  in 
Fig.  (9).  We  see  that  at  the  second  detection  time  the  v '  velocity 
is  decreased  by  30%  while  the  (negative)  v!  velocity  is  increased 
in  magnitude  by  over  40%.  In  spite  of  these  substantial  modifica¬ 
tions  to  the  flow  the  Reynolds  stress  remains  approximately  con¬ 
stant  and  ultimately  the  controlled  flow  rejoins  the  uncontrolled 
flow.  Furthermore,  we  have  performed  flow  visualizations  of  the 
vortical  structures  in  both  the  uncontrolled  and  controlled  flows 
in  the  comparable  control  volumes  for  similar  detected  events.  In 
the  visualizations  we  have  found  that  the  vortical  structures  in  the 
buffer  region  are  essentially  unchanged  in  shape  but  are  shifted  in 
the  streamwise  direction.  There  is  some  alteration  in  vorticity  in 
the  viscous  sublayer  in  the  vicinity  of  the  EMHD  actuator.  Overall, 
based  on  this  and  several  other  visualizations  of  event  structures, 
we  believe  that  the  current  EMHD  actuators  are  not  significantly 
changing  the  large-scale  vortical  structures  but  rather  inducing  a 
streamwise  phase  shift  in  space  as  the  structures  advect  above  the 
control  actuator. 

In  Fig.  (10)  we  have  plotted  the  percentage  change  in  skin 
friction  for  a  spatial  region  centered  about  one  single  turbulent 
ejection  both  with  and  without  EMHD  control.  The  detection  lo¬ 
cation  (of  locally  maximal  Reynolds  stress)  is  at  (x+,2+)  =  (0,0) 
in  the  figure.  We  can  see  a  very  striking  pattern  of  skin  friction 
modification  in  the  left  hand  side  of  this  figure  where  we  also  see 
three  very  clear  “footprints”  of  the  EMHD  actuators.  We  note 
that  this  footprint  is  very  similar  to  the  long-time  average  foot¬ 
prints  obtained  in  our  earlier  work  [2].  This  instantaneous  image 
of  the  local  flow  modification  reinforces  two  aspects  of  the  cur¬ 
rent  control  actuator  under  study.  First,  the  actuators  can  effect  a 
significant  localized  flow  modification:  the  maximum  reduction  in 
local  wall  shear  stress  between  these  two  equivalent  ejection  events 
is  —22%  and  the  maximum  increase  is  +27%.  Second,  the  average 
change  in  wall  shear  between  these  two  events  (averaged  over  the 
control  volume)  is  extremely  small  at  —0.2%  which  is  statistically 
insignificant. 


Figure  9:  Fluctuating  streamwise  and  wall-normal  velocity  and 
Reynolds  stress  for  strongest  detected  Q2  events  with  control  OFF 
(solid,  filled)  and  ON  (dotted,  unfilled). 


X+ 


Figure  10:  Contours  of  percentage  change  in  skin  friction  for  con¬ 
trol  OFF/ON  for  a  single  turbulent  ejection  event.  Contour  spac¬ 
ing  is  5%  and  negative  contours  are  indicated  with  dotted  curves. 
The  x,  z  axes  are  given  in  wall  units  centered  about  the  detection 
location. 


VII.  CONCLUSIONS 

We  have  implemented  a  rational  active  control  scheme  using 
EMHD  microtile  actuators  with  no  reduction  in  skin  friction.  The 
control  activation  was  based  on  the  uu-detection  scheme  developed 
by  Alfredsson  and  Johansson  [10].  We  have  also  performed  short- 
duration  passive  control  simulations  in  order  to  ascertain  the  in¬ 
stantaneous  flow  response  to  the  applied  Lorentz  force  controllers. 
We  discovered  that  the  particular  design  we  have  investigated  in¬ 
duces  a  deceleration/acceleration  phase  shift  during  the  advection 
of  strong  Q2  ejection  events  above  the  EMHD  actuators.  We  com¬ 
pared  time  series  for  control  volumes  centered  around  the  location 
of  a  number  of  ejection  events  both  with  and  without  EMHD  con¬ 
trol.  Despite  the  fact  that  the  control  had  a  significant  effect  on 
the  fluctuating  velocity  this  effect  was  subsequently  reversed  with 
essentially  no  change  in  Reynolds  stress  during  the  passage  of  the 
ejection  structure.  Although  significant  localized  deviations  in  skin 
friction  on  the  order  of  15  —  18%  were  found  to  occur  and  spatial 
mean  skin  friction  within  a  control  volume  could  change  by  ±4—5% 


417 


we  observed  almost  no  net  change  in  (spatial)  mean  wall  shear.  In 
flow  visualizations  we  did  not  observe  significant  changes  in  stream- 
wise  vortical  structure  apart  from  the  spatial  phase  shifting.  These 
results  together  with  the  antisymmetric  spatial  Lorentz  force  dis¬ 
tribution  (of  the  design  considered)  leads  us  to  conclude  that  the 
control  is  ineffective.  The  reason  appears  to  be  that  the  applied 
Lorentz  force  interacts  linearly  with  passing  flow  structures  and 
then  reverses  the  interaction  as  the  structure  advects  above  the 
downstream  half  of  the  actuator.  A  possible  improvement  in  the 
design  might  be  to  reverse  the  polarity  of  the  electrodes  during  this 
second  half  of  the  passage  above  an  actuator.  This  should  have  the 
effect  of  reinforcing  the  initial  effect  of  the  actuator  rather  than  un¬ 
doing  it. 

At  a  more  fundamental  level  the  work  we  have  described  here 
indicates  that  a  somewhat  more  complex  picture  of  vortex  dynam¬ 
ics  in  the  boundary  layer  is  appropriate.  Although  hairpin  vortices 
are  ubiquitous  they  appear  to  occur  in  groups  very  frequently. 
Therefore  a  rational  control  scheme  should  most  likely  be  pred¬ 
icated  on  controlling  these  trains  of  hairpin  vortices  rather  than 
single  isolated  and  independent  vortices.  Further  research  needs 
to  be  done  to  substantiate  this  picture  more  firmly  and  possibly 
develop  a  better  rational  control  principle. 

Finally,  we  surmise  that  in  view  of  this  more  complex  vortex 
structure  of  turbulent  bursts  it  may  be  more  prudent  for  EMHD 
control  to  utilize  a  simpler  Lorentz  force  actuator  than  the  one  con¬ 
sidered  here.  For  example,  it  is  possible  to  take  the  uni-directional 
force  actuator  developed  by  Henoch  and  Stace  [6]  but  to  use  finite 
electrodes  and  magnets  rather  than  producing  a  global  Lorentz 
force  in  the  streamwise  direction.  In  this  approach  it  would  be  pos¬ 
sible  to  generate  a  highly  directional  Lorentz  force  that  could  be 
used  to  act  directly  upon  the  low  speed  streaks  (since  the  Lorentz 
force  has  an  exponential  decay  with  y ).  The  persistence  of  low 
speed  streaks  is  well  documented  [11],  a  fact  which  may  be  ex¬ 
ploitable  for  EMHD  control  in  particular.  An  analogous  span- 
wise  force  could  also  be  applied  which  could  be  used  to  produce 
oppositely-signed  streamwise  vorticity  conditioned  upon  the  oc¬ 
currence  of  aligned,  strong  near-wall  streamwise  vorticity.  Both 
of  these  methods  would  bypass  the  three  dimensional  character  of 
the  Lorentz  force  generated  by  the  microtile  designs  that  we  have 
studied  here.  This  simpler  but  localized  EMHD  actuator  based 
on  a  single  component  Lorentz  force  will  be  the  focus  of  a  future 
investigation. 


4.  D.  M.  Nosenchuck  &  G.  L.  Brown.  Discrete  Spatial  Control  of 
Wall  Shear  Stress  in  a  Turbulent  Boundary  Layer.  In  R.  M.  C. 
So,  C.  G.  Speziale  &  B.  E.  Launder,  eds.  ,  Near-Wall  Turbu¬ 
lent  Flows ,  pp.  313-343.  Elsevier,  1993.  Proceedings  of  an 
International  Conference  on  Near- Wall  Turbulent  Flows  held 
at  Arizona  State  University,  Tempe,  AZ,  March  15-17,  1993. 

5.  P.  R.  Bandyopadhyay,  1997.  (Private  communication). 

6.  C.  Henoch  &  J.  Stace.  Experimental  investigation  of  a  salt  wa¬ 
ter  turbulent  boundary  layer  modified  by  an  applied  stream- 
wise  magnetohydrodynamic  body  force.  Physics  of  Fluids ,  7 
(6)  pp. 1371-1383,  1995. 

7.  C.  H.  Crawford  &  G.  E.  Karniadakis.  Reynolds  stress  anal¬ 
ysis  of  EMHD-controlled  wall  turbulence.  Part  I.  Streamwise 
Forcing.  Physics  of  Fluids ,  9  (3)  pp. 788-806,  1997. 

8.  W.  J.  Jung,  N.  Mangiavacchi  &  R.  Akhavan.  Suppression  of 
turbulence  in  wall-bounded  flows  by  high-frequency  spanwise 
oscillations.  Physics  of  Fluids  A,  4  (8)  pp. 1605-1607,  1992. 

9.  F.  Laadhari,  L.  Skandaji  h  R.  Morel.  Turbulence  reduction 
in  a  boundary  layer  by  a  local  spanwise  oscillating  surface. 
Physics  of  Fluids,  6  (10)  pp. 3218-3220,  1994. 

10.  P.  H.  Alfredsson  &  A.  V.  Johansson.  On  the  detection  of 
turbulence- generating  events.  Journal  of  Fluid  Mechanics , 
139  pp. 325-345,  1984. 

11.  C.  R.  Smith  &  Metzler.  The  characteristics  of  low-speed 
streaks  in  the  near-wall  region  of  a  turbulent  boundary  layer. 
Journal  of  Fluid  Mechanics ,  129  pp.27-54,  1983. 


ACKNOWLEDGEMENTS 

We  wish  to  thank  Dr.  Patrick  Purtell  for  his  continued  inter¬ 
est  in  this  research.  We  are  also  grateful  to  Dr.  Bandyopadhyay 
at  NUWC  Division,  Newport,  RI  for  many  lively  and  fruitful  dis¬ 
cussions  related  to  this  research.  This  work  has  been  supported  by 
the  Office  of  Naval  Research  under  grant  number  DOD  N00014- 
95-1-0419.  Partial  funding  was  also  available  from  NSF  Grant  No. 
ECS-9725504.  Computations  were  performed  on  a  Cray  C916  at 
the  US  Army  Corps  of  Engineers,  Waterways  Experiment  Station, 
Vicksburg,  MS. 


References 

1.  F.  F.  Hatay,  P.  L.  O’Sullivan,  S.  Biringen  h  P.  R.  Bandy¬ 
opadhyay.  Numerical  Simulation  of  Secondary  Flows  in  Chan¬ 
nels  Driven  by  Applied  Lorentz  Forces.  AIAA  J.  of  Thermal 
Physics  and  Heat  Transfer ,  11  (3)  pp. 446-453,  1997. 

2.  P.  L.  O’Sullivan  &;  S.  Biringen.  Direct  Simulations  of  Low 
Reynolds  Number  Turbulent  Channel  Flow  with  EMHD  Con¬ 
trol.  Physics  of  Fluids,  10  (5)  pp. 1169-1181,  1998. 

3.  P.  R.  Bandyopadhyay  &  J.  M.  Castano.  Micro-tiles  for  electro¬ 
magnetic  turbulence  control  in  saltwater-preliminary  investi¬ 
gations.  In  Symposium  on  Turbulence  Modification  and  Drag 
Reduction,  ASME  Summer  Meeting,  1996.  Invited  paper. 


418 


Interactive  Electro-Magnetohydrodynamic  Control  of  Near- Wall  Streaks 

Stephen  R.  Snarski 
529  Audubon  Rd.,  Kohler,  WI  53044 

An  electro-magnetohycfrodynamic  transducer  array  that  can  be  operated  in  both  passive  (electromagnetic  induction  velocity  sensor)  and 
active  (magnetohydrodynamic  force  actuator)  modes  to  detect  and  subsequently  manipulate  the  turbulent  velocity  field  associated  with  near-wall, 
high-  and  low-speed  streaks  is  presented.  By  examining  the  physics  of  the  passive  and  active  modes,  it  is  shown  that  both  modes  are 
characterized  by  the  same  spatial  field  function  which  can  be  tuned  to  respond  directly  to  the  characteristic  spanwise  wavelength  of  the  near-wall 
streaks.  Because  the  near- wall  streaks  are  the  most  reliable  indicator  of  the  preburst  turbulence  production  process,  this  device  would  be  an  ideal 
candidate  for  use  in  an  interactive  (feedback)  turbulence  control  scheme  in  electrically  conducting  (e.g.,  seawater)  turbulent  boundary  layers. 
Experiments  are  being  planned  to  validate  the  predicted  transducer  characteristics  and  to  initiate  the  development  of  a  feedback  control  algorithm. 


1.  INTRODUCTION 

Electromagnetic  turbulence  control  has  recently  become  an  active 
area  of  research  in  pursuits  to  reduce  drag  in  seawater  applications 
(Nosenchuck  and  Brown  [1],  ONR  [2],  Bandyopadhyay  [3],  Henoch  and 
Stace  [4],  Crawford  and  Karniadakis  [5]).  Due  to  the  intrinsic 
relationship  which  exists  between  electric  and  magnetic  fields  and 
moving  conducting  fluids,  these  approaches  attempt  to  reduce  drag  by 
globally  applying  an  electromagnetic  (or  magnetohydrodynamic)  body 
force  to  the  flow  to  alter  the  fundamental  structure  of  the  boundary  layer. 
Although  such  global  control  strategies  have  revealed  overall  reductions 
in  turbulence  levels  and  drag,  the  net  savings  after  the  cost  of  the  required 
energy  expenditure  is  considered  makes  these  approaches  impractical. 

Another  equally  active  area  of  research  is  interactive  turbulence 
control.  Rather  than  apply  some  global  forcing  function  to  the  boundary 
layer,  these  approaches  attempt  to  reduce  drag  by  selectively  targeting, 
sensing,  and  subsequently  manipulating  some  turbulent  structure  or  event 
in  the  flow  through  the  use  of  a  closed-loop  feedback  control  system 
which  attempts  to  maintain  an  unstable  system  in  a  stable  state  by  making 
small  time-dependent  adjustments  (based  on  pertinent  measurements  of 
some  kind)  to  one  of  the  parameters  governing  the  system's  behavior 
(Gad-el-Hak  [6],  Moin  and  Bewley  [7]).  Proposed  control  schemes 
typically  involve  the  use  of  a  large  surface  matrix  of  micro-machined 
sensors  and  actuators  (microelectromechanical  systems,  or  MEMS)  to 
sense  some  targeted  wall  perturbation  (e.g.,  fluctuating  wall  pressure  or 
wall  shear  transducers)  associated  with  turbulence  generating  events  near 
the  wall  and  to  subsequently  modulate  the  event  with  an  actuator  located 
downstream  from  the  sensor  before  it  breaks  down  (e.g.,  resonant 
membranes,  micro-flaps,  aspiration  ports).  Although  recent  experiments 
conducted  with  wall-based  shear  sensors  and  a  resonant  membrane  have 
shown  promising  reductions  in  fluctuating  velocity  and  wall  pressure  rms 
levels  (Rathnasingham  and  Breuer  [8]),  actuator  frequency  response  and 
power  consumption  is  considered  a  major  limiting  factor  for  practical 
application  of  real-time  MEMS-based  control  schemes.  Researchers  at 
Stanford  have  recently,  however,  reported  the  development  of  MEMS- 
based  actuators  with  millisecond  rise  times  and  power  consumptions  in 
the  milliwatt  range  (Kumar  and  Reynolds  [91)  -  well  below  the  estimated 
0.0 18W  per  element  requirement  to  break  even  (Gad-el-Hak  [6]). 
Nevertheless,  the  inherent  mechanical  problems  associated  with  using  a 
large  matrix  of  micro-mechanical  devices  (e.g.,  mechanical  failure, 
fouling)  in  harsh  seawater  environments  still  needs  to  be  addressed. 

Because  of  the  low  energy  consumption,  high  frequency  response, 
low  fouling  potential,  and  lack  of  moving  parts  associated  with 
electromagenetic  devices,  a  natural  solution  would  be  to  merge  the 
electromagnetic  and  interactive  turbulence  control  methodologies. 
Although  some  attempts  have  been  made  to  do  just  that  (Bandyopadhyay 
[3],  Meng  [10],  Singh  and  Bandyopadhyay  [1 1]),  the  proposed  schemes 
still  rely  upon  MEMS  devices  to  sense  the  targeted  flow  perturbation. 
Furthermore,  these  approaches,  much  like  their  purely  MEMS-based 
counterparts,  rely  upon  a  feedback  control  methodology  which  senses  a 
flow  perturbation  (wall  pressure,  wall  shear)  whose  correlation  and  phase 
relationship  to  the  flow  structure  being  controlled  (ejections,  sweeps, 
vortical  structures)  is  only  partially  understood.  As  suggested  by  Gad-el- 
Hak  [6],  because  the  near-wall  low-speed  streaks  are  the  most  visible, 
reliable  and  detectable  indicators  of  the  preburst  turbulence  production 
process  (see  Section  2),  the  most  natural  control  scheme  would  be  one 
which  detects  low  velocity  near  the  wall  and  then  removes  (i.e., 
accelerates)  the  low-speed  region  before  it  breaks  down.  However,  for 
this  approach  to  be  successful,  a  reliable  means  to  both  sense  and 
manipulate  the  near-wall  velocity  field  is  required.  This  paper  is  a  direct 
response  to  this  need. 


What  is  proposed  and  examined  in  this  study  is  a  nonobtrusive 
electro-magnetohydrodynamic  transducer  (Snarski  [12])  that  can  be  used 
in  both  passive  (electromagnetic  induction)  and  active  (magneto¬ 
hydrodynamic  force)  modes  to  sense  and  manipulate  the  velocity  of  the 
near-wall  fluid.  Because  the  sensor  and  actuator  functions  are  combined 
into  a  single  device  that  detects  and  manipulates  the  same  flow  variable 
(i.e.,  streamwise  velocity),  a  direct  coupling  exists  between  the  drag 
reduction  methodology  and  the  fundamental  near-wall  turbulence  physics. 

This  paper  is  organized  as  follows.  In  Section  2,  the  structure  of 
turbulent  boundary  layers  relevant  to  this  study  are  reviewed.  In  Section 
3,  the  physics  of  both  the  passive  and  active  transducer  modes  are 
described  and  used  to  develop  a  closed  form  analytical  solution  for  the 
sensor  spatial  sensitivity  function  and  actuator  force  field.  The  main 
theme  of  the  paper  is  in  Section  4,  which  describes  the  operational 
characteristics  of  using  an  array  of  such  devices  for  interactive  control  of 
near-wall  streaks  by  examining  the  wavenumber  response  of  the 
transducer  array.  Implementation  and  scaling  considerations  are  also 
discussed  as  well  as  planned  proof-of-concept  experiments  that  will  be 
conducted  in  a  laminar  salt-water  boundary  layer  with  artificially 
generated  streaks.  Conclusions  are  provided  in  Section  5. 


2.  TURBULENT  BOUNDARY  LAYER  STRUCTURE  AND  THE 
ROLE  OF  NEAR- WALL  STREAKS 

In  general  terms,  two  types  of  coherent  structures  or  organized 
motions  can  be  defined  in  the  turbulent  boundary  layer  (see  Snarski  and 
Lueptow  [13]).  The  first  are  large-scale  motions  that  emanate  from  the 
outer  portions  of  the  boundary  layer,  scale  with  the  boundary  layer 
thickness  S,  and  have  an  influence  across  the  entire  boundary  layer.  The 
second  is  a  quasi-cyclical,  ordered  sequence  of  events  in  the  near-wall 
region  known  as  the  burst-sweep  cycle.  Although  a  complete 
understanding  of  the  cause-and-effect  relationships  between  the  near-wall 
and  outer  flow  structure  is  not  universally  agreed  upon  (Robinson  [14], 
Kline  and  Robinson  [15])  what  is  certain  is  that  the  majority  of  turbulence 
production  in  the  boundary  layer  occurs  during  the  bursting  process.  This 
process,  originally  visualized  and  measured  by  Kline  et  al.  [16],  is 
initially  marked  by  the  formation  of  streaks  of  relatively  low-  and  high¬ 
speed  fluid  very  near  the  wall  as  conceptually  illustrated  in  Fig.  1.  As  the 
streaks  convect  downstream,  the  low-speed  regions  gradually  lift  away 
from  the  wall  until  at  some  downstream  location  where  they  move 
abruptly  away  from  the  wall  in  what  is  termed  an  ejection.  At  this  point, 
the  low-speed  streaks  undergo  rapid  oscillations  that  ultimately  lead  to  a 
complete  break-up  of  the  structure  known  as  bursting.  Following  the 
burst,  an  in-rush  or  sweep  of  fluid  toward  the  wall  has  been  observed, 
hence,  the  name  burst-sweep  cycle.  It  is  generally  believed  that  the  near¬ 
hairpin  vortex 

-  structure 


Figure  1.  Conceptual  illustration  of  the  near-wall  streaks  and  vortex 
structures  beneath  a  turbulent  boundary  layer. 


419 


wall  streaks  are  the  consequence  of  a  redistribution  of  streamwise 
momentum  resulting  from  the  formation  and  growth  of  hairpin  vortex 
structures  and  counter-rotating  vortices  near  the  wall 

The  ensemble  averaged  character  of  the  near-wall  streaky  structure 
is  conceptually  illustrated  in  Fig.  1.  Indicated  in  the  figure  are  the 
coordinate  system  x  =  {x,y,z}  and  the  corresponding  components  of  the 
turbulent  boundary  layer  velocity  field  u  =  { u ,  v,  w }  consisting  of  mean 
(time-averaged)  and  fluctuating  (zero-mean)  quantities  of  the  form 
(U(x)  +  u'(x,t),  v'(x,t),w'(x,t)},  where  the  prime  denotes  the 
fluctuating  quantity.  Low-  and  high-speed  streaks  thus  correspond  to  the 
conditions  «'  <  0  and  u’  >  0,  respectively.  All  variables  with  a  superscript 
”+"  have  been  nondimensionalized  with  the  viscous  length  scale  v/wT 
(e.g.,  y+  =  yur  /  V),  where  v  is  the  kinematic  viscosity,  wT2  =  r w  f  p  is 
the  friction  velocity,  tw  is  the  mean  wall  shear  stress,  and  p  is  the  fluid 
density.  Typically,  ux  ~  0.04  U M  where  U„  is  the  free-stream  velocity 
exterior  to  the  boundary  layer.  As  shown  in  Fig.  1,  the  low-speed  (or 
high-speed)  streaks  have  a  well  defined  average  spanwise  spacing  of 
X\  ~  100  and  are  concentrated  very  near  the  wall  (y+  <  40).  Because 
streak  lengths  are  typically -1000,  the  *-scale  in  Fig.  1  has  been 
compressed  for  clarity.  The  spanwise  variation  in  streamwise  velocity 
u'{z)  as  well  as  the  inflectional  velocity  profile  u(y)  =  U(y)  +  u'(y) 
associated  with  the  streaks  are  indicated.  The  velocity  perturbation  of  the 
low-  and  high-speed  streaks  is  typically  one  half  the  local  mean  velocity 
lw'l~0.5f/  where  at  this  region  of  the  flow  U  ~  1 0uT.  Taking  as  an 
example  an  underwater  vehicle  moving  at  =  10  m/s,  the  friction 
velocity  is  ur  =  0.4  m/s  and  the  viscous  length  is  v/uT  =  2.5  pm  such 
that  the  streaks  have  a  mean  spacing  of  Xz  =0.25  mm,  convection 
velocity  of  Us  =  4  m/s,  and  perturbation  velocity  of  w'  =  ±2  m/s. 

Because  the  majority  of  turbulence  production  in  the  boundary  layer 
occurs  during  the  bursting  process  and  bursts  are  always  preceded  by  low- 
speed  near-wall  streaks,  removing  the  streaks  as  they  form,  before  they 
lift  from  the  wall,  should  act  to  stabilize  the  near- wall  flow  and  hence 
control  (or  at  least  delay)  the  production  of  turbulence  in  the  boundary 
layer.  Because  the  most  definitive  indicator  of  streak  formation  is  a 
spanwise  variation  in  streamwise  velocity  u’(z )  near  the  wall  (y+  <  40), 
the  goal  becomes  one  of  finding  a  reliable  means  to  sense  and  manipulate 
the  form  of  the  near-wall  streamwise  velocity  profile  (i.e.,  accelerate  the 
low-speed  streaks  and  decelerate  the  high-speed  streaks).  As  discussed  in 
the  next  two  sections,  the  electro-magnetohydrodynamic  transducer 
accomplishes  this  goal. 

3.  EMHD  TRANSDUCER  PHYSICS 

The  electro-magnetohydrodynamic  (EMHD)  transducer  geometry 
considered  here  is  illustrated  in  Fig.  2  relative  to  the  turbulent  boundary 
layer  velocity  field  u  =  { u ,  v,  w} .  As  shown,  the  EMHD  transducer 
consists  of  a  pair  of  electrodes  of  opposite  polarity  that  are  mounted 
parallel  to  each  other  in  the  streamwise  direction  and  flush  with  the  wall 
with  streamwise  length  x  =  2 c  and  spanwise  separation  z  =  2a.  Mounted 
beneath  the  electrodes  is  a  permanent  magnet  of  length  x~2d  and  width 
Z  -  2b  oriented  such  that  the  net  magnetic  flux  lines  B  above  the  face  of 
the  magnet  point  up  into  the  fluid  (i.e.,  north  pole  top,  south  pole  bottom). 
Depending  upon  the  voltage  condition  at  the  electrodes,  the  transducer 
can  be  operated  in  either  a  passive  (open-circuit)  sensor  mode  or  in  an 
active  (applied  voltage)  actuator  mode.  The  physics  of  these  two 
transducer  modes  are  described  below. 

3.1  Passive  Mode:  Electromagnetic  Induction  (EMI)  Velocity  Sensor 

The  passive  mode  of  operation  of  the  EMHD  transducer  or 
electromagnetic  induction  (EMI)  velocity  sensor  is  illustrated  in  Fig.  2 
following  the  initial  work  of  Langston  and  Kasper  [17]  later  extended  by 
Snarski  [18].  The  principle  of  operation  pivots  around  the  process  of 
Faraday  induction  in  which  the  motion  of  a  conducting  fluid  of  velocity 
u(x,t )  through  a  magnetic  field  B(x)  induces  an  electric  field  in  the  fluid 
according  to  E{x,t)  =  u(x,t)x  B(x).  If  we  concern  ourselves  with  just 
the  fluctuating  part  of  the  signal  (i.e.,  a.c.  couple  the  sensor  electronics), 
this  can  be  written  E'(x,t)  =  u'(x,t) x  B(x)  (u'  <  0  is  illustrated  in  Fig. 
2).  Because  this  electromagnetic  induction  process  occurs  at  all  points  in 
the  fluid  at  which  there  exists  a  velocity  and  magnetic  field,  the  potential 
difference  <p12  (f )  =  (p\  (/)  -  (p2  (f )  measured  between  a  pair  of  electrodes 
at  the  wall  is  the  integral  effect  of  the  induced  electric  fields  throughout 
the  flow,  or  (Shercliff  [19],  Bevir  [20]) 

<Pn  (0  =  J («'(*. 0 x  B(x))*jv  (x)d3x  ,  (1) 

91 


Active  Mode 

Passive  Mode  (EM  Lorentz  Force) 


Figure  2.  EMHD  transducer  mounted  flush  with  wall  beneath  a  turbulent 
boundary  layer  illustrating  passive  and  active  modes  of  operation. 


where  jv(x ),  referred  to  as  the  virtual  current  density,  is  the  current 
density  field  per  unit  current  that  would  be  produced  if  a  current  was 
passed  through  the  electrodes  with  no  flow  present.  Because  jv(x)  is 
determined  entirely  by  the  electrode  shape  and  electrical  boundary 
conditions,  it  can  be  interpreted  according  to  Eq.  (1)  as  a  receiving 
function  that  maps  the  induced  electric  field  in  the  fluid  to  a  voltage  at  the 
electrodes.  Although  B(x)  in  Eq.  (1)  is  the  total  magnetic  field  consisting 
of  the  applied  magnetic  field  and  a  secondary  magnetic  field  induced  by 
the  motion  of  the  conducting  fluid,  for  low  conductivity  flows  of  interest 
hear  the  induced  magnetic  field  can  be  neglected  (Branover  [21]). 

Using  vector  identities,  Eq.  (1)  can  be  written  in  the  form 


(pl2(t)  =  ju'(x,t)*h(x)d3x  ,  (2) 

* 

where 

h(x)  =  B(x)xj,(x) ,  (3) 

and  represents  the  entire  half  space  above  the  wall(lxl,lzl<  <*>,y  >  0). 
Equation  (2)  illustrates  that  the  output  voltage  of  the  EMI  sensor  results 
from  a  volume  integral  of  velocity  fluctuations  throughout  the  boundary 
layer  weighted  by  an  electromagnetic  field  term  B(x)  x  jv  (x ) .  Because 
Eq.  (2)  is  merely  the  input-output  relation  for  a  linear  space-time  system 
(Strawderman  [22]),  h(x)  as  defined  by  Eq.  (3)  represents  the  spatial 
sensitivity  distribution  function,  or  Greens  function,  for  the  EMI  sensor. 
Thus,  to  understand  the  response  characteristics  of  the  sensor,  one  only 
needs  to  evaluate  the  character  of  h(x) . 

Although  closed  form  solutions  for  all  three  components  of  the 
electric  and  magnetic  fields  in  Eq.  (3)  can  be  determined  by  evaluating 
Maxwell's  equations  for  the  electrode  and  magnet  geometry  in  Fig.  2 
(Snarski  [18]),  several  assumptions  can  be  introduced  which  simplify  the 
ensuing  analysis  and  greatly  clarify  the  pertinent  sensor  characteristics. 
First,  by  assuming  that  the  electrodes  are  long  relative  to  their  separation 
(c  »  a)  such  that  electrode  end  effects  can  be  neglected,  then 
jv  «  jv  ,jv  such  that  the  current  density  vector  field  is  essentially  2- 
dimensional  and  spatially  uniform  along  the  length  of  the  electrodes,  or 
jv  (x )  =  [0,jv  (y,z),jv^  (y,z)j  for  IjcI<  c .  If  it  is  also  assumed  that  the 
magnet  dimensions  are  farge  relative  to  the  electrode  dimensions  (d  »  c, 
b  »  a ),  then  By  »  BX,BZ  in  the  vicinity  of  the  electrodes  such  that  the 
magnetic  vector  field  is  essentially  one-dimensional  and  spatially  uniform 
in  planes  parallel  to  the  wall,  or  B(x)  =  [0,/^  (y),0J  for 
Ul<<  d ,  lzl«  b .  Asa  result,  Eq.  (3)  reduces  to 

h(x)  =  i[By(x)jVz(x)]  ,  (4) 

such  that  the  induced  electric  field  is  produced  by  only  the  streamwise 
velocity  fluctuations,  or 

(pl2(t)  =  ju'(x,t)h(x)d3x  ,  .(5) 

where  h(x)  =\h(x)\.  Experimental  verification  for  the  form  of  Eq.  (5) 
has  been  provided  by  the  measurements  of  Towe  [23]  which  illustrated 
that  the  electrodes  act  to  vectorize  the  sensor  response  such  that  the  output 
is  produced  essentially  by  just  the  velocity  fluctuations  aligned  with  the 
electrodes.  Additionally,  measured  voltage  spectra  for  an  EMI  sensor  in  a 


420 


folly  developed  turbulent  pipe  flow  by  Keith  and  Abraham  [24]  obtained 
over  a  range  of  Reynolds  numbers  collapse  well  with  a  scaling  valid  for 
turbulent  velocity  fluctuations  indicating  that  a  linear  relationship  exists 
between  the  sensor  output  and  streamwise  velocity  as  indicated  by  Eq. 
(5).  Finally,  dimensional  analysis  of  the  full  3 -dimensional  solution  also 
indicates  that  the  contributions  to  the  sensor  output  from  u'  are  at  least  an 
order  of  magnitude  greater  than  contributions  resulting  from  either  w'orv' 
(Snarski  [18]). 

The  virtual  current  density  field  jv  (x)m  Eq.  (4)  can  be  obtained 
from  the  Poisson  solution  for  the  voltage  field  ty(x)  produced  by  a  line- 
sink/line-source  pair  at  the  wall,  or 


— In 
4  710 


y2  +  (Z+a)2 
y2  +  (z-a)2 


(6) 


and  Ohm’s  law  in  the  form 


Jz(x)=oEz(x) 

=  ,  C7) 

°  dZ 


where  /  is  the  current  per  unit  electrode  length  (A/m),  a  is  the  fluid 
electrical  conductivity  (mho)  and  Ez(x)  is  the  spanwise  electric  field  in 
the  fluid  (V/m).  By  definition,  the  virtual  current  density  field  is 
where  /  is  the  electrode  current  (A).  Using  an 
exponential  function  to  describe  the  decay  of  the  magnetic  field  with 
distance  from  the  wall  of  the  form  B0  expf  -  y  /  XB  ]  (T)  and  taking  the 
voltage  field  to  be  uniform  along  the  length  of  the  electrodes  (consistent 
with  the  assumption  c»  a ),  we  can  substitute  i  =  I/2c  for  1*1  sc  and 
/  =  0  for  \x\>  c  such  that  Eq.  (4)  with  Eqs.  (6)  and  (7)  becomes 


h(x)=~ 


_y_ 
B„e  *• 


4  JZC 


z  +  a 


z-a 


y2  +(z  +  a)2  y1 +(z-a)2 


M  =  (8) 


and  h(x)=0  elsewhere.  In  Eq.  (8),  ft  ■  Afl  / a  represents  the 
penetration  depth  A  B  of  the  magnetic  field  into  the  fluid  relative  to  that  of 
the  electric  field  which  is  proportional  to  a  (Snarski  [18]). 

Equation  (8)  is  plotted  in  the  nondimensionalized  form 
h  (x)  =  ach(x)/  BQ  in  Fig.  3(a)  as  a  function  of y/a  and  z/a.  A  value  of 
/S  =  100  is  assumed  consistent  with  a  typical  turbulent  boundary  layer 
application  (see  Section  4.2).  Fig.  3(a)  illustrates  that  the  EMI  sensor 
weights  the  fluctuations  near  the  electrodes  much  more  heavily  than  those 
further  out  in  the  flow  and  that  the  sensor  contains  negative  and  positive 
sensitivities  between  and  outside  of  the  electrodes,  respectively.  These 
properties  which  are  a  direct  result  of  the  dipole  character  of  the  virtual 
current  field  as  shown  in  Fig.  3(b)  are  in  agreement  with  measurements  of 
the  spatial  response  function  of  an  EMI  sensor  similar  to  that  shown  in 
Fig.  2  by  Bruno,  et  al.  [25],  Figure  3  thus  indicates  that  although  the  EMI 
sensor  output  is  produced  by  velocity  fluctuations  throughout  the 
boundary  layer,  it  is  dominated  by  contributions  from  velocity 
fluctuations  near  the  wall.  In  addition,  because  the  sign  of  the 
contribution  to  the  output  depends  upon  the  spanwise  position  of  the 
fluctuation  relative  to  the  electrodes,  the  EMI  sensor  acts  as  a  spatial  filter 
with  maximum  output  occurring  for  spatial  disturbances  with  a  preferred 
spanwise  wavelength.  Details  and  the  resulting  implications  of  these 
sensor  characteristics  to  the  proposed  interactive  control  scheme  are 
discussed  in  Section  4. 

3.2  Active  Mode:  Magnetohvdro dynamic  (MHD1  Force  Actuator 

The  active  mode  of  operation  of  the  EMHD  transducer  is  also 
illustrated  in  Fig.  2.  As  with  the  passive  mode,  the  principle  of  operation 
stems  around  the  process  of  Faraday  induction  except  here  the  interaction 
of  mutually  orthogonal  applied  magnetic  B(  *)and  electric  E(x)  fields 
induces  a  magnetohydrodynamic  (MHD)  force  on  the  fluid  according  to 

FMHD(xJ)~-J{xyt)xB(x)  ,  (9) 

P 

where 

J(x,t)  -  <^E(x)  +  u(x,t)x  jB(jc)]  ,  (10) 


(a) 


(-)  z/a 


Figure  3.  (a)  Nondimensionalized  spatial  sensitivity  distribution  for  the 
EMHD  transducer  for  \x\  ^  c  and  —  100,  Eq.  (8),  (b)  virtual  current 
density  vector  field  jf„(y,z)=-oVi^(y,z). 


and  p  is  the  fluid  density  (kg/m3).  The  first  term  in  Eq.  (10)  is  the  applied 
electric  field  produced  by  applying  a  voltage  across  the  electrodes.  The 
second  term  is  the  induced  electric  field  resulting  from  the  interaction  of 
the  flow  field  with  the  magnetic  field.  Except  for  high  speed  flows  with 
very  strong  magnetic  fields,  the  second  term  can  generally  be  neglected. 
For  example,  with  E  ~  Vl2  1 2 a  (Eq.  7),  V12  =  0.5  V,  2a  -  0.25  mm, 
U  -  10  m/s,  and  B0  =  IT  (e.g.,  a  typical  turbulent  boundary  layer 
application,  see  Section  4.2)  UBl  E  ~  10-3.  Thus,  neglecting  the  induced 
electric  fields  in  Eq.  (10)  and  neglecting  second  order  end  effects  as  was 
done  in  connection  with  Eq.  (4),  then  Jx  «  Jy,  Jz  and  By»  Bx  ,BZ 
such  that  the  induced  MHD  force  acts  only  in  the  axial  direction. 


or  with  Eq.  (4), 


Fmhd  (x  )  ~ 1 


—  Jz  (x)By(x) 
P 


(11) 


FmHd(X ) -  k(X)  y  (17) 

P 

where  E (x)  M  F (x) I  and  In  is  the  applied  electrode  current 
defined  as  positive  if  current  flows  from  electrode  (1)  to  (2)  in  Fig.  2  and 
negative  if  current  flow  is  reversed.  Strictly  speaking,  FMHD(x)  for  the 
interactive  turbulence  control  application  is  still  a  function  of  time  since  it 
is  not  a  steady-state  input  but  one  that  is  modulated  on  and  off  by  the 
control  scheme.  However,  because  of  the  largely  resistive  character  of 
EM  devices,  the  transducer  response  can  be  assumed  instantaneous 
without  any  loss  of  generality.  From  Eq.  (12),  it  is  clear  that  the  MHD 
force  field  produced  by  the  active  transducer  mode  is  functionally 
equivalent  to  the  spatial  sensitivity  distribution  for  the  passive  transducer 
mode  given  by  Eq.  (8)  and  plotted  in  Fig.  3.  Asa  result,  the  MHD  force 
produced  by  the  electrodes  is  concentrated  near  the  wall  and  spatially 
distributed  in  such  a  way  as  to  produce  a  maximum  effect  at  a  particular 
spanwise  wavelength.  The  implications  of  these  force  field  characteristics 
are  discussed  further  in  the  next  section. 


421 


4.  INTERACTIVE  EMHD  CONTROL  OF  NEAR- WALL  STREAKS 
4.1  EMHD  Array  Physics 

Both  the  spatial  sensitivity  function  for  the  passive  EMI  sensor 
mode  and  the  induced  axial  force  field  for  the  active  MHD  actuator  mode 
of  a  single  pair  of  electrodes  are  described  by  Eq.  (8),  shown  plotted  in 
Fig.  3.  As  stated  earlier,  because  the  function  h(x),  referred  to  herein  as 
the  EMHD  spatial  field  function,  has  positive  and  negative  values  to 
either  side  of  the  electrodes,  the  transducer  will  respond  strongly  to 
particular  wavelengths  in  the  flow.  This  effect  can  be  illustrated  more 
clearly  by  examining  the  character  of  the  function  h(x)  in  wavenumber 
space.  For  the  EMI  sensor  mode,  the  input-output  relation  given  by  Eq. 
(5)  can  be  written  in  wavenumber-frequency  space  as  (Strawderman  [22]) 

®(p(k,co)  =  G(k)<i>u(k,G))  ,  (13) 

where  <*>^(£,£0)  and  <&u(k,co)  are  the  wavenumber-frequency  spectra 
of  the  EMI  sensor  and  turbulent  velocity  field,  respectively, 
k  =  { kx,ky,kz  j  is  the  wavenumber  vector,  co  is  the  circular  frequency, 
and  G(k)  is  the  wavenumber  response  for  the  sensor  defined  by 

G(k)  =  \H(kf  ,  (14) 


Figure  4.  Wavenumber  response  for  the  EMHD  transducer  at  kxc  =  0 
and  ^3=  100,  Eq.  (16). 


H(k)=  [h{x)eUcXd3x  . 

(15) 

G  (k)  G*(k) 

G  (k)  = - 2Z - 5-  = - 

^(-iy  e-*u-wz° 

J 

army  ( n-Y)2{B0a )2  (n- 1)2 

Because  according  to  Eq.  (13)  the  output  spectrum  of  the  sensor  is  simply 
the  product  of  the  spectrum  of  the  streamwise  turbulent  velocity  field  and 
the  sensor  wavenumber  response,  G(k )  provides  a  clear  representation  of 
what  components  of  the  input  field  contribute  to  the  sensor  output.  If 
G(k)  =  1,  the. spectral  components  are  measured  without  distortion  while 
if  G(k )  -  0,  the  turbulent  field  components  are  suppressed  completely. 

Evaluating  Eqs.  (14)  and  (15)  with  Eq.  (8),  the  nondimensionalized 
wavenumber  response  for  the  EMI  sensor  is  given  by 

c»(/.)=  G(k)  _  sin2 (kxc)  sin2^)  (,6) 

(B0a)2  ( kxcf  [(V)2 +(/)-!+ 1 V|)2]  ' 


Because  the  spatial  distribution  of  the  MHD  force  field  produced  by  the 
active  mode  is  given  by  h(x),  Eq.  (16)  also  provides  a  direct 
representation  of  the  wavenumber  characteristics  of  the  applied  force 
field.  Equation  (16),  shown  plotted  in  Fig.  4  at  kxc  -  0  and  p  -  100, 
characterizes  the  relative  level  at  which  the  EMHD  transducer  interacts 
with  various  wall-normal  and  spanwise  wavenumbers  (or  wavelengths, 
Xt  =27t/ki)  in  the  flow.  As  is  illustrated,  the  transducer  responds  most 
strongly  to  a  selective  band  of  spanwise  wavenumbers  I kza\~  n!  2  due  to 
the  combined  effects  of  cancellation  of  low  spanwise  wavenumbers 
resulting  from  the  positive  and  negative  sensitivities  (e.g.,  electrodes)  in 
the  spanwise  direction  and  attenuation  of  the  high  wavenumbers  resulting 
from  the  finite  spanwise  dimensions  of  the  transducer.  This  result 
suggests  that  the  transducer  can  be  tuned  to  respond  to  selective 
wavelengths  in  the  flow  such  as  the  mean  streak  spacing.  The  effect  can 
be  greatly  enhanced  however  by  considering  an  array  of  transducers. 

For  an  array  of  n  transducers  (n  +  1  electrodes)  connected  in  parallel 
and  centered  about  z  =  0  with  each  electrode  separated  by  z  =  2 a,  the 
EMHD  spatial  field  function  for  the  array  harray(x)  and  the  associated 
nondimensionalized  wavenumber  response  G*array  ( k )  become, 


«(*)  =  - 


Z  +  na 


y2  +(z  +  na)2 


n-l 

+2£(~l)y 


M 


z  +  (n-2j)a 
y2  +  [z  +  (n-2j)af 


+  (-!)"  T7 - 72 

y  +(z-na ) 


(17) 


4  nc 


M<c, 


and 


where  G*  (k)  in  Eq.  (18)  is  given  by  Eq.  (16).  Equation  (17),  in  the  form 
h.*array  =  acharray  /  Ba,  and  Eq.  (18)  are  plotted  in  Figs.  5  and  6, 
respectively,  for  the  case  n  =  5  corresponding  to  6  electrodes.  As  can  be 
seen,  by  the  addition  of  just  two  more  electrode  pairs,  the  sign  of  the 
EMHD  spatial  field  function  in  Fig.  5  alternates  uniformly  in  the 
spanwise  direction  throughout  the  entire  spanwise  domain  of  the  array. 
As  a  result,  the  array  wavenumber  response  in  Fig.  6  is  dominated  by  the 
single  spanwise  wavenumber  \kza\=  n!2  corresponding  to  the  spanwise 
wavelength  Xz  =  4 a  in  Fig.  5.  This  implies  that  the  EMHD  transducer 
array  can  be  tuned  to  respond  directly  to  the  near-wall  streaks  if  the 
electrode  half-spacing  a  is  set  equal  to  one  quarter  of  the  mean  streak 
spacing  Xz  =  100 ,  or  a+  =  25. 

Although  the  specified  electrode  spacing  will  assure  that  the 
transducer  array  responds  to  the  spanwise  wavelength  of  the  streaks,  the 
array  will  only  be  able  to  efficiently  sense  and  manipulate  the  streaks  if 
the  EMHD  spatial  field  function  h(x)  predominantly  acts  in  the  region 
near  the  wall  occupied  by  the  streaks  (y+  <  40).  This  can  be  shown  to  be 
the  case  by  integrating  h(x)  as  a  function  of  y,  as  shown  in  Fig.  7 
normalized  by  the  total  integrated  value  for  four  values  of  the  magnet 
strength  parameter  (0=1,  10,  100,  ~).  Because  the  effect  of  increasing 
p  =  XB  /a  is  to  increase  the  penetration  depth  of  the  magnetic  field  into 
the  fluid,  increasing  p  causes  the' effect  of  the  EMHD  transducer  to  extend 
further  from  the  wall.  However,  even  for  the  case  p  =  °°  corresponding  to 
the  limiting  case  of  extremely  high  magnet  strength  and  very  close 
electrode  spacing  (i.e.,  the  magnetic  field  does  not  decay  in  the  region  in 
which  the  electrodes  have  an  effect  on  the  flow),  the  region  y+  <  40 
corresponding  to  y/a  <1.6  for  a+  =  25  accounts  for  over  60%  of  the  total 
integrated  value.  As  a  result,  the  EMHD  transducer's  zone  of  influence 
will  be  predominantly  that  region  of  the  flow  occupied  by  the  near-wall 
streaks,  as  required. 

Support  for  this  near-wall  influence  of  the  transducer  indicated  in 
Fig.  7  can  be  found  in  the  work  of  Henoch  and  Stace  [4]  in  which  they 
experimentally  investigated  the  use  of  a  steady,  globally  applied 
streamwise  MHD  force  to  control  the  shape  of  the  mean  velocity  profile 
and  hence  the  ability  of  the  boundary  layer  to  resist  transition.  In  all  cases 
examined,  the  effect  of  the  MHD  force  on  the  mean  velocity  profile  never 
exceeded  much  beyond  y/a  —1.2,  consistent  with  what  would  be  expected 
from  Fig.  7  and  the  value  of  p  ~  1  used  in  their  experiments.  Although 
Keith  and  Abraham  [24]  attempted  to  deduce  the  locations  in  the 
boundary  layer  in  which  the  primary  contributions  to  the  EMI  sensor 
output  occur  by  examining  the  scaling  behavior  of  the  various  frequency 
ranges  of  their  measured  voltage  spectra  (P  =  1.2-7. 1),  their  scaling  results 
were  inconclusive  due  to  the  spatial  averaging  and  filtering  effects  at  high 
and  low  frequencies  described  by  Eq.  (13). 


422 


(a) 


Figure  5.  Nondimensionalized  EMHD  array  spatial  field  function  for 
bd  <  c ,  b  =  100,  and  n  =  5,  Eq.  (17);  (a)  surface  plot  in  (y-z)-plane,  (b) 
line  plots  at  y/a  =  0.2  ( - ),  0.6  ( — ),  1 .0  ( — ),  and  1 .4  ( - ). 


4.2  Implementation  and  Scaling  Considerations 

The  EMHD  interactive  control  scheme  proposed  here  is 
conceptually  illustrated  in  Fig.  8.  Although  the  number  of  transducers  in 
the  full  array  would  need  to  be  large  enough  to  cover  the  spanwise  extent 
of  the  boundary  surface  under  control,  sub-arrays  of  transducers  with 
spanwise  extents  which  scale  with  the  spanwise  coherence  length  of  the 
mean  streak  spacing  would  likely  be  used  as  individual  array  elements 
(e.g.,  2 na  ~  8).  For  convenience,  5  transducers  (6  electrodes)  are  shown 
in  Fig.  8.  The  control  scenario  involves  first  detecting  the  existence  of  a 
spanwise  variation  in  streamwise  velocity  u'(z)  associated  with  the  near¬ 
wall  streaks  by  measuring  the  open-circuit  voltage  induced  across  the 
electrodes  (passive  EMI  sensor  mode),  <p12.  For  the  streak  orientation 
shown  in  the  figure  (i.e.,  low-speed  streak  between  the  reference 
electrodes  (1)  and  (2)),  the  induced  passive  response  according  to  Eq.  (5) 
and  as  illustrated  in  Fig.  8  is  <p12  *  ju'(z)h(z)dz  >  0 .  When  the 
magnitude  of  this  sensor  output  exceeds  some  pre-established  threshold 
level  representative  of  a  developing  streak,  the  EMHD  transducer  would 
be  switched  to  an  active  mode  by  applying  a  voltage  Vl2  =  V\  -  V2 
across  the  electrodes  of  appropriate  polarity  to  attenuate  the  velocity 
perturbation  and  stabilize  the  near- wall  flow  (i.e.,  to  accelerate  the  low- 
speed  fluid  and  decelerate  the  high-speed  fluid).  Because  a  low-speed 
streak  resides  between  the  reference  electrodes  in  Fig.  8,  the  sign  of 
Vl  -  V2  must  be  such  to  produce  a  positive  MHD  force  in  this  region. 
Since  the  applied  MHD  force  between  the  reference  electrodes  and  the 
applied  electrode  voltage  are  related  through  Eqs.  (7)  and  (11)  according 
to 


_  <y By  d\ \ff 

p  dz 

.  ^1-^2  , 


p  2  a 


(19) 


the  required  condition  is  Vl-V2>0.  This  voltage  is  also  consistent 
with  the  required  sign  of  the  applied  current  field  /12  >0  in  Eq.  (12) 
necessary  to  produce  the  force  field  FMHD(z) — ha rray(z)  that  is 


2pi 


Figure  6.  Wavenumber  response  for  the  EMHD  array  for  kxc  =  0, 
P=  100,  and  n  =  5,  Eq.  (18). 


required  to  remove  the  spanwise  variation  in  streamwise  velocity.  If  the 
streaks  were  oriented  opposite  to  that  shown  in  Fig.  8  (i.e.,  high-speed 
streak  between  reference  electrodes),  the  induced  passive  and  required 
active  responses  would  be  (pn  <0,Vj  - V2  <0,  /12<0,  and 

Fmhd(z)  ~  harrayW-  It  should  be  pointed  out  that  because  the  mean 
streak  spacing  is  a  predictable  function  of  the  free  stream  velocity,  the 
array  could  be  operated  at  a  large  number  of  discrete  flow  speeds  by 
grouping  other  than  adjacent  electrodes,  provided  the  spacing  of  adjacent 
electrodes  is  established  from  the  largest  anticipated  flow  speed.  Also,  if 
full  arrays  of  electrodes  were  appropriately  spaced  in  jc,  one  could 
theoretically  delay  the  production  of  turbulence  indefinitely. 

Although  the  required  polarity  of  the  applied  voltage  is  straight 
forward,  the  goal  of  the  interactive  control  scheme  or  feedback  control 
algorithm  is  to  apply  just  enough  energy  to  counteract  the  spanwise 
perturbation  in  the  near-wall  streamwise  velocity  profile.  This  requires 
being  able  to  relate  the  magnitude  and  duration  of  the  applied  voltage  to 
the  magnitude  of  the  detected  velocity  perturbation  (as  calibrated  from  the 
EMI  sensor  output,  see  Section  4.3)  in  the  feedback  control  algorithm. 
An  order  of  magnitude  estimate  of  the  voltage  required  to  stabilize  the 
flow  can  be  obtained  by  examining  the  magnitude  of  the  required  applied 
MHD  force  relative  to  the  inertial  forces  associated  with  accelerating  or 
decelerating  the  near- wall  fluid,  or  the  ratio 


N  _  Fmhd 
‘  du\  /  dt 


-rrf-  M , 

pus  2  a 


(20) 


where  At  is  the  duration  of  the  applied  voltage  andw'  is  the  perturbation 
velocity  of  the  near-wall  streaks  we  wish  to  remove.  The  variable  Nt 
represents  an  imposed  interaction  parameter  similar  to  those  defined  by 
Henoch  and  Stace  [4]  and  Crawford  and  Kamiadakis  [5]  but  referenced 
here  to  the  unsteady  rather  than  steady  inertial  force  ~  pw2  /  5  since  our 
goal  is  to  apply  an  impulse  FMHDAt  to  remove  the  streak  momentum 
pu's  rather  than  apply  a  steady  state  force  field  to  alter  the  global 
character  of  the  boundary  layer.  In  the  experimental  work  of  Henoch 
and  Stace  [4],  they  found  that  an  imposed  interaction  parameter  of  0.03 
was  sufficient  to  effect  a  desirable  change  in  the  mean  velocity  profile 
with  minimum  drag  reductions  occurring  for  a  value  of  0.3.  Because  the 
goal  here  is  again  to  apply  small  adjustments  to  small  perturbations  in  the 
near-wall  velocity  field,  even  smaller  values  may  be  required. 

Because  the  perturbation  in  the  near-wall  flow  must  be  removed 
before  it  convects  out  of  the  electrode  control  volume,  it  is  necessary  to 
impose  the  condition  At  <2cl  Us  where  Us  ~  10wT  is  the  convection 
velocity  of  the  near- wall  streaks.  In  addition,  because  it  is  desirable  to 
attenuate  the  streaks  early  in  their  development,  a  velocity  perturbation  of 
u's  ~  ur  is  assumed  (see  Section  2).  Then,  considering  as  an  example  a 
seawater  vehicle  (p  =  1000  kg/m3,  <7=4  mho,  v  =  10‘°  m2/s)  moving  at 


423 


Although  Crawford  and  Karniadakis  [5]  did  study  computationally  the  effect  of  time-dependent 
forcing  ,  their  forcing  was  periodic  (pulsed)  and  not  intended  to  be  coupled  with  any  near-wall 
turbulence  phenomena. 


Figure  7.  Integrated  normalized  value  of  EMHD  spatial  field  function 
as  a  function  of  y/a  for  b  =1  ( - ),  10  ( — ),  100  ( — ),  and  ©©  ( — ). 


U„  =  10  m/s  ( uT  ~  0.4  m/s)  with  a  magnetic  field  induction  of  B0  =  IT 
(e.g.,  Neodymium  Iron-Boron  magnet),  and  imposing  an  electrode  half¬ 
separation  of  a+= 25  (i.e.,  a  -  0.125  mm  for  above  conditions)  as 
discussed  in  Section  4.1,  the  required  electrode  voltage  and  duration  are 


10 


pux 


Nt 


B0 (c  /  a) 


-  400 


(c  la) 


(V)  ,  (21) 


and 


At 


~  0.2-y[a+(c/o)]  =  3.125  x  10_5(c/a)  (s)  .  (22) 


Passive  Mode  Active  Mode 

(-)  (+)  (-)  (+)  (-)  (+)  (-)  (+)  (-)  (+)  (-)  (+) 


Feedback  Control  Algorithm 

V,  2=ju'(z)hm„(z)dz  >  0  =>  V,  2=  V,-V2  >  0  (1, 2  >  0) 


To  proceed,  an  appropriate  value  for  c/a  is  required.  This  can  be  obtained 
by  considering  the  per  element  power  requirements  P,  equivalent  to  the 
product  of  the  applied  voltage  Vl2,  electrode  current  density 
7,  ~  oV,2  12a  ,  and  effective  flow  area  through  which  the  current  acts 
~4 ac,  or 


P  ~  200 


P™ 


A,V 


&o  (cl  a) 


-  80 


{cl  a) 


(W)  .  (23) 


Assuming  P-  0.01  W  (satisfying  0.018W  requirement  established  by 
Gad-el-Hak  [6]  for  an  interactive  control  schemes  to  achieve  a  net 
savings)  and  an  imposed  interaction  parameter  of  Nt  =0.1,  Eq.  (23) 
yields  c/a  =  80  (c  =  10  mm)  such  that  the  required  voltage  and  duration 
are  Vl2  =0.5  V  and  At  =  2.5  ms.  Reducing  the  power  requirement  to 
0.001W  results  in  c/a  =  800  (c  =  10  cm),  Vn  =  0.05  V  and  At  =  25  ms. 

As  a  final  note,  an  exponential  fit  to  measurements  of  the  magnetic 
field  produced  by  a  neodymium  boron  magnet  with  B0  =  0.3T  (Kasper  et 
al  [26])  yields  =  7.2mm  such  that  f5  =  XB  / a  =  58  for  the  above 
example.  Because  larger  values  of  Ba  and  hence  /?  would  likely  be  used 
in  any  interactive  turbulence  control  scheme  and  since  the  form  of  the 
EMHD  field  function  in  Fig.  7  does  not  change  much  for  >  100,  a  value 
of  j5  =  100  was  used  throughout  this  paper. 

4.3  Experimental  Validation 

Although  experimental  results  exist  in  the  literature  which  support 
the  passive  and  active  EMHD  transducer  physics  presented  here,  no 
attempt  has  been  made  to  use  the  transducer  for  the  direct  detection  or 
manipulation  of  streaks.  As  a  result,  experiments  will  be  undertaken  by 
the  author  in  a  laminar  saltwater  channel  flow  using  artificially  generated 
low-  and  high-speed  streaks  to  validate  the  predicted  performance 
characteristics.  The  low-  and  high-speed  streaks  will  be  generated  with 
the  use  of  mixing  tabs  developed  by  Gretta  and  Smith  [27]  that  have  been 
shown  to  produce  flow  structures  similar  to  what  is  observed  in  a  fully 
developed  turbulent  boundary  layer  as  shown  in  Fig.  9a.  The  response 
characteristics  of  the  passive  sensor  mode  will  be  evaluated  by  varying 
the  wavenumber  content  and  perturbation  magnitude  of  the  near-wall 
velocity  field  through  systematic  variation  of  the  tab  separation  Az  and 
tab-to-electrode  separation  Ax,  respectively,  indicated  in  Fig.  9b  and  9c. 
Variations  in  Ax  will  also  be  used  to  evaluate  the  required  electrode 


Figure  8.  Interactive  EMHD  turbulence  control  scheme  to  detect  and 
manipulate  near-wall  low-  and  high-speed  streaks. 


voltage  necessary  to  eliminate  a  given  spanwise  variation  level  in 
streamwise  velocity  produced  by  the  tabs.  Although  the  MHD  force  field 
derived  from  the  potential  field  solution  in  Fig.  5(a)  has  a  finite  value  at 
y  =  z  =  0,  the  real  force  field  is  known  to  decay  exponentially  to  zero  at 
the  wall  (Tsinober  [28]).  This  behavior  of  FMHD(y)  will  be  addressed  in 
future  modelling  efforts  and  is  thus  illustrated  in  Fig.  9c.  Particle  image 
velocimetry,  wall  pressure,  and  hot  film  measurements  will  be  used  to 
characterize  the  effect  of  the  applied  MHD  force  field  on  near-wall 
velocity  field,  fluctuating  wall  pressure  and  wall  shear  levels.  The  results 
of  this  work  will  then  be  used  as  the  basis  for  developing  an  appropriate 
feed-back  control  algorithm. 


5.  CONCLUSIONS 

A  nonobtrusive  electromagnetohydrodynamic  transducer  array  that 
can  both  detect  and  manipulate  the  near-wall  streamwise  velocity  field 
associated  with  low-  and  high-speed  streaks  has  been  presented.  Owing 
to  the  intrinsic  relationships  which  exist  between  electric  and  magnetic 
fields  and  moving  conducting  fluids,  the  passive  (electromagnetic 
induction  velocity  sensor)  and  active  (magnetohydrodynamic  force 
actuator)  modes  of  the  transducer  are  both  characterized  by  the  same 
spatial  field  function  which  can  be  tuned  to  respond  to  the  spanwise 
wavelength  At  =  100  and  near-wall  domain  y+  <40  of  the  streaks  by 
suitable  choice  of  electrode  separation,  2a  Because  the  near-wall  streaks 
are  the  most  reliable  indicator  of  the  preburst  turbulence  production 
process,  this  device  would  be  an  ideal  candidate  for  use  in  an  interactive 
turbulence  control  scheme  in  electrically  conducting  (e.g.,  seawater) 
turbulent  boundary  layers.  Since  the  same  device  is  used  to  sense  and 
manipulate  the  same  flow  variable  (i.e.,  streamwise  velocity)  at  the  same 
spatial  location,  a  direct  coupling  exists  between  the  drag  reduction 
methodology  and  the  fundamental  near-wall  turbulence  physics.  Initial 
estimates  also  indicate  that  effective  drag  reduction  can  occur  with  per 
array  element  power  inputs  in  the  milliwatt  range.  Experiments  are  being 
planned  to  calibrate  the  sensor  output,  quantify  the  electrode  voltage 
required  to  remove  the  streaks,  and  lay  the  foundation  for  developing  a 
feedback  control  algorithm. 


424 


(a) 


(b)  plan  view 


Figure  9.  Planned  EMHD  experiments:  (a)  development  of  vortex 
structures  and  streaks  in  wake  of  mixing  tab  (Gretta  and  Smith  [27]), 

(b)  plan  view  of  tabs  and  EMHD  array  in  laminar  salt  water  channel, 

(c)  edge  view  at  location  of  low-speed  streak  ( z  =  0). 

ACKNOWLEDGMENTS 

This  work  was  initially  supported  by  the  Naval  Undersea  Warfare 
Center  (NUWC)  Division  Newport,  RI  Independent  Research  (IR) 
Program  during  the  authors  tenure  at  NUWC  Detachment  New  London, 
CT.  The  IR  Program  is  funded  by  the  Office  of  Naval  Research. 


REFERENCES 

1.  D.M.  Nosenchuck  and  G.L.  Brown,  "Discrete  Spatial  Control  of  Wall 
Shear  Stress  in  a  Turbulent  Boundary  Layer,"  Near-Wall  Turbulent 
Flows ,  ed.  R.M.C.  So,  C.G.  Speziale  and  B.E.  Launder,  Elsevier 
Publishers,  Amsterdam,  pp.  689-698,  1993. 

2.  ONR  Workshop  on  Electromagnetic  Flow  Control  (EFC),  org.  L.  P. 
Purtell,  Naval  Surface  Warfare  Center,  Carderock,  MD,  19  May  1994. 

3.  P.R.  Bandyopadhyay,  "Development  of  a  Microfabricated  Surface  for 
Turbulence  Diagnostics  and  Control,"  Application  of  Microfabrication 
to  Fluid  Mechanics,  ASMEFED-Vol.  197,  1994. 

4.  C.  Henoch  and  J.  Stace.,  "Experimental  Investigation  of  a  Salt  Water 
Turbulent  Boundary  Layer  Modified  by  an  Applied  Streamwise 
Magnetohydrodynamic  Body  Force,"  Phys.  Fluids,  Vol.  7,  No.  6,  pp. 
1371-1383,  1995. 

5.  C.H.  Crawford  and  G.E.  Karniadakis,  "Reynolds  Stress  Analysis  of 
Emhd-Controlled  Wall  Turbulence.  Part  I.  Streamwise  forcing,"  Phys. 
Fluids ,  Vol.  9,  No.  3,  pp.  788-806,  March  1997. 

6.  M.  Gad-el-Hak,  "Interactive  Control  of  Turbulent  Boundary  Layers:  A 
Futuristic  Overview,"  AIAA  Journal ,  Vol.  32,  No.  9,  p.  1753,  1994. 

7.  P.  Moin  and  T.  Bewley,  "Feedback  control  of  turbulence,"  Appl.  Mech. 
Review,  Vol.  47,  S3,  1994. 


8.  R.  Rathnasingham  and  K.S.  Breuer,  "System  Identification  and  Control 
of  a  Turbulent  Boundary  Layer,"  Phys.  Fluids,  Vol.  9,  No.  7,  pp.  1867- 
1869,  July  1997. 

9.  S.M.  Kumar  and  W.C.  Reynolds,  "Characteristics  of  MEMS  Based 
Actuators  for  Flow  Control,"  presented  at  American  Physical  Society, 
50th  Annual  Meeting  of  the  Division  of  Fluid  Dynamics,  25  Nov.  1997. 

10.  J.C.S.  Meng„  "Electromagnetic  Control  Based  on  Micro-Turbulence 
Phenomenology,"  Flow  Noise  Modeling,  Measurement,  and  Control , 
ASME  NCA-Vol.  19,  FED- Vol.  230,  pp.  39-54,  1995. 

11.  S.N.  Singh  and  P.R.  Bandyopadhyay,  "Linear  Feedback  Control  of 
Boundary  Layer  Using  Electromagnetic  Microtiles,"  ASME  -  J.  Fluids 
Eng.,  Vol.  119,  pp.  852-858,  Dec.  1997. 

12.  S.R.  Snarski,  Device  for  Interactive  Turbulence  Control  in  Boundary 
Layers,  Patent  Application,  Navy  Case  #77883,  15  Jul  96. 

13.  S.R.  Snarski  and  R.M.  Lueptow,  "Wall  Pressure  and  Coherent 
Structures  in  a  Turbulent  Boundary  Layer  on  a  Cylinder  in  Axial 
Flow,"  J.  Fluid  Meek,  Vol.  286,  pp.  137-171,  1995. 

14.  R.L.  Robinson,  "A  Review  of  Vortex  Structures  and  Associated 
Coherent  Motions  in  Turbulent  Boundary  Layers.,"  Structure  of 
Turbulence  and  Drag  Reduction  IUTAM  Symposium,  Zurich, 
Switzerland,  1989,  Springer- Verlag  Berlin,  pp.  23-50,  1990. 

15.  S.J.  Kline  and  S.K.  Robinson,  "Quasi-coherent  Structures  in  thp 
Turbulent  Boundary  Layer:  Parts  I  &  II.,"  in  Near-wall  turbulence: 
Proceedings  of  the  1988  Zoran  Zaric  Memorial  Conference,  ed.  S.J. 
Kline  and  N.H.  Afgan,  Hemisphere,  New  York,  pp.  200-247,  1990. 

16.  S.J.  Kline,  W.C.  Reynolds,  F.A.  Schraub,  and  P.W.  Runstadler,  "The 
Structure  of  Turbulent  Boundary  Layers,"  J.  Fluid  Mech.  Vol.  30,  part 
4,  pp.  741-773,  1967. 

17.  L.  S.  Langston  and  R.G.  Kasper,  "Analysis  of  an  Electromagnetic 
Boundary  Layer  Probe  for  Low  Magnetic  Reynolds  Number  Flows," 
ASME  -J.  Fluids  Eng.,  Vol.  115,  Dec.  1993. 

18.  S.R.  Snarski,  The  Response  of  an  Electromagnetic  Induction  Sensor  to 
Isotropic  Turbulence,  NUWC-NPT  Tech.  Report  10809,  Naval 
Undersea  Warfare  Center  Detachment,  New  London,  CT,  15  Mar  95. 

19.  J.A.  Shercliff,  The  Theory  of  Electromagnetic  Flow  Measurement , 
Cambridge  University  Press,  Cambridge,  1962. 

20.  M.K.  Bevir,  "The  Theory  of  Induced  Voltage  Electromagnetic 
Flowmeters",  J.  Fluid  Mech.  ,  Vol.  43,  part  3,  pp.  577-590,  1970. 

21.  H.  Branover,  Magnetohydrodynamics  Flow  in  Ducts,  John  Wiley  & 
Sons,  New  York,  1978. 

22.  W. A.  Strawderman,  Wavevector-frequency  Analysis  with  Applications 
to  Acoustics,  U.S.  Government  Printing  Office,  SN008-047-00408-7, 
Naval  Undersea  Warfare  Center  Detachment,  New  London,  CT,  1994. 

23.  B.C.  Towe,  Underwater  Electromagnetic  Turbulent  Velocimeter, 
NUSC  Contractor  Report,  Contact  N66604-89-M-B873,  Naval 
Underwater  Systems  Center,  New  London,  CT,  15  Sep  89. 

24.  W.L.  Keith  and  B.M.  Abraham,  Spectral  Measurements  From  an 
Electromagnetic  Boundary  Layer  Probe  in  a  Turbulent  Pipe  Flow, 
NUWC-NPT  TR  10755,  Naval  Undersea  Warfare  Center,  New 
London,  CT,  1994. 

25.  A.B.  Bruno,  R.G.  Kasper,  and  B.C.  Towe,  Development  of 
Underwater  Electromagnetic  Velocimeter,  NUWC-NL  Technical 
Document  10065,  Naval  Undersea  Warfare  Center,  New  London,  CT, 
16  June  1992. 

26.  R.G.  Kasper,  A.B.  Bruno,  and  L.S.  Langston,  Preliminary 
Underwater  Electromagnetic  Turbulence  Measurements,  NUSC 
Technical  Document  8909,  Naval  Underwater  Systems  Center,  New 
London,  CT,  1991. 

27.  W.J.  Gretta  and  Smith,  “The  Flow  Structure  and  Statistics  of  a  Passive 
Mixing  Tab,”  J.  Fluids  Eng.,  Vol.  1 15,  pp.  255-263,  1993. 

28  A.  Tsinober,  "MHD  Flow  Drag  Reduction,"  in  Viscous  Drag 
Reduction  in  Boundary  Layers,  ed.  D.L.  Bushnell,  AIAA,  1990. 


425 


Turbulent  Drag  Reduction 
Methods:  Biology  Based 
Drag  Reduction 


427 


DOLPHIN  DRAG  REDUCTION:  MYTH  OR  MAGIC 


James  A.  Fein 

Office  of  Naval  Research 
800  North  Quincy  Street 
Arlington,  VA  22217 
feinj  @onr.  navy,  mil 

Abstract  -  The  swimming  performance  of  dolphins  has  been  the  inspiration  for  numerous  proposed  drag  reduction  techniques,  including 
compliant  coatings  and  riblets.  Speculation  has  focused  on  the  existence  of  laminar  flow  in  order  to  explain  the  difference  between  the 
available  power  and  the  measured  swimming  speeds.  Gray  first  postulated  the  paradox  between  power  and  speed  capability  in  1936  with  his 
claims  based  on  a  dolphin  swimming  speed  of  10.3  m/s.  This  survey  paper  explores  the  basis  for  that  paradox,  which  are  the  measurements  of 
dolphin  speed  used  by  Gray  and  others.  The  reliability  and  error  margins  of  the  early  measurements  are  discussed.  The  range  of  realistic 
speed  values  of  up  to  8.3  m/s  for  very  short  durations  and  half  that  for  longer  periods  is  established  for  both  captive  and  wild  dolphins.  This  is 
well  within  the  dolphins’  capabilities  based  on  available  muscle  mass  without  any  exotic  drag  reduction.  Thus  Gray’s  Paradox  may  be 
attributed  to  incorrect  data  for  dolphin  swim  speed.  Marine  mammals  other  than  dolphins  are  discussed,  although  data  is  much  less  plentiful  for 
whales.  The  conclusion  is  that  there  is  no  reason  to  believe,  based  on  the  swimming  speed  data,  that  dolphins  have  frictional  drag  reduction 
systems  or  techniques.  In  order  to  establish  extraordinary  performance  of  biological  creatures,  swim  speed  data  must  be  repeatable,  have 
acceptable  error  bounds  and  points  that  lie  far  from  the  majority  of  the  data  should  be  rejected.  This  recommendation  will  impact  the  level  of 
data  required  to  establish  the  existence  of  other  seawater  drag  reduction  mechanisms  as  well.  In  conclusion,  while  dolphins  are  streamlined 
swimming  organisms  that  may  avoid  some  form  drag  and  some  wave  drag,  there  is  no  evidence  that  they  reduce  skin  friction  drag  or  that  they 
postpone  transition  from  laminar  to  turbulent  flow. 


L  BACKGROUND 

The  supposed  drag  reduction  attributes  of  dolphins  and  other 
marine  mammals  have  been  the  source  of  speculation  for  some  time, 
The  interest  related  to  translating  those  attributes  for  use  in  increasing 
the  speed  or  endurance  of  ships,  weapons  and  underwater  vehicles. 
The  dolphin  is  a  biological  system  that  is  an  evolution  driven 
compromise  for  survival.  Its  shape,  skin,  body  fat  distribution  and  other 
characteristics  have  favored  adaptations  that  efficiently  solve  problems 
of  regulating  temperature,  finding  food  and  avoiding  danger.  It  is 
reasonable  to  assume  that  since  mobility  and  speed  are  important  in 
avoiding  predators,  the  dolphin  may  have  unusual  attributes  that  allow 
high-speed  swimming. 

In  this  century,  the  speculation  can  be  said  to  have  begun 
with  the  well-known  Gray 's  Paradox.  Gray  (1),  writing  in  1936  in  the 
Journal  of  Experimental  Biology,  states,  "If  the  resistance  of  an  actively 
swimming  dolphin  is  equal  to  that  of  a  rigid  model  towed  at  the  same 
speed '  the  muscles  must  be  capable  of  generating  energy  at  a  rate  at 
least  seven  times  greater  than  that  of  other  types  of  mammalian 
muscle  ."  Gray  goes  on  to  identify  the  proposition  that  the  rhythmic 
movements  of  the  dolphin  in  some  way  prevent  the  fluid  from 
generating  turbulence  along  the  body.  Furthermore,  if  the  flow  is  free 
of  turbulence,  the  horsepower  per  pound  of  muscle  agrees  closely  with 
other  mammal  muscles,  Thus  Gray  not  only  proposed  the  paradox,  but 
also  identified  the  first  theory  to  explain  it  He  speculated  that  laminar 
flow  existed  along  the  body. 

The  solutions  to  Gray’s  Paradox  have  centered  on 
explanations  of  the  muscle  power  available  in  dolphins  and  on  the  fluid 
mechanics  of  the  drag  producing  boundary  layer.  Fluid  mechanical 
explanations  have  included  various  mechanisms  to  maintain  laminar 
flow  and/or  turbulent  drag  reduction.  Techniques  considered  include 
polymer  surface  chemistry,  surface  ridges  such  as  riblets,  compliant 
coatings,  surface  folds  and  subsurface  energy  absorption.  There  is  no 
satisfactory  explanation  for  other  accounts  of  even  higher  swimming 
speeds  by  an  assortment  of  observers. 

This  paper  will  not  add  to  the  speculation,  but  will  examine 
the  original  source  of  the  paradox,  the  speed  measurements  for  dolphin 
swimming.  It  will  be  demonstrated  that  the  early  measurements  used 
by  Gray  and  others  do  not  stand  up  to  scrutiny.  The  later,  much  lower, 
swimming  speed  measurements  can  be  explained  without  unusual 
physical  mechanisms.  There  is  still  a  great  deal  of  misinformation 
about  dolphin  swim  speeds  and  drag  reduction  abilities  as  demonstrated 
by  the  proposals  received  at  Office  of  Naval  Research  that  still  refer  to 
Gray’s  Paradox. 

IL  EARLY  MEASUREMENTS 

It  is  a  well-accepted  postulate  in  science,  going  back  to 
Ockham’s  razor,  that  the  simplest  explanation  that  fits  the  facts  is  to  be 
preferred.  A  corollary  is  that  a  very  high  level  of  experimental 
verification  and  documentation  should  back  up  extraordinary  claims. 
Claims  of  very  fast  swimming  by  dolphins  (and  other  marine  creatures) 
which  require  unusual  physical  explanations,  should  be  established  by 


high  quality  data  and  rigorous  error  analysis.  The  early  speed 
estimates  are  described  in  Table  I,  with  discussion  below. 

Gray’s  Measurement: 

Gray’s  Measurement  (1)  consists  of  the  following  quotation 
from  his  work,  “The  velocity  of  a  rapidly  moving  dolphin  has  seldom 
been  determined  with  great  accuracy t  and  no  doubt  it  has  often  been 
exaggerated.  The  following  observation  made  by  Mr.  E.  F.  Thompson 
whilst  in  the  Indian  Ocean  is  therefore  of  interest.  A  dolphin  swimming 
approximately  30  ft.  from  the  side  of  the  ship  passed  the  ship  in  the 
direction  of  stem  to  bow  in  just  under  7.0  sec .  As  timed  by  a  stopwatch: 
the  length  of  the  ship  was  136  ft.  and  its  speed  was  logged  at  8.5  knots. 
This  dolphin  must  therefore  have  been  traveling  at  20  knots  (==33 
ft/sec)  ”  (or  10.3  m/s).  The  rest  of  his  arguments  related  to  laminar 
flow  and  muscle  power  are  all  based  on  this  single  observation.  First  it 
is  clear  that  the  measurement  is  not  Gray’s,  but  Mr.  Thompson’s.  Gray 
was  nowhere  near  the  observation  himself  and  offers  nothing  in  terms 
of  the  credibility  of  the  observer.  There  is  no  information  on  the 
accuracy  of  the  various  components  of  the  measurement.  For 
example,  while  the  length  of  the  ship  may  be  given  some  credence,  the 
calibration  of  the  ship’s  speed  log  is  unknown.  Particularly  suspect  is 
the  stop  watch  measurement  which  by  necessity  must  have  been  taken 
from  one  location.  This  would  require  estimates  of  the  time  the  dolphin 
crossed  the  stem  and  then  the  bow  plane  of  the  ship.  It  is  unlikely  that 
the  observer  ran  along  the  side  with  the  dolphin  since  that  would  have 
required  an  unimpeded  deck  and  sprinter  running  speed  by  Mr. 
Thompson.  A  system  of  multiple  observers  and  hand  signals  is  possible 
but  no  less  fraught  with  error.  The  speed  log  and  the  timing  could  be 
expected  to  have  a  combined  error  of  at  least  +  or  - 10%.  The  overall 
uncertainty  of  the  measurement  would  be  greater.  The  largest  source 
of  error,  however,  is  the  proximity  of  the  dolphin  to  the  side  of  the  ship. 
If  the  dolphin  came  within  the  boundary  layer  or  detached  separated 
flow  field  of  the  ship,  which,  for  a  blunt  bow  freighter,  could  be  30  feet 
from  the  ship  at  the  stem,  the  animal  would  have  been  swimming 
through  water  that  was  moving  forward  with  a  significant  velocity.  This 
would  invalidate  the  measurement.  If  the  dolphin  were  farther  from 
the  ship,  say  50  to  60  feet,  the  errors  in  timing  the  run  would  be 
exaggerated.  Another  problem  that  creates  uncertainty  is  that  the 
measurement  seems  to  be  taken  only  once.  It  is  unclear  whether  other 
measurements  were  taken  that  gave  lower  speeds  or  if  this  was  the 
single  measurement.  Either  way,  the  case  for  an  over  10  m/s  swimming 
speed  is  weak. 

Measurements  of  Johaitnessen  and  Harder  (2): 

This  publication  of  1960  is  the  second  common  source  of 
high-speed  measurements  for  dolphin  swimming.  The  authors  did  not 
make  the  observations  themselves  but  asked  the  navigation  officer,  Mr. 
Anderson,  of  the  S.S.  Monterey ,  a  freighter  traveling  from  California  to 
Australia.  The  publication  has  a  number  of  anecdotal  observations. 
One  is  that  while  the  ship  was  traveling  at  9.8  to  10.8  m/s,  dolphins 
would  swim  alongside  for  periods  of  up  to  2  minutes.  This  can  be 


429 


explained  by  the  dolphins  utilizing  the  ship  boundary  layer  and  in  fact  it 
is  noted  that  some  of  the  animals  rode  the  bow  wave  of  the  ship  during 
the  encounters.  There  are  five  other  observations  of  groups  of  1  to  500 
animals  going  from  7.2  to  20.6  m/s.  Four  of  them  are  for  dolphin 
species  and  estimate  speeds  of  7.2  to  9.3  m/s.  In  most  cases  the  animals 
were  a  quarter  to  a  half-mile  away  from  the  ship.  The  other  is  a  single 
animal,  a  killer  whale,  going  10.3  to  20.6  m/s.  The  speed  range  of  7  to 
9  m/s  for  the  dolphins  is  close  to  the  well-established  values  of  later 
researchers.  The  killer  whale  data  point  was  taken  as  the  animal 
approached  the  ship  head  on  with  no  fixed  reference  frame  for  a 
measurement.  There  is  no  mention  of  an  empirical  technique  for  any 
of  the  observations,  so  the  data  points  must  be  considered  estimates, 
which  can  be  affected  greatly  by  the  distances  and  the  moving 
observer. 

There  is  an  additional  anecdotal  report  in  the  paper,  a 
private  communication  from  William  von  Winkle  of  what  is  today 
NUWC,  “ that  a  school  of  blackfish  had  been  observed  circling  a  Navy 
vessel,  which  was  cruising  at  22  knots,  for  several  days  at  a  time .  ” 
Again  there  is  no  speed  calibration,  current  information  or  quantitative 
data.  Dr.  von  Winkle  is  a  scientist  and  his  observations  are  more 
credible  than  those  of  non-scientists.  However  the  estimate  of  1 1.3  m/s 
at  a  duration  of  several  days  is  far  higher  than  any  other  more  exact 
measurement  made  on  either  whales  or  dolphins.  This  single  data  point 
also  does  not  address  the  motivation  of  the  animals,  which  appears  to 
be  non-existent.  Blackfish,  also  known  as  pilot  whales  is  a  dolphin 
species  that  is  larger  than  common  dolphins,  but  smaller  than  most 
whales.  It  was  hunted  extensively  by  the  early  whalers,  which  relied 
on  sail  or  rowing  power  to  overtake  the  whales.  The  indirect  evidence 
that  these  animals  were  not  capable  of  speeds  of  over  11  m/s  and 
durations  of  several  days,  is  that  these  animals  were  often  taken  and 
greatly  reduced  in  numbers  during  the  whaling  era  (3). 

It  is  whaling  experience  that  provides  the  key  data  for 
establishing  the  swimming  speeds  of  whales.  In  whale  hunting  the 
animal’s  motivation  is  clear.  The  importance  of  any  mechanism  to 
increase  speed  is  also  clear.  Humans  are  one  predator  where 
extraordinary  speed  would  have  been  an  effective  strategy  for 
survival.  The  blackfish  described  in  Murphy  (3)  cannot  outrun  the  sail 
powered  whalers  and  instead  use  the  strategy  of  diving  and  reemerging 
in  a  different  direction.  This  sometimes  works,  but  often  fails  as  the 
evidence  of  40  or  more  blackfish  taken  by  a  single  ship  testifies.  While 
the  clipper  ships  reached  10.3  m/s,  the  whaling  ships  rarely  went  over 
half  that  speed  and  the  oar  and  sail  powered  longboats  were  even 
slower.  For  larger  whales  the  data  is  also  clear.  Gawn  (4)  and 
Kermack  (5)  both  document  maximum  whale  swimming  speeds  based 
on  the  known  speeds  of  the  powered  catcher  boats  used  in  the  1940s  to 
overtake  them.  For  large  blue  and  fin  whales,  the  maximum  speeds 
for  10  minutes  were  estimated  to  be  10.3  m/s.  For  any  longer  duration 
the  speeds  did  not  exceed  7.7  m/s  in  any  case.  See  Gawn  (4)  for  a 
good  discussion  of  the  muscle  power  available  to  large  whales.  The 
incidents  where  whales  were  able  to  tow  ships  are  discussed.  More 
recently  Williamson  (6)  accompanied  Japanese  whalers  and  recorded 
a  8.2  m/s  top  speed  for  up  to  10  minutes  for  blue,  fin,  sei,  bryde,  and 
minke  whales.  There  was  anecdotal  information  from  the  whalers  that 
an  occasional  blue  or  fin  whale  could  reach  10.3  m/s  for  short 
durations.  Humpback,  gray,  right  and  sperm  whales  had  a  top  speed  of 
only  4. 1  m/s.  If  marine  mammals  had  a  drag  reduction  mechanism,  it 
could  be  expected  that  the  larger  species  would  have  a  higher  top 
speed.  These  top  speeds  for  the  largest  whales,  which  are  well  within 
the  capabilities  of  die  animals’  muscles  with  a  fully  turbulent  boundary 
layer,  are  a  strong  argument  for  no  special  mechanisms. 

Kellogg’s  Results: 

Another  reference  that  is  frequently  sighted  is  Kellogg  (7). 
Kellogg’s  article  is  a  collection  of  information  on  characteristics  of 
marine  mammals.  It  is  not  a  scholarly  paper  and  it  offers  no 
information  to  back  up  its  swimming  speed  claims.  He  gives  a  blue 
whale  swim  speed  of  7.2  m/s,  a  long  snout  dolphin  (near  ships)  swim 
speed  of  6.2  to  7.7  m/s  and  a  delphinius  species  dolphin  swim  speed  of 
7,7  to  9.3  m/s  with  no  additional  details.  This  is  slightly  below  the  Gray 
estimate  and  may  be  based  on  it  or  on  other  anecdotal  estimates.  There 
is  no  reason  to  give  any  credibility  to  the  estimates  in  Kellogg. 

Dolphins  riding  the  bow  wave  of  ships: 

Dolphins  are  recorded  to  have  ridden  on  the  bow  wave  of 
ships  from  ancient  times.  In  Woodcock  (8),  this  behavior  is  described 
and  attributed  to  a  laminar  flow  mechanism  that  is  based  on  Gray’s 


analysis.  Peny,  Acosta  and  Kiceniuk  (9)  conducted  experiments  to 
show  that  there  is  plenty  of  forward  velocity  flow  on  the  wave  front  in 
the  bow  region  of  a  ship  to  allow  the  dolphin  to  ride  the  flow  field. 
That  dolphins  are  capable  of  sensing  flow  fields  and  getting  a  ‘free 
ride’  has  been  demonstrated  many  times  by  the  marine  mammal 
training  and  physiology  communities.  This  explains  some  of  the  high 
speeds  observed  when  dolphins  are  swimming  near  a  ship  or  in  its 
wake. 

Lang’s  Measurements: 

Prior  to  1 960  the  dolphin  swim  speed  estimates  were  based 
on  sparse  data  subject  to  exaggeration  and  influenced  by  moving 
observers  and  the  flow  field  of  the  moving  ship.  Dr.  Tom  Lang  of  the 
Naval  Laboratory  conducted  the  most  extensive  series  of 
measurements  of  dolphin  swimming  hydrodynamics  during  the  1960s. 
These  experiments  with  captive  animals  spanned  a  number  of  species 
and  techniques  and  are  documented  in  Lang  and  Daybell  (10),  Lang 
and  Norris  (11)  and  Lang  and  Pryor  (12).  Published  in  1963,  Lang  and 
Daybell  (10)  explores  the  fluid  phenomena  of  the  swimming  by 
attaching  drag  and  turbulence  inducing  collars,  conducting  studies  of 
dolphin  forms  in  the  towing  tank  and  analyzing  the  propulsive  power 
available.  To  quote  from  the  abstract  of  (10),  “ Results  of  the  tests 
indicated  no  unusual  physiological  or  hydrodynamic  phenomena: 
power  values  were  comparable  to  human  performance.  These  results, 
however,  are  in  conflict  with  observations  of  unusual  sea-animal 
performance  reported  in  the  open  literature.  ’’The  tests  were  conducted 
in  seawater  in  the  former  Convair  Corporation  tank  in  San  Diego.  The 
top  speed  of  the  lagenorhynchus  porpoise  in  the  tow  tank  in  35  runs 
was  only  7.7  m/s.  However  Lang  and  Daybell  could  not  explain  the 
high  swimming  speeds  reported  by  others  in  the  open  literature  and  thus 
looked  for  flaws  in  their  own  work.  One  concern  was  the  size  of  the 
tow  tank.  This  led  to  the  next  series  of  his  experiments.  He  moved  to 
an  open  test  range  at  Coconut  Island  in  Kaneohe  Bay,  Hawaii. 

An  important  factor  in  the  research  of  Lang  and  Norris  (11) 
and  Lang  and  Pryor  (12)  was  that  the  animals  were  trained  to  go  fast. 
In  all  three  sets  of  experiments  the  animals  showed  significant 
improvement  after  repeatedly  undergoing  the  trial.  This  implies  that 
wild  dolphins  do  not  utilize  unusual  speed,  but  that  like  trained  athletes 
they  could  improve  their  speed  by  exercising  the  muscles  involved  in 
fast  swimming.  With  a  stenella  dolphin  in  Lang  and  Pryor, 
instantaneous  speed  measurements  were  made  along  the  swimming 
course.  In  over  300  data  runs  there  ^ere  three  instantaneous  top 
speeds  of  over  10.3  m/s.  The  maximum  was  11.1  m/s.  These  data 
points  were  taken  by  comparing  frame  to  frame  camera  data  and  not 
averaged  over  any  length.  As  instantaneous  points  they  are  interesting, 
but  not  conclusive,  because  they  were  reached  only  once  during  the 
run  and  the  average  speed  over  the  few  seconds  around  that  point  was 
20%  lower  or  no  more  than  about  8  m/s.  There  is  a  good  chance  that 
the  camera  system  or  the  analysis  failed  during  these  few  data  points  as 
the  massive  bulk  of  the  data  was  at  much  lower  values  and  all  sustained 
measurements  were  also  lower.  The  often  quoted  dolphin  speed  for 
this  experiment  is  1 1.1  m/s,  when  a  speed  based  on  the  vast  majority  of 
the  data  points  would  be  much  lower.  An  interesting  observation  in 
Lang  and  Pryor  is,  “An  alternate  check  of  top  speed  was  made  in  an 
oceanarium  at  Sea  Life  Park,  where  two  S.  attemiata  were  trained  with 
four  spinner  porpoises  to  swim  at  high  speed  around  a  70  m  path 
circling  a  small  island  in  the  park.  The  animals  appeared  to  travel  at 
extremely  high  speed,  but  reduction  of  the  data  showed  top  speeds  of 
only  7.7  to  8.3  m/s.  ”  In  Lang  and  Norris  (11),  a  tursiops  species  was 
tested  under  similar  conditions.  For  very  short  durations  (frame  to 
frame)  a  top  speed  of  7  to  8.3  m/s  was  observed.  For  longer  durations 
an  average  of  about  3  m/s  was  noted. 

Other  Speed  Claims: 

A  number  of  reference  works  on  marine  mammals  also  repeat  some  of 
the  early  high  speeds.  These  claims  can  be  traced  back  to  the  work  of 
References  (1)  or  (2)  and  thus  do  not  have  to  be  treated  separately. 
There  is  some  Russian  research  on  the  implications  of  dolphin 
swimming  speed.  The  researchers  tend  to  repeat  the  speed  claims  of 
Gray  and  the  other  anecdotal  observers  and  throw  in  some 
unsubstantiated  results  from  the  1 930s  in  Russia  as  well.  They  assume 
laminar  flow  and  other  mechanisms  exist,  then  study  them. 

III.  RECENT  MEASUREMENTS 

In  the  last  20  years  there  have  been  a  number  of 
experiments  that  utilize  more  accurate  speed  measurement  techniques 


430 


and  larger  numbers  of  data  points  than  the  previous  results.  Many  of 
these  results  and  the  implications  of  the  results  on  the  fluid  dynamics 
issues  of  drag  reduction  can  be  found  in  Fish  and  Hui  (13).  They  find 
that  there  is  no  evidence  of  unusual  frictional  drag  reduction 
mechanisms  with  dolphins.  Each  potential  mechanism  such  as 
compliant  damping,  dermal  ridges,  secretions  and  heating  is  discussed 
and  found  unsubstantiated.  Adequate  metabolic  output  for  the  likely 
swimming  speed  is  found  within  the  animal’s  normal  muscle  abilities. 
Williams  et  al.  (14)  and  van  Oossanen  and  Oosterveld  (15)  present 
arguments  about  the  amount  of  energy  available.  Since  about  twice  as 
much  power  is  required  to  travel  at  a  sustained  10  m/s  than  at  8  m/s,  the 
inflated  swim  speeds  can  be  a  crucial  factor  in  the  analysis.  Reference 
(15)  finds  that  at  8  m/s  there  is  sufficient  power  from  the  muscles  to 
overcome  the  turbulent  drag.  Reference  (14)  documents  that  the  cost 
of  a  dolphin  swimming  is  1/12*  the  power  required  by  a  human 
swimmer  at  the  same  speed.  More  recent  results  in  the  U.S.  address  a 
number  of  the  controversial  issues  with  credible  data  and  will  be 
discussed  in  what  follows. 

Laminar  Flow  Mechanisms: 

One  of  the  issues  that  continues  to  be  subject  to  controversy 
was  addressed  conclusively  by  Lang  and  Daybell  (10).  This  was  the 
existence  of  laminar  flow  where  turbulence  should  be  present.  For 
example  the  careful  use  of  collars  to  trip  the  boundary  layer  at  speeds 
of  up  to  4  m/s,  led  to  the  conclusion,  “The  boundary  layer  is  probably 
about  20%  laminar :  ”  This  is  similar  to  underwater  bodies  in  the  same 
speed  and  size  regime  where  Reynolds  Number  at  the  point  of 
transition  is  roughly  1  to  2  million  based  on  the  distance  from  leading 
edge  to  transition  point.  (See  Streeter  (16).)  Other  factors  such  a 
smoothness  and  pressure  gradient  dire  to  shaping  come  into  play,  but 
will  not  affect  this  value  much.  This  approximate  transition  location 
was  verified  by  Rohr  et  al.  (17)  through  the  use  of  Bioluminescent 
Marine  Plankton  Lang  and  Daybell  make  a  further  observation,  “Also, 
small  particles  suspended  in  the  water  can  produce  turbulence  where 
laminar  would  otherwise  exist.  ”  If  other  researchers  had  noted  this  a 
great  deal  of  effort  in  seawater  drag  reduction  might  have  been 
avoided. 

Captive  animals: 

There  has  been  much  concern  about  the  speed  capability  of 
wild  versus  captive  animals.  A  definitive  study  in  that  regard  has  been 
made  by  Rohr  et  al.  (18).  They  took  data  on  a  wide  range  of  both  wild 
and  captive  animals  using  digital  cameras  with  fixed  reference  planes 
for  accurate  measurements  and  many  repeat  runs  to  determine 
swimming  speeds.  The  circumstances  were  quite  different,  ranging 
from  aircraft  driving  schools  of  animals  to  captive  animals  being 
released  in  shallow  water.  Motivation  was  at  least  reasonable  given 
that  the  early  data  indicating  high  swimming  speeds  had  no  motivation 
at  all.  The  conclusion  was  that  the  captive  dolphins  were  as  fast  as  or 
faster  than  the  wild  animals.  This  confirms  the  early  evidence  that 
captive  animals  can  be  trained  to  swim  faster.  In  general,  captive 
animals  are  healthy  and  well  fed.  Captive  animals  can  be  trained  to 
swim  fast  to  jump  high  to  get  even  more  performance.  Wild  animals 
often  have  scars  on  the  head  from  encounters  with  predators  or  other 
dolphins  that  would  defeat  any  frictional  resistance  reduction  anyway. 
Even  among  the  captive  animals,  the  analysis  of  930  speed  runs  shows 
a  maximum  short  duration  speed  of  8. 15  m/s,  as  shown  in  Table  II.  The 
average  speed  for  the  distance  of  the  run  was  around  6  m/s.  No  overall 
average  speed  for  the  run  exceeded  7  m/s.  For  the  wild  dolphins,  over 
1000  runs  were  analyzed  and  the  maximum  velocity  was  found  to  be 
6.7  m/s,  with  an  overall  average  of  4.18  m/s,  as  shown  in  Table  III. 
Because  of  the  digital  camera  technique  all  the  durations  for  the 
analysis  were  on  the  order  of  1  to  2  seconds. 

Duration: 

The  short  durations  associated  with  the  higher  dolphin  speed 
numbers  raises  an  interesting  issue.  There  is  a  large  difference 
between  the  power  that  can  be  exerted  over  a  one-second  period  and 
that  over  a  1  minute  period.  A  very  short  time  speed  burst  would  be  of 
little  value  to  an  animal  since  it  would  not  create  a  very  large  distance 
between  the  animal  and  its  predator.  A  distance  generated  by  a  2  m/s 
burst  over  1  second  would  be  about  one  body  length.  Any 
hydrodynamic  phenomena  that  would  be  leading  to  such  a  burst  would 
have  to  act  over  the  length  of  the  animal  and  that  in  itself  would  take  a 
significant  fraction  of  a  second  to  take  effect.  This  makes  it  even  less 
likely  that  a  burst  is  due  to  hydrodynamic  effects  and  more  likely  that  it 


is  due  to  a  short-term  oxygen  deficit.  The  short-term  exertion  involved 
in  a  jump  is  a  good  example  of  the  levels  that  can  be  reached. 

Quality  and  Quantity  of  Data: 

It  is  worthwhile  to  contrast  two  published  papers  on  the 
swimming  speed  of  tursiops  trucatus.  One  is  Lockyer  and  Morris  (19) 
and  the  other  is  Wursig  and  Wursig  (20).  Reference  (19)  gives  a 
couple  veiy  high  speed  points  out  of  a  total  of  12  data  points.  The 
observational  technique  is  prone  to  subjective  interpretation  of  the 
position  of  markers  and  the  start  and  stop  times.  These  points  are 
questionable  since  the  distance  traveled  was  estimated  from  charts  and 
the  observation  was  taken  from  a  considerable  distance  looking  down 
from  a  cliff.  No  attempt  is  made  to  repeat  the  clearly  extraordinary 
data  point  of  15  m/s  for  a  duration  of  20  seconds.  The  efforts  of 
Reference  (20)  are  for  the  same  species,  but  taken  over  a  long  period 
with  over  1000  measurements.  Theodolites  from  two  positions 
recorded  the  animals  at  specified  time  intervals  to  give  a  triangulation 
of  the  position  and  the  time  interval  (usually  30  seconds).  There  is  still 
some  inherent  error  in  the  technique,  but  the  credibility  of  the  results  is 
enhanced  by  the  quantity  of  the  data  points.  Recorded  speeds  did  not 
exceed  6  m/s  and  averages  were  less  than  5  m/s.  The  animals  were 
engaged  in  normal  behaviors  such  as  chasing  prey  and  did  not  interact 
with  a  ship. 

The  implication  is  that  the  extraordinary  speed  observations 
are  for  cases  with  sparse  data  and  crude  measurement  techniques. 
The  outlying  points  are  quoted  as  the  speed  capability  instead  of  being 
thrown  out  as  bad  data.  In  some  cases  the  expectation  of  high-speed 
results  may  have  colored  the  estimates  being  made.  This  naturally  led 
to  a  misunderstanding  about  dolphin  speed  and  power  capability  and 
led  to  a  great  deal  of  research  directed  at  finding  the  ‘secret’  of  the 
dolphin.  In  the  future,  drag  reduction  researchers  should  be  especially 
aware  of  the  pitfalls  of  believing  sparse  data  showing  unusual 
capabilities.  It  is  the  first  concern  when  an  unexplainable,  but  very 
promising  data  point  is  claimed,  to  repeat  the  experiment  in  a  neutral 
facility  or  with  neutral  observers.  This  must  be  undertaken  before  a 
scale  up  or  follow-on  research  effort  is  approved.  Extraordinary 
results  always  should  require  an  extraordinary  level  of  proof. 

IV.  FUTURE  RESEARCH  ISSUES 

While  the  dolphin  does  not  possess  a  frictional  drag 
reduction  mechanism,  there  are  still  interesting  naval  architecture 
issues  involved  with  the  biological  system.  One  is  the  mechanism  for 
the  dolphins’  jumping  ability.  They  seem  to  be  able  to  jump  higher  than 
the  swimming  speed  alone  can  explain.  This  is  noted  in  Reference 
(18).  Another  interesting  research  direction  is  the  area  of  wave  drag 
reduction  through  body  shaping  and  particularly  the  way  the  body 
changes  shape  during  propulsion.  The  dolphin  usually  swims  near  the 
surface  because  it  needs  to  breathe  air.  Thus  its  swimming  should  be 
optimized  to  be  efficient  close  to  the  surface.  This  may  be  tied  to  the 
dolphin’s  up/down  rather  than  side  to  side  propulsive  motion  that  fish 
possess.  In  Reference  (17)  it  is  noted  that  the  swim  speeds  of  the 
dolphins  were  significantly  higher  in  deep  rather  than  shallow  water. 
Also,  the  usual  dolphin  swimming  speeds  correspond  to  a  length  Froude 
number  of  close  to  one.  Advanced  computational  modeling  might  be 
able  to  shed  some  light  on  these  issues. 

V.  CONCLUSIONS 

Dolphins  and  other  marine  mammals  are  well  adapted  to 
swimming  in  the  ocean.  Their  bodies  are  streamlined  and  their 
physiology  takes  into  account  the  heat  and  respiratory  constraints  of 
living  in  the  sea.  The  dolphins  swim  fast,  but  do  not  exceed  what  they 
would  be  capable  of  doing  without  exotic  drag  reduction  mechanisms. 
The  range  of  realistic  swim  speed  values  is  up  to  8.3  m/s  for  very  short 
durations  and  half  that  for  longer  periods.  These  speed  levels  seem  to 
hold  for  both  captive  and  wild  dolphins.  Thus  Gray’s  Paradox  is  based 
on  incorrect  data  for  swim  speed  of  marine  mammals.  The  evidence  is 
that  the  amount  of  laminar  flow  is  about  what  would  be  expected  for 
that  range  of  Reynold’s  Number  and  not  prolonged  in  any  way.  Thus 
there  is  no  reason  to  believe,  based  on  the  swimming  speed  data,  that 
dolphins  have  frictional  drag  reduction  systems  or  techniques. 

In  order  to  establish  extraordinary  performance  of 
biological  creatures,  swim  speed  data  must  be  repeatable,  have 
acceptable  error  bounds  and  points  that  he  far  from  the  majority  of  the 
data  should  be  rejected.  This  recommendation  will  impact  the  level  of 
data  required  to  establish  the  existence  of  other  seawater  drag 
reduction  mechanisms  as  well.  In  conclusion,  while  dolphins  are 


431 


streamlined  swimming  organisms  that  may  avoid  some  form  drag  and 
some  wave  drag,  there  is  no  convincing  evidence  that  they  reduce  skin 
friction  drag  or  that  they  postpone  transition  from  laminar  to  turbulent 
flow. 

VL  ACKNOWLEDGMENT 

This  paper  is  dedicated  to  the  late  Dr.  Arthur  E.  Bisson  Dr. 
Bisson  was  interested  in  this  subject  and  urged  me  to  see  that  the 
correct  values  for  dolphin  swimming  speeds  became  widely  known. 
The  technical  discussions  and  advice  from  Dr.  J.  Rohr  and  Prof.  F.  Fish 
are  greatly  appreciated.  This  paper  was  prepared  under  the  ONR 
Research  Opportunities  for  Program  Officers  Program. 


VIL  REFERENCES 

1.  Gray,  J.,  ‘Studies  in  Animal  Locomotion  VI:  The  Propulsive  Power 
of  the  Dolphin,'  Journal  of  Experimental  Biology,  V13:  p  192-199, 
1936. 

2.  Johannessan,  C.L.  and  J.A.  Harder,  ‘Sustained  Swimming  Speeds  of 
Dolphins,'  Science,  V132:  pl550-1551, 1960. 

3.  Murphy,  Robert  C.,  Logbook  for  Grace,  TimeLife  Books,  1947 

4.  Gawn,  R.  W.  L.,  ‘Aspects  of  the  Locomotion  of  Whales,'  Nature, 
V161:p4446, 1948. 

5.  Kermack,  K.  A.,  ‘The  Propulsive  Powers  of  Blue  and  Fin  Whales,' 

Journal  of  Experimental  Biology,  v25:  p  237-240, 1948. 

6.  Williamson,  G.  R.,  ‘The  True  Body  Shape  of  Roqual  Whales,' 
Journal  of  Zoology,  London,  V167:  p  277-286,  1972. 

7.  Kellogg,  R.,  ‘Whales,  Giants  of  the  Sea,'  National  Geographic,  V 
67,  1940 

8.  Woodcock,  A.  H.,  ‘The  Swimming  of  Dolphins,'  Nature,  V161:  p 
602,  1948. 

9.  Perty,  B.  and  A.  Acosta  and  T.  Kiceniuk,  ‘Simulated  Wave  Riding 
Dolphins,'  Nature,  V192:  p!48-150,  1961. 


10.  Lang,  T.G.  and  D.A  Daybell,  ‘Porpoise  Performance  Tests  in  a 
Seawater  Tank,'  NOTS  Technical  Publication  3063,  Naval  Ordnance 
Test  Station,  China  Lake,  CA,  1963 

11.  Lang,  T.  G.  and  K.  S.  Norris,  ‘Swimming  Speed  of  a  Pacific 
Bottlenose  Porpoise,'  Science,  VI 51:  p588-590, 1966. 

12.  Lang,  T.  G.  and  K.  Pryor,  ‘Hydrodynamic  Performance  of 
Porpoises  ( Stemlla  Attentuata ),'  Science,  V 1 52 :  p  531-533, 1966. 

13.  Fish,  F.  and  C.A  Hui,  ‘Dolphin  Swimming  -  A  Review,'  Mammal 
Review,  V21:  pl81-195,  1991. 

14.  Williams,  T.  and  W.  Friedl,  M.  Fong,  R.  Yamada,  P.  Sedivy,  J. 
Haun,  'Travel  at  Low  Energetic  Cost  by  Swimming  and  Wave-Riding 
Dolphins,'  Nature,  V355:  p  821-823,  1992. 

15.  van  Oossanen,  P.  and  M.  Oosterveld,  ‘Hydrodynamic  Resistance 
Characteristics  of  Humans,  Dolphins,  and  Ship  Forms,'  Schiffstechnik, 
V36:p  31-48,  1989. 

16.  Streeter,  V.  L.,  Fluid  Mechanics,  McGraw  Hill,  1966... 

17.  Rohr,  J.  and  M.  Latz,  E.  Hendricks,  J.  Nauen,  ‘Experimental 
Approaches  Towards  Interpreting  Dolphin-Stimulated 
Bioluminescence,'  Journal  of  Experimental  Biology,  (in  Press). 

18.  Rohr,  J.  and  E.  Hendricks,  L.  Quigley,  F.  Fish,  J.  Gilpatrick,  L 
Scardino-Ludwig,  ‘Swindling  Observations  of  Captive  and  Free- 
Ranging  Dolphins’,  SPAWARS  Systems  Center  Technical  Report  1769, 
1998. 

19.  Lockyer,  C.  and  R.  Morris,  ‘Observations  on  Diving  Behavior  and 
Swimming  Speeds  in  wild  Juvenile  Tursiops  truncates'  Aquatic 
Mammals,  V13:  p31-35,  1987. 

20.  Wursig,  B.  and  M.  Wursig,  ‘Behavior  and  Ecology  of  the 
Bottlenose  Dolphin,  Tursiops  trucatus,  in  the  South  Atlantic,'  Fishery 
Bulletin,  V77,  No.  2,  1979. 


432 


Table  I.  Early  speed  observations  for  dolphin  species. 

Species 

Speed  (m/s) 

Methodology 

Speed  Classification 

“Dolphin” 

10.3 

Stopwatch 

Along  Ship  (7  s) 

“Dolphin” 

7.2  to  9.3 

Ship  Estimation 

Various 

Globicephala 

11.3 

Ship  Estimation 

Maximum  Sustained 

Orcinus  Orca 

15.5 

Ship  Estimation 

Maximum  Sustained 

Delphinus  delphi 

9.3 

Unknown 

? 

Tursiops  truncates 

15 

Cliff  Estimation 

Burst 

Tursiops  truncates 

8.3 

Theodolite  Tracking 

Burst 

Tursiops  truncates 

1.7 

Theodolite  Tracking 

Average  Cruising 

Tursiops  truncates 

4.2 

Cliff  Estimation 

Average  Cruising 

Tursiops  truncates 

7.01  to  8.3 

Trained  in  Captivity 

Burst  (7.5-lOs) 

Tursiops  truncates 

6.09 

Trained  in  Captivity 

Maximum  Sustained 

Tursiops  truncates 

3.08 

Trained  in  Captivity 

Average  Cruising 

Reference 


1 


2 


2 


2 


Table  II.  Summary  of  trained  captive  dolphin  swimming  speed.  (Ref.  18) 


All  Velocity  Data 

Species 

Max  Vel 
m/s 

Avg  Vel 

in/s 

Tursiops  truncates 

97 

7.74 

6.52 

Tursiops  truncates 

68 

6.67 

5.45 

Tursiops  truncates 

111 

6.79 

5.72 

Tursiops  truncates 

26 

7.49 

6.71 

Tursiops  truncates 

142 

8.15 

6.55 

Tursiops  truncates 

189 

7.76 

6.39 

Tursiops  truncates 

633 

8.15 

6.24 

Delphinus  delphi 

103 

8.0 

6.67 

Pseudorca  crassidens 

191 

8.0 

6.38 

Table  III.  Summary  of  wild  dolphin  {Delphinus  capensis )  photogrammetric  speed  measurements.  (Ref.  18) 


Pass 

#of 

Observations 

Maximum 

Velocity 

(m/s) 

Velocity 

Range 

(m/s) 

Duration 

Of  Pass 
(s) 

Average 
Speed  Duration 
(§) 

1 

80 

6.60 

2.69  to  6.60 

18.6 

1.44 

2 

106 

5.89 

2.49  to  5.89 

15.2 

1.24 

3 

310 

6.70 

3.07  to  6.70 

18.4 

1.42 

4 

377 

5.56 

2.27  to  5.56 

14.2 

1.23 

5 

171 

5.78 

2.40  to  5.78 

18.4 

1.48 

1  to  5 

1044 

6.60 

2.27  to  6.60 

513.2 

1.34 

433 


HYDRODYNAMICS  OF  WAVE-LIKE  CURVATURE  ON  BODIES  OF  SWIMMING  ANIMALS 


Rudolf  Bannasch 

Technische  Universitat  Berlin 
FG  Bionik  &  Evolutionstechnik 
Ackerstrasse  71-76 
D-13355  Berlin,  Germany 
E-mail:  bannasch@lblO.tu-berlin.de 


Abstract  -  Experimental  studies  on  live  penguins  and  measurements  with  life-sized  models  of  their  trunk  in  a  water  tank  revealed 
extremely  low  drag  coefficients.  An  axi  symmetric  body  based  on  the  body  geometry  of  three  medium  sized  penguin  species  was  found  to 
be  an  excellent  low-drag  laminar  body  by  drag  measurements  in  a  water  tank.  When  the  transition  from  laminar  to  turbulent  flow  was 
triggered  at  5  %  of  the  body  length,  the  surface  drag  coefficients  remained  even  lower  than  those  of  a  turbulent  flat  plate  of  equal  length, 
and  they  declined  at  a  higher  rate  with  increasing  Reynolds  numbers.  Viscous  drag  was  reduced  by  the  characteristic  “stepwise” 
pressure  and  velocity  distribution  developed  along  the  multiply  curved  (wave-like)  outlines  of  that  body.  Turbulent  velocity  fluctuations 
in  the  boundary  layer  remained  at  a  low  level  even  in  the  rigid  model.  Flow  visualization  experiments  on  live  penguins  showed  the  wavy 
contour  to  be  most  efficient  in  conjunction  with  a  compliant  wall.  In  most  cases,  a  regular  pattern  of  transverse  waves  (wave  length  2  -3 
cm)  was  observed  over  the  plumage.  Since  most  flying  and  swimming  vertebrates  have  wavy  body  contours,  comparative  studies  on  the 
development  of  the  respective  proportions  with  size  progression  will  be  useful. 


L  INTRODUCTION 

Evolutionary  adaptation  of  animals  to  sustained  fast  flying  and 
swimming  has  faced  the  same  tasks  as  engineering  of  modem  aircraft,  cars, 
ships  and  submarines,  namely  to  transport  a  given  body  mass  or  volume 
with  minimum  costs  and  to  maintain  optimal  maneuverability  under 
changing  flow  conditions.  Contrary  to  engineering,  nature  had  a  huge 
experimental  ground.  Over  millions  of  years,  a  wealth  of  designs  have  been 
created,  tested  and  optimized.  The  sometimes  spectacular  achievements  of 
animal  locomotion  in  air  and  water  can  be  explained  only  by  optimal 
combinations  of  mechanically  highly  efficient  propulsion  systems  and 
extraordinary  (complex)  drag  reduction  measures.  Here,  engineers  can  still 
learn  from  nature. 

Indeed,  a  comparison  of  the  costs  of  transport  of  animal  flight  with 
that  of  aircraft  and  helicopter  in  a  dimensionless  way  shows  that  nature  has 
found  much  more  economic  solutions  [1].  But  animals  fly  at  quite  low 
Reynolds  numbers  ranging  from  just  under  200  for  small  insects  to  less 
than  106  for  the  fastest  large  birds.  Scaling  rules  predict  that  they  may  not 
deal  with  the  same  flow  and  drag  problems  as  does  engineering.  In  the 
aquatic  environment,  however,  at  least  the  fastest  swimmers  may 
encounter  flow  regimes  comparable  to  those  of  technical  bodies  (e.g. 
subsonic  aircraft,  small  ships  and  submarines).  But,  due  to  the  enormous 
diversity  in  life  styles,  feeding  and  survival  strategies,  principles  of  force 
generation  and  the  many  other  functions  incorporated  in  the  animal's  body, 
many  details  and  structural  solutions  to  the  problem  of  natural  drag 
reduction  still  remain  undiscovered  or  ill-understood. 

This  paper  focuses  on  mechanisms  of  hydrodynamic  drag  reduction. 
Apart  from  other  mechanisms  widely  used  in  nature  (like  polymer  ejection, 
drag  reducing  surfaces  etc.),  shape  optimization  represents  the  basic  and 
most  important  factor  for  drag  reduction. 

II.  LAMINAR  VERSUS  TURBULENT  BODIES 

As  early  as  1800  Cayley  (cited  in  [2])  had  proposed  to  take  the  shape 
of  the  trout  as  an  model  for  the  (future)  design  of  aircraft  fuselages.  About 
one  hundred  years  later,  streamlining  led,  indeed,  to  fish-like  designs,  for 
example  in  the  Parseval-17  airship.  For  such  huge  constructions,  the 
prevention  of  flow  separation  represented  the  most  important 
consideration. 

In  the  sixties,  Hertel  [2,  3]  concluded  that  the  body  geometry  of 
trout,  tuna,  sharks,  dolphins  and  blue  whale,  in  comparison  to  technical 
profiles,  represent  "laminar-flow  spindles".  He  used  this  as  an  argument  to 
replace  the  “transport  tubes”  of  commercial  aircraft  by  laminar  fuselages 
since  the  latter  offer  the  largest  volume  for  the  lowest  drag.  However,  it  is 
obvious  that  Hertel  was  not  interested  in  the  details  of  the  natural  design. 
For  example,  in  considering  the  shape  of  dolphins,  he  totally  ignored  the 
rostrum  and  smoothed  out  the  slightly  wave-like  contour  of  the  body  by 
superimposition  of  a  low  drag  NACA  profile.  Strictly  speaking,  Hertel  did 
just  show  that  the  existing  engineering  knowledge  could  help  to  estimate 
natural  shapes,  but  he  did  not  study  natural  phenomena  experimentally. 

In  feet,  our  knowledge  about  the  boundary  layer  development  in  fast 
swimming  animals  is  rather  poor.  For  the  most  part,  conclusions  have  been 
made  solely  on  the  base  of  technical  analogies. 


Experimental  studies  of  the  fluid  dynamic  properties  of  live  swimming 
animals  are  crucial.  Their  flexible  bodies  are  adaptable  to  particular  flow 
conditions.  In  fish  and  dolphins  the  body  is  strongly  involved  in  the  process 
of  thrust  generation,  and  is  thus  exposed  to  highly  unsteady  effects  which 
can  hardly  be  reproduced  experimentally.  For  the  most  part,  studies  with 
rigid  models  have  been  rather  disappointing,  and  various  numerical 
approaches  to  discover  the  secrets  of  the  dolphin  swimming,  namely  to  solve 
Gray’s  Paradox  [4],  led  to  controversial  results.  Some  authors  [5,  6]  reject 
the  existence  of  any  drag  reducing  mechanisms  in  dolphins,  but  concluded 
that  these  animals  are  more  powerful  than  assumed  before.  Others  [7] 
contend  that  the  hydrodynamic  efficiency  of  the  fluke  has  been  largely 
overestimated.  After  respective  correction  it  turned  out  that.  Gray  was  right. 
These  animals  must  be  able  to  use  special  methods  for  drag  reduction.  Apart 
from  the  ability  to  delay  considerably  the  laminar-turbulent  transition  in  the 
boundary  layer  by  compliant  wall  effects  [8-10]  possibly  in  conjunction 
wife  polymer  secretion  from  the  eye  [1 1]  to  keep  the  turbulence  at  a  low 
level,  drag  reduction  was  referred  by  Romaneko  [7]  mainly  to  favorable 
pressure  gradients  actively  generated  by  the  wave-like  body  motion.  He  had 
conducted  first  measurements  on  the  pressure  fluctuation  and  wall  shear 
stress  on  live  animals. 

However,  the  laminar  hypothesis  might  be  not  applicable  to  all  marine 
animals.  Sharks  seems  to  have  developed  another  mechanism  for  drag 
reduction.  Their  skin  was  found  to  reduce  turbulent  wall  shear  stress  by  its 
“riblef’  structure  [12  - 14]. 

Earlier  results  of  Russian  scientists  summarized  by  Aleyev  [15]  and 
recently  reconsidered  by  Videler  [1]  point  to  a  further  interesting 
mechanism  of  drag  reduction  used  in  nature.  In  swordfish,  the  rostrum 
forms  a  long  and  slender  pre-body  (blade),  which  was  found  both  to  reduce 
the  dynamic  pressure  peak  at  the  frontal  part  of  the  main  body  and  to 
smooth  the  pressure  distribution  further  downstream.  It  may  also  reduce  the 
wall  shear  stress  by  increasing  the  local  Reynolds  numbers  downstream.  But 
most  interesting,  due  to  its  rough  surface,  it  is  likely  to  stimulate  an  early 
transition  from  laminar  to  “micro-turbulent”  turbulent  flow.  Videler’ s 
conclusion  that  the  boundary  layer  can  be  kept  in  that  state  by  the  following 
concave-convex  shape  of  the  head,  and  the  theoretical  assumption  that  such 
a  “micro-turbulent  boundary  layer”  may  behave  like  a  laminar  one,  clearly 
require  experimental  confirmation.  Nevertheless  -  apart  from  sharks  -  the 
swordfish  gives  another  example  for  the  early  development  of  a  turbulent 
boundary  layer  in  marine  animals.  Moreover,  it  represents  a  first  indication 
of  turbulence  management  by  a  multiply  curved  body  profile  in  nature. 

III.  THE  PENGUIN  PHENOMENON 

As  examples  of  shape  optimization  for  fluid-dynamic  purposes, 
penguins  are  a  particularly  interesting  group  of  animals.  Derived  from 
highly  evolved  flying  birds,  they  changed  to  aquatic  life  and  became  the  best 
adapted  birds  to  wing-propelled  diving  and  swimming.  After  several  studies 
conducted  on  different  penguin  species  in  zoos  had  pointed  to  excellent 
hydrodynamic  properties  [16,  17,  18],  a  comprehensive  approach  to  the 
marine  ecology,  energetics,  swimming  and  diving  performances  of  penguins 
was  developed  in  the  framework  of  the  German  Antarctic  Expeditions  [19  — 
23]. 


435 


Telemetry  showed  that  medium  sized  penguins  (body  length  0,65  - 
0,70  m  in  the  swimming  posture)  can  swim  more  than  100  km  per  day  and 
dive  to  maximum  depths  of  ca.  450  m.  Their  preferred  travel  speed  ranges 
from  2  to  3  m/s,  and  the  maximum  speed  is  about  4,5  m/s.  The  larger 
Emperor  penguins  are  somewhat  fester,  and  can  reach  a  maximum  speed 
above  7  m/s. 

Field  metabolic  studies  supplied  evidence  for  low  energy 
consumption  in  under-water  locomotion.  Assuming  the  energy  content  of 
krill  to  be  3700  kJ/kg,  1  kg  of  that  food  would  allow  for  example  a  4  kg 
Adelie  penguin  to  travel  up  to  200  km.  One  may  try  to  illustrate  this  result 
in  technical  terms:  if  this  penguin  would  be  able  to  utilize  benzine  (46700 
kJ/kg)  instead  of  krill,  1  1  of  this  fuel  would  suffice  for  a  ca.  2500  km  long 
trip  in  the  cold  ice  sea! 

These  data  point  to  high  mechanical  efficiency  of  the  propulsion 
system  and  to  particularly  high  achievements  in  body  drag  reduction,  since 
the  biochemistry  of  the  flight  muscles  does  not  differ  from  that  of  other 
birds.  Unlike  in  fish  and  dolphins,  the  penguin’s  trunk  does  not  contribute 
to  thrust  production;  trunk  oscillations  during  a  wing  beat  cycle  are 
moderate.  Therefore,  the  spindle-like  penguin  trunk  may  well  serve  as  live 
example  for  how  energy  may  be  saved  by  shape  optimization  of  stiff 
bodies.  Our  aim  was  to  study  this  experimentally. 

IV.  PENGUIN  BODY  GEOMETRY 

For  a  complex  of  morpho-fiinctional  studies  including  also 
hydrodynamic  investigations,  ten  individuals  were  collected  from  each  of 
the  three  pygoscelid  species:  Gentoo  ( Pygoscelis  papua\  Adelie  (P. 
adeliae )  and  Chinstrap  penguin  (P.  antarctica).  After  measuring  body 
mass,  body  length,  maximum  girth,  that  individual  of  each  specues  which 
was  closest  to  the  mean  values  was  mounted  in  swimming  posture  and 
frozen.  Then,  models  in  glass  fiber  reinforced  plastic  were  made  [24]. 

The  geometry  of  the  casts  (without  wings)  was  compared  to  that  of 
the  original  penguins.  No  differences  were  found,  and  even  very  small 
details  of  the  plumage  were  copied.  The  contours  of  the  three  models  (from 
the  dorsal  and  lateral  view)  were  drawn  to  the  same  scale  with  the  body 
length  taken  as  a  standard  reference  (Fig.  1). 


Fig.  1  Geometry  of  the  penguin  bodies  (three  projections):  Solid 
line:  Adelie,  dashed  line:  Chinstrap,  dotted  line:  Gentoo  penguin. 

Table  1  Geometry  of  penguin  bodies.  A  frontal  area  [m2],  d 
diameter  of  the  frontal  area  [m],  /  body  length  [m],  x<j  abscissa  of  the 
maximum  thickness  [m],  l/d  length  to  thickness  ratio,  x<i  /  /  maximum 
thickness  position. 


Species 

l/d 

xd// 

A 

d=j(4AI  7T) 

P.  antarctica 

4,54 

0,44 

0,01959 

0,158 

P.  adeliae 

4,35 

0,47 

0,02083 

0,163 

P.  papua 

4,00 

0,44 

0,02706 

0,186 

body  of  revolution 

4,237 

0,443 

0,02147 

0,165 

The  body  shapes  of  the  three  species  resemble  one  another  in  being 
spindles  with  high  values  of  maximum  thickness  position  and  thickness 
ratio  (see  also  Table  1).  A  small  degree  of  dorso-ventral  asymmetry  was 
evident  from  the  lateral  view  (Fig.  1  above).  At  the  position  of  maximum 
thickness,  the  cross  section  was  almost  circular.  Overall,  the  geometry  of 
the  penguin  bodies  would  characterize  them  as  laminar-flow  spindles 
(sensu  Hertel  [2,  3].  However,  the  structure  of  the  beak  and  a  certain 


roughness  at  the  beginning  of  the  plumage  suggests  that  the  transition  from 
laminar  to  turbulent  boundary  layer  may  be  triggered  in  the  very  frontal 
part  of  the  body,  and  moreover  the  "wave-like"  outlines  of  the  forebody  look 
somewhat  unusual. 


Based  on  the  arithmetic  means  of  the  respective  diameters  at  70  points 
along  the  axis,  an  axisymmetric  body  of  revolution  (Table  1,  Fig.  2)  was 
turned  on  a  lathe. 


Fig.  2  Body  of  rotation  derived  from  the  penguin  data 

V.  FLOWVISUALISATION  AND  DRAG  MEASUREMENTS 

Visualisation  experiments  in  a  smoke-wind  tunnel  showed  a  smooth 
flow  around  the  penguin  body  (Fig.  3).  Even  at  a  free  stream  velocity  of  1 1 
m/s  (which  corresponds  to  0,7  m/s  in  Antarctic  seawater)  separation 
occurred  only  in  the  tail  region.  Some  increase  of  the  velocity  caused  a 
downstream  shift  of  the  point  of  detachment  and  thereby  a  reduction  in  the 
diameter  of  the  wake.  It  can  be  predicted,  that  at  the  normal  travel  speed  of 
penguins  (ca.2  -  2,5  m/s)  flow  separation  at  the  body  surface  does  not  occur 
at  all. 


Fig.  3  Model  of  a  Gentoo  penguin  in  the  smoke-wind  tunnel  (steam 

velocity  1 1  m/s) 

In  order  to  cover  the  range  of  Reynolds  numbers  used  by  the 
respective  penguin  species  in  their  natural  environment,  drag  measurements 
were  conducted  in  the  large  circulating  tank  of  the  Versuchsanstalt  fur 
Wasserbau  und  Schiflbau  (VWS;  the  Berlin  Model  Basin).  In  the  test 
section  (8  m  long  and  5  m  wide)  wall  effects  were  excluded.  The  water 
depth  was  adjusted  to  1.5  m  by  elevation  of  the  floor.  The  turbulence  in  the 
circulating  tank  was  relatively  high.  The  turbulence  factor  was  1.8  -  2.0 
(determined  by  means  of  the  critical  Reynolds  number  of  an  ideal  sphere). 
The  penguin  models  were  fixed  to  steel  bars  (length  1  m,  diameter  15  mm) 
placed  in  the  long  axis  of  the  body.  The  end  of  the  bar  was  attached  to  a 
vertical  rod  encapsulated  by  a  low  drag  cowling,  and  the  rod  was  attached 
to  a  balance.  The  models  were  submerged  to  a  depth  of  75  cm.  This  was 
much  deeper  than  3  times  the  vertical  height  of  the  body  in  a  swimming 
position,  which  is  a  depth  below  which  drag  augmentation  by  surface  effects 
is  negligible  [2], 


436 


Fig.  4  shows  the  frontal  drag  coefficients  cDf  of  the  penguin  models 
plotted  against  Reynolds  numbers  Red  (using  the  diameter  d  as  reference 
length).  All  three  models  showed  a  very  similar  characteristic  best 
approximated  by  a  logarithmic  function  cDf  —  11.975  Red  _0’4434 
(correlation  coefficient  R  -  -0,943,  p  -  0,001). 


10° 

7 

# 

5 

a  * 


10-2 


°  P.  adeliae 

□  P.  papua 

*  P.  antarctica 

•  body  of  revolution 

♦  body  of  revolution 


with  turbulence  generator 


5  0  7  8  8  1  0s  2  3  *  5  8  7  8  9  1  03 


Red 


Fig.  4  Frontal  drag  coefficients  plotted  against  Reynolds 
numbers.  In  this  graph,  Re  was  calculated  by  using  the  maximum 
diameter  d  as  reference  length. 

At  lower  Re,  the  results  coincided  with  those  of  other  authors  [17], 
but  the  best  values  (cp/  =  0,03)  obtained  from  the  Adelie  and  Gentoo 
models  at  Red,max  (flow  velocity  4,5  m/s)  were  surprisingly  low. 

The  body  of  revolution  showed  an  opposite  tendency.  Starting  with 
lowest  values  (just  under  0,02  !)  the  cDf  declined  first  to  0,0156  (at  Red  = 
2,33 HO5).  Thereafter  it  increased  to  finally  0.03  and  then  decreased  again 
following  the  regression  line  of  the  original  penguin  models.  This  was 
clearly  an  effect  of  transition  from  laminar  to  turbulent  flow  in  the 
boundary  layer.  To  prove  this  experimentally,  a  1  mm  thick  wire  ring  was 
attached  to  the  nose  of  the  body  in  order  to  trigger  the  transition  at  5  %  of 
the  body  length.  Thereafter,  the  body  of  revolution  showed  nearly  the  same 
characteristics  observed  in  the  penguin  models  (Fig.  4).  From  this 
similarity  we  concluded  that  the  boundary  layer  in  our  penguin  models 
must  also  have  been  turbulent.  At  this  stage,  we  could  not  answer  the 
question  about  applicability  to  live  animals,  but  the  axisymmetric  penguin¬ 
like  body  seemed  to  offer  promising  perspectives  for  technical  applications. 


Re  i 

Fig.  5  Surface  drag  coefficients  of  the  body  of  rotation  plotted 
against  Reynolds  numbers.  Note  that  in  this  graph  Re  was  calculated 
by  using  the  body  length  /  as  reference  length.  The  two  values  in 
brackets  should  be  neglected  (artificial  drag  increase  due  to 
unfavourable  Froude  numbers  in  the  test  section).  Dotted  lines: 
laminar  (below)  and  turbulent  (above)  flat  plate.  Dashed  line  on  top: 
turbulent  bodies  with  a  length  to  thickness  ratio  of  4.2,  cf.  [25]. 

To  compare  the  results  obtained  from  the  body  of  rotation  to  those 
reported  in  [25],  the  surface  drag  coefficients  cDo  were  plotted  against 
Reynolds  numbers  using  the  body  length  /  as  characteristic  length  (Fig.  5). 
Most  surprising,  in  the  turbulent  case  the  surface  drag  coefficients  of  our 
axisymmetric  body  remained  even  lower  than  those  of  a  turbulent  flat  plate 
of  equal  length,  and  with  increasing  Reynolds  numbers  they  declined  at  a 


higher  rate.  Drag  coefficients  were  some  30-35  %  lower  than  those  reported 
for  the  best  turbulent  technical  bodies  [25]. 

VI.  SOME  INSIGHTS  INTO  THE  MECHANISM  OF  DRAG 
REDUCTION 

1.  Unusual  pressure  and  velocity  distribution  along  the  contour  of 
the  axisymmetric  penguin-body 

Together  with  students  of  the  Institut  fur  Luff-  und  Raumfahrttechnik 
der  TU  Berlin,  another  (hollow)  model  of  the  body  of  rotation  was  built  and 
equipped  with  pressure  holes.  We  had  to  cut  off  the  tail  of  the  body  to 
facilitate  connection  of  the  tubes  glued  inside  the  holes  to  a  pressure 
transducer  (via  a  scanivalve)  outside  of  the  test  section.  The  pressure 
distribution  was  determined  in  a  wind  tunnel  at  various  flow  velocities. 
Additional  comparative  measurements  were  carried  out  on  both  bodies  of 
rotation  with  an  external  static  pressure  sonde  (diameter:  1  mm), 

Fig.  6  shows  the  distribution  of  the  dimensionless  pressure  coefficients 
cP  obtained  experimentally  by  both  methods  in  comparison  with  potential 
flow  calculations  (panel  method  without  consideration  of  the  displacement 
thickness). 


Fig.  6  Pressure  distribution,  experimental  and  numerical  data. 

Apart  from  small  deviations  at  the  points  indicated  by  arrows 
(probably  two  defective  pressure  holes),  the  results  coincide  well  for  the 
frontal  part  of  the  body.  At  the  rear,  the  differences  became  somewhat  larger 
since  each  method  implied  certain  disadvantages.  The  general  tendency, 
however,  was  similar  in  all  three  approaches. 

Contrary  to  conventional  bodies,  where  the  pressure  continuously 
decreases  towards  and  increases  beyond  the  maximum  girth  position,  a  more 
stepwise  pressure  distribution  was  found  in  the  present  case,.  Most 
remarkable  were  the  roughly  similar  gradients  (slopes)  along  the  forehead, 
the  beginning  of  the  trunk,  and  -  with  the  opposite  sign  -  also  at  the  end  of 
the  trunk.  Consequently  over  the  convex  areas,  the  flow  was  accelerated  or 
decelerated  at  a  nearly  constant  rate,  respectively.  Over  the  intervening 
slender  (concave)  parts,  the  pressure  -  and  consequently  also  the  flow 
velocity  -  remained  nearly  constant  (plateau).  This  unusual  pressure 
fluctuation  can  be  described  by  a  secondary  wave  superimposed  on  the  main 
curve.  The  wave  length  increased  in  correspondence  with  the  local  Reynolds 
number.  It  should  be  noted,  however,  that  at  the  beak,  the  depression  in  the 
pressure  distribution  changed  to  a  plateau  when  the  transition  from  laminar 
to  turbulent  flow  was  triggered  at  that  point  by  a  wire  ring.  The  downstream 
pressure  distribution  was  not  altered  by  this  measure. 

The  relatively  good  coincidence  of  the  experimental  results  with  those 
obtained  from  potential  flow  calculations  indicates  a  low  pressure  drag.  The 
total  drag  of  the  given  body  seems  to  be  mostly  due  to  friction. 


2.  Paint  flow  visualisation 

To  get  some  insight  into  the  development  of  the  near  wall  flow 
pattern,  the  paint  flow  method  was  used.  The  body  of  rotation  was  evenly 
painted  with  a  mixture  of  petroleum,  oil  acid  and  titanium  white  and 
exposed  then  to  an  air  stream  of  20  m/s  (Re/  =  9.3  105).  This  was  the 

maximum  speed  allowed  by  the  free  steam  wind  tunnel  of  our  department. 
After  evaporation  of  the  oil,  the  remaining  titanium  gave  an  impression  of 
the  flow  pattern  at  the  surface  of  that  multiple  curved  body.  Fig.  7  shows  the 


437 


result  from  two  different  experiments  (without  and  with  turbulence 
generator  at  the  base  of  the  beak). 


Fig.  7  Paint-flow  visualisation  on  the  body  of  rotation  without 

(above)  and  with  turbulence  generator  (below).  Top  view  in  both 

cases. 

In  the  picture  without  turbulence  generator  (Fig.  7  above),  three 
main  zones  can  be  distinguished.  In  the  frontal  part  (up  to  ca.  40%  of  the 
body  length),  the  flow  was  stepwise  accelerated  and  remained  laminar.  The 
tiny  structure  of  the  pigments  indicates  a  relatively  high  wall  shear  stress. 
Friction  was  highest  over  the  convex  parts  (tip  of  the  beak,  forehead, 
frontal  part  of  the  trunk).  However,  some  relaxation  of  the  boundary  layer 
(increase  of  the  structures  imprinted)  could  be  observed  along  the  concave 
parts  at  the  origin  of  the  beak  and  in  the  neck  region.  The  second  zone 
reaches  from  ca.  40  to  70  %  of  the  body  length.  Here,  the  flow  seemed  to 
be  still  laminar,  but  the  structures  imprinted  grew  very  fast.  The  diverging 
paint  flow  lines  indicate  a  considerable  relaxation  of  the  boundary  layer. 
Especially  at  the  sides  of  the  body,  the  pigments  were  driven  in  an  oblique 
direction  since  gravity  started  to  dominate  over  the  friction  forces.  Finally, 
with  a  sharp  border,  a  (probably)  laminar  detachment  zone  with  turbulent 
reattachment  at  the  tail  was  formed. 

Possibly  in  the  present  visualisation  experiment,  the  wind  velocity 
was  too  low  to  keep  the  flow  fully  attached.  It  was  also  possible  that  the 
rear  of  the  body  was  not  optimally  shaped.  When  constructing  the 
axisymmetric  body,  we  did  not  know  how  to  deal  with  the  feet.  Finally, 
that  part  was  smoothed  by  hand.  The  design  was,  however,  not  that  bad.  At 
the  tail,  the  flow  reattached,  and  a  drag  penalty  due  to  an  unbalanced 
pressure  distribution  could  be  avoided.  Otherwise  the  extremely  low  drag 
coefficients  (CDo  -  0.018)  measured  at  similar  Reynolds  numbers  in  the 
water  tank  could  hardly  be  explained. 

The  picture  changed  completely  when  the  turbulence  generator  (wire 
ring)  was  placed  at  the  nose  of  the  body  (Fig.  7  below).  The  concentration 
of  titanium  white  pigments  at  the  base  of  the  beak  marked  a  stationary  ring 
vortex  generated  by  the  wire.  The  respective  separation  area  had  a  sharp 
border.  In  the  first  experiment,  a  similar  patch  was  formed  in  that  area,  but 
its  margins  were  blurred;  possibly  a  ring  vortex  or  laminar  detachment 
bubble  was  also  formed  at  the  end  of  the  beak  without  turbulence 
generator.  However,  due  to  the  laminar  reattachment  it  did  not  influence 
the  flow  pattern  downstream.  But  in  the  second  case,  the  flow  reattached 
turbulentiy.  Although  larger  disturbances  were  immediately  dampened  out 
due  to  the  flow  acceleration  at  the  following  convex  forehead,  certain 
microstructures  introduced  into  the  boundary  layer  by  the  wire  ring 
survived.  The  paint  flow  pattern  increased  in  size  continuously  but  rather 
slowly.  Even  at  the  end  of  the  body,  these  structures  remained  much 
smaller  than  in  the  experiment  without  a  turbulence  generator.  The 
influence  of  gravity  on  the  direction  of  the  paint  flow  was  less  pronounced, 
implying  that  the  wall  shear  stress  was  higher.  Since  the  boundary  layer 
contained  more  energy,  the  detachment  zone  was  shifted  towards  the  tail  of 
the  body.  This  picture  corresponds  well  with  Fig.  3  (smoke  visualisation 
on  the  cast  of  an  original  Gentoo  penguin). 

In  general,  the  paint  flow  pattern  obtained  in  the  second  experiment 
suggests  a  certain  similarity  with  the  structure  of  the  plumage  in  real 
penguins,  in  which  the  size  of  the  feathers  increases  from  the  head  towards 
the  end  of  the  body  at  a  similar  rate.  It  might  be  worth  noting  here  also  that 
the  microstructure  of  the  penguin  plumage  is  somewhat  reminiscent  of  the 


riblet  pattern  known  from  the  shark  skin  to  reduce  the  turbulent  wall  shear 
stress  [14]. 

3.  Hot-wire  anemometry 

Further  insights  into  the  near  wall  flow  at  the  penguin-like  body  of 
rotation  were  gained  by  using  hot-wire  anemometry  in  the  large  (closed) 
wind  tunnel  of  the  Hermann-Fottinger  Institut  fur  Thermo-  und 
Fluiddynamik  der  TU  Berlin.  Here,  we  could  obtain  a  flow  velocity  of  25 
m/s  at  which  the  Reynolds  number  (Rei  =  1,2 TO6)  corresponded  to  that 
preferably  used  by  the  pygoscelid  penguins  in  the  Antarctic  Sea  (mean 
travel  speed:  2.3  m/s  in  saltwater  at  4  °C). 

Owing  to  the  limited  experimental  time  provided,  detailed 
investigations  could  be  conducted  only  on  the  flow  around  the  wave-like 
frontal  part  of  the  body.  Fig.  8  shows  the  velocity  distribution  in  the  outer 
flow  field. 


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Fig.  8  Velocity  distribution  in  the  outer  flow  around  the  frontal  part 

of  the  axisymmetric  penguin  body. 

In  this  picture,  the  stagnation  point  was  not  well  marked.  It  lay  close 
to  the  tip  of  the  beak.  Generally,  the  influence  of  the  body  on  the  flow  field 
in  front  remained  moderate.  A  zone  of  decelerated  flow  was  vertically 
extended  over  the  concave  part  of  the  beak.  Following  a  short  acceleration 
over  the  convex  forehead,  the  flow  velocity  near  the  wall  remained  nearly 
constant  at  the  neck.  This  corresponds  to  the  first  pressure  plateau  in  Fig.  6. 
At  about  26  %  of  the  body  length,  the  free  stream  velocity  was  reached  (no 
variation  with  distance  from  the  body  surface).  This  was  the  point  where  the 
pressure  curve  crossed  the  abscissa  (Fig.  6).  Downstream,  a  zone  of 
hypervelocity  was  developed,  with  as  expected,  centre  at  the  thickest  part  of 
the  body. 

The  effect  of  this  unusual  flow  pattern  on  the  velocity  profiles  within 
the  boundary  layer  is  shown  in  Fig.  9.  Most  remarkable  in  both  experiments 
(without  and  with  turbulence  generator)  was  that  the  thickness  of  the 
boundary  layer  increased  suddenly  at  the  base  of  the  beak  and  thereafter 
remained  nearly  constant.  In  the  laminar  case,  the  S-shaped  velocity  profiles 
C-F  might  suggest  the  flow  was  close  to  separating.  That  would  point  to 
extremely  low  friction  in  this  area. 

It  was  evident  from  the  doubly  curved  profile  C  that  a  shallow 
separation  bubble  was  formed  at  the  base  of  the  beak  (see  discussion  of  the 
paint  flow  experiment). 

When  the  body  was  equipped  with  the  turbulence  generator,  the 
boundary  layer  was  about  three  times  thicker  than  in  the  laminar  case,  and 
the  velocity  profiles  were  more  rounded.  The  unusual  shape  of  profile  C  can 
be  explained  as  a  registration  of  the  wake  of  the  wire  which  was,  obviously, 
somewhat  too  large  (diameter  of  the  wire  in  this  case:  2  mm).  The 
downstream  profiles  were  no  longer  S-shaped. 

The  turbulence  profiles  shown  in  Fig.  10  support  the  ideas  developed 
from  the  paint  flow  experiments.  The  huge  disturbances  introduced  by  the 
wire  ring  serving  as  turbulence  generator  (profile  C)  were  quickly 
dampened  out.  Further  downstream  the  turbulent  velocity  fluctuations  were 
considerably  reduced  and  were  restricted  to  a  relatively  thin  layer  near  the 
wall.  Although  the  overall  frequency  spectrum  was  quite  broad,  at  the 
maximum  thickness  position  of  the  body  a  definite  peak  was  observed  at  3. 1 
kHz. 


438 


Fig.  9  Velocity  profiles  in  the  boundary  layer  at  the  wavy  frontal 
part  of  the  body  measured  by  hot-wire  anemometry.  The  horizontal 
lines  indicate  the  boundary  layer  thickness  corresponding  to  99  %  of 
the  velocity  of  the  outer  flow.  Top:  position  of  the  measuring  points; 
middle:  velocity  profiles  without  turbulence  generator;  bottom:  with 
turbulence  generator. 


Fig.  10  Turbulence  profiles.  Transition  was  stimulated  at  ca.  5%  of 

the  body  length.  Points  of  measurement  same  as  indicated  in  Fig.  9. 

TU  =  •y/fr^/Uoo’  with  mean  of  the  turbulent  velocity  fluctuation, 

free  stream  velocity,  cf.  [26]. 

When  an  early  transition  was  stimulated,  the  magnitude  of  the 
velocity  fluctuation  within  the  boundary  layer  was  much  lower  at  the  end 
of  the  body  than  in  the  case  of  natural  transition  (Fig.  11).  Although  in  the 
last  experiment,  the  flow  velocity  was  higher,  so  that  the  detachment  zone 
at  the  end  of  the  body  was  likely  to  disappear,  the  result  coincided  well 
with  the  pictures  observed  in  the  paint  flow  experiments. 

Apart  from  the  99  %  thickness,  the  boundaiy  layer  is  characterised 
also  by  the  displacement  thickness  8i  and  the  momentum  thickness  82  [26]. 
Our  investigations  focused  only  on  the  frontal  part  of  the  penguin-like 
body  of  rotation,  but  even  here  remarkable  differences  from  those  of  a  flat 
plate  and  conventional  streamlined  bodies  could  be  observed.  In  the 
axisymmetric  penguin  body,  the  development  of  8i  and  82  was  in  general 
analogous  to  that  of  the  99  %  thickness.  At  the  end  of  the  beak,  all  three 
boundary  layer  thickness  parameters  suddenly  increased  to  values  1.5  - 
2.0  times  higher  than  those  of  the  flat  plate  at  a  similar  distance  from  the 
leading  edge.  In  the  body  of  rotation,  the  first  pressure  step  seemed  to 
generate  boundary  layer  conditions  which  can  be  found  on  a  flat  surface 
only  at  considerably  higher  local  Reynolds  numbers,  and  in  usual  (three- 
dimensional)  bodies  even  later.  This  mechanism  may  contribute  to  a 
drastic  reduction  of  the  local  wall  shear  stress.  But  it  involves  also  a  certain 
risk.  At  the  pressure  step  at  the  end  of  the  beak,  82  did  not  jump  as  much  as 
8|.  Consequently,  the  shape  parameter  Hi2  (Hi2  -  81  /  82)  showed  a  peak 
at  this  point.  In  the  laminar  as  well  as  in  the  turbulent  case,  it  considerably 
exceeded  the  respective  values  known  to  be  crucial  in  view  of  flow 
detachment  from  a  flat  surface.  Downstream  that  point,  the  shape 


parameter  recovered  to  values  slightly  below  the  critical  ones  (laminar 
case),  or  became  even  more  stable  (in  the  turbulent  case). 


Fig.  1 1  Velocity  fluctuations  at  the  rear  of  the  body  (position:  see 
arrow  in  Fig.  9).  a  (left  side):  without  and  b  (right  side)  with 
turbulence  generator;  h  distance  from  the  body  surface  (from  top  to 
bottom:  0.1  mm,  0.6  mm,  3.1  mm,  and  7.1  mm). 

It  should  also  be  noted  that  the  nose  of  the  test  body  might  have  been 
less  optimally  shaped  than  the  asymmetrical  beak  of  a  real  penguin.  It  was 
possible  that  the  separation  bubble  observed  in  our  experiments  was  an 
artefact  resulting,  on  the  one  hand,  from  the  means  of  the  contour  co¬ 
ordinates  being  used  and,  on  the  other  hand  form  the  large  diameter  of  the 
wire  ring  attached.  So,  there  seems  to  be  some  potential  for  further 
optimisation  of  the  artificial  body. 

Independent  investigations  of  the  wake  of  the  axisymmetric  penguin 
body  conducted  in  another  wind  tunnel  using  hot-wire  anemometry  as  well 
as  studies  on  a  somewhat  smaller  model  in  a  circulating  water  tank  by 
means  of  Laser-Doppler-Anemometry  supported  the  very  low  drag 
coefficients  of  the  given  body  shape. 

The  penguin  body  seems  to  be  evolved  to  get  use  from  several  drag 
reducing  mechanisms  in  combination.  At  the  tip  of  the  beak,  the  only  way  to 
reduce  the  effect  of  the  unavoidably  high  friction  on  the  total  drag  is  to  keep 
the  diameter,  and  thereby  the  wetted  surface,  small.  Since  the  transition 
causes  a  peak  in  the  wall  shear  stress,  it  might  effective  to  trigger  the 
transition  while  the  circumference  is  still  small.  The  drag  penalty  resulting 
from  early  onset  of  turbulence  might  be  moderate  since,  simultaneously, 
much  stress  is  taken  out  by  making  the  boundary  layer  thicker.  Here,  one 
may  question  the  advantage  of  an  early  increase  of  the  boundary  layer 
thickness  since  the  total  drag  equals  the  momentum  loss  at  the  end  of  the 
body.  Unfortunately,  we  could  not  systematically  study  what  really 
happened  at  the  rear  or  in  the  wake  of  the  penguin-like  body.  However,  at 
the  position  of  the  maximum  diameter,  all  three  thickness  parameters  of  the 
boundaiy  layer  were  about  half  to  two  thirds  of  the  values  for  a  flat  plate. 
The  convex  forehead  serves  as  a  kind  of  high-pass  filter  allowing  only  a 
certain  micro-turbulence  to  survive.  Keeping  the  boundary  layer  at  a  nearly 
constant  thickness,  then,  may  help  to  restrict  the  frequency  band.  Ideally 
(and  hypothetically)  this  “tuning”  mechanism  may  restrict  the  turbulent 
pressure  and  velocity  fluctuations  to  those  best  controllable  by  the 
dampening  properties  of  a  compliant  body  surface.  Although,  this  has  to  be 
verified  experimentally;  there  is  every  indication  that  this  mechanism  plays 
an  important  role  in  drag  reduction  of  life  penguins. 

VlL  FLOW-VISUALIZATION  IN  LIFE  PENGUINS 

During  our  last  Antarctic  expeditions,  special  hydrodynamic  studies 
were  carried  out  on  live  penguins  swimming  in  a  2 1  m  long  still  water  tank 
(cross  section  ca.  lx  1  m).  For  this  purpose,  a  novel  method  for  flow 
visualization  in  live  animals  with  controlled  dye  ejection  from  underneath  of 
the  plumage  was  developed.  In  combination  with  conventional  video  and 
high-speed  video  analyses,  fundamental  insights  into  the  details  of  the 
boundary  layer  development  in  various  flow  conditions  and  into  its 
interaction  with  the  vortex  system  generated  by  the  wings  could  be  obtained. 
These  visualization  experiments  confirmed  that  transition  occurred  in  the 
most  frontal  part  of  the  bird’s  body.  However,  the  boundary  layer  never 
became  „chaotic“  further  downstream.  In  most  cases,  a  quite  regular 


439 


wavelike  pattern  (wave  length  2  -3  cm  with  only  the  amplitude  increasing 
towards  the  end  of  the  body)  was  formed.  The  waves  had  a  velocity  of 
approx.  95  %  of  the  swimming  speed,  and  appeared  to  be  nearly  stationary 
in  the  fluid  (Fig.  12). 


Fig.  12  Boundary  layer  visualisation  in  a  live  Gentoo  penguin. 
Above:  a  single  picture  printed  out  from  video  records.  Below: 
Scheme  obtained  from  the  entire  sequence.  1  air  bubble,  2  and  3 
indicate  the  places  of  dye  application.  Note  the  quite  regular  pattern 
of  the  intermittent  flow. 

Corresponding  to  the  change  in  sense  of  wing  circulation  during  each 
stroke  phase,  the  waves  became  more  pronounced  on  the  dorsal  and  ventral 
side  of  the  body  during  the  up-stroke  and  down-stroke,  respectively.  By 
means  of  the  high-speed  video  (250  frames  per  second),  the  formation  of 
closed  looped  roll  cells  could  be  observed  in  the  boundary  layer  of  an 
Adelie  penguin  gliding  at  a  relatively  low  speed  (ca.  1.2  m/s)  (Fig.  13). 


Fig.  13  Schematic  graph  of  a  rare  high-speed  video  picture  showing 
the  development  of  ring  structures  in  the  boundary  layer  of  an  Adelie 
penguin. 

Apart  from  passive  mechanisms  (multiple  curvature  effects, 
compliance  and  microstructure  of  the  plumage)  possibly  responsible  for 
maintaining  boundary  layer  turbulence  an  overall  low  level,  the  flow 
visualization  experiments  showed  that  the  structure  of  the  near  wall  flow 
can  be  managed  by  a  number  of  active  mechanisms.  Tiny  adjustments  of 
the  body  shape  (changes  in  the  position  of  the  head,  neck,  feet  and  tail)  and 
thereby  of  the  pressure  and  velocity  distribution  had  a  remarkable 
influence  on  the  flow  pattern. 

Additionally  in  some  cases,  in  the  beginning  of  diving,  some  parts  of 
the  body  became  covered  by  a  thin  film  of  air  that  reduces  the  wall  shear 
stress  locally  to  an  absolute  minimum.  These  areas  corresponded  well  to 
those  characterized  by  a  low  pressure  gradient  in  the  earlier  model 
experiments.  For  the  most  part,  the  air  was  squeezed  out  of  the  plumage. 
The  most  persistent  air  bubble  was  the  one  in  the  neck  (see  Fig.  12),  which 
was  frequently  renewed  by  exhalation,  and  was  subjected  to  oscillation.  At 
this  location  a  vortex  seems  to  be  formed  which  is  assumed  to  underlie  the 
same  oscillation.  This  could  be  a  possible  explanation  for  the  mechanism 
generating  the  running  wave  observed  further  downstream  in  the  boundary 
layer. 


Based  on  the  pictures  on  the  boundary  layer  development  in  life 
penguins,  one  may  speculate  that  the  early  generation  of  coherent  vortex 
structures  might  be  an  effective  measure  to  stabilize  the  near-wall  flow,  and 
to  prevent  “chaotic”  developments  even  at  the  end  of  the  body.  The  special 
pressure  distribution  along  the  wavy  contour  of  the  body  and  the 
compliance  of  the  surface  of  the  plumage  seem  to  be  the  mechanisms  to 
control  this  process. 

Finally,  it  should  be  mentioned  that  an  extraordinary  measure  to 
drastically  reduce  body  drag  temporarily  could  be  a  sudden  ejection  of 
large  amounts  of  air  bubbles  by  the  bird.  Occasionally,  the  saturation  of  the 
boundary  layer  with  gas  bubbles  can  be  observed  when  the  animals  try  to 
achieve  extreme  acceleration  e.g.  during  escape  reactions  or  before  jumping 
out  of  the  water. 

VIII.  DISCUSSION  AND  OUTLOOK 

The  possibility  to  reduce  viscous  drag  by  alternating  concave-convex 
surfaces  has  been  explored  experimentally  and  theoretically  in  the  NASA 
Langley  Research  Centre  [27  -29].  Most  interesting  in  the  present  context 
are  the  experiments  with  nose  bodies.  These  experiments  were  aimed  to 
make  application  of  the  fact  that  compared  to  a  flat  surface,  the  effect  of 
streamwise  convex  curvature  is  to  reduce  skin  friction,  and  the  level  remains 
lower  even  after  the  curvature  is  removed.  However,  the  axial  distribution 
of  the  cross-sectional  area  ratio  was  found  to  be  critical  to  separation.  A 
solution  to  this  problem  was  found  by  implementing  the  drag  reduction 
concept  over  several  short  fetches  of  curvatures  instead  of  a  single  long 
fetch.  In  result,  a  three-stage  nose  body  was  developed  (Fig.  14). 


1.0 


B/d 


Fig.  14  Computed  surface  pressure  distribution  (above),  and  wall 
shear  stress  (below)  in  a  three-stage  nose  body  (solid  line)  compared 
with  equivalent-area  (dashed  line)  and  equivalent-volume  (chain  line) 
half-elliptic  noses  (redrawn  from  [27]). 

Thus,  the  application  of  the  convex  curvature  concept  led  to  a 
structural  solution  quite  similar  to  that  developed  by  nature  in  40  million 
years  of  evolution.  The  respective  proportions  of  the  three  stages  in  the 
frontal  part  of  the  penguin  body  were,  however,  different  from  that  of  the 
three-stage  nose  body,  and  a  local  pressure  increase  was  observed  only  at 
the  end  of  the  beak.  But  even  this  part  of  the  pressure  curve  changed  to  a 
plateau  when  a  turbulence  generator  was  attached  to  the  model.  In  the 
“natural”  design,  the  convex  parts  were  connected  not  by  cylinders  but  by 
concave  sections.  In  order  to  take  advantage  of  the  “memory  effect”  along 
these  parts,  it  might  be  more  effective  to  maintain  the  flow  velocity  constant 
instead  of  decelerating  it  before  acceleration  follows  in  the  next  stage.  With 
the  exception  of  maximum  girth  position,  the  surface  flow  velocity  vector 
include  always  a  component  directed  perpendicularly  to  the  axis  of  the 
body.  If  maintaining  this  constant  as  well,  the  local  cross-sectional  area 
must  change  also  along  the  intervening  sections.  In  this  way,  the  length  to 
thickness  ratio  and  thereby  the  surface  to  volume  ratio  of  the  body  can  be 
reduced.  The  design  of  respective  axisymmetric  bodies  seems  to  be  a  good 
way  to  obtain  a  better  understanding  of  wave-like  curvature  effects. 


440 


Recently,  some  numerical  approaches  have  proved  the  Evolution 
Strategy  [30,  3 1]  to  be  an  appropriate  method  to  achieve  optimisation  in  a 
parallel  way  as  used  by  nature.  The  first  attempt  in  this  direction  was  made 
by  Pinebrook  already  in  1982  [32].  Fig.  15  shows  the  result  of  an 
optimisation  experiment  aimed  to  minimise  the  drag  of  a  turbulent  body  of 
revolution  at  Re  =  108.  The  transition  from  laminar  to  turbulent  flow  was 
fixed  at  3  %  of  the  body  length. 


Fig.  15  Evolution  of  an  axisymmetric  body  profile  in  the  process  of 
numerical  shape  optimisation  (after  [32]).  Reynolds  number  108;  the 
numbers  indicate  the  respective  generation;  below:  profile  of  a  thick 
body;  dotted  line:  initial  shape,  solid  line:  final  shape. 

In  Pinebrook’ s  approach,  the  body  contour  was  described  by  only  20 
contur  points  equidistant  with  respect  to  the  central  axis.  These  points  were 
varied,  with  the  restriction  that  the  maximum  diameter  and  the  fineness  ratio 
were  maintained.  Compared  to  the  initial  shape,  the  body  drag  could  be 
(numerically)  reduced  by  20  -  30  %,  After  600  generations,  a  tuna-like 
shape,  and  thereafter  a  spindle  somewhat  reminiscent  of  the  penguin  shape 
with  a  well  pronounced  tail  and  a  more  pointed  nose  was  developed. 
Obviously,  most  of  the  drag  reduction  resulted  from  reduction  of  the  body 
surface.  In  consequence,  the  bodies  lost  a  considerable  part  of  their  volume. 

In  a  new  approach  developed  in  co-operation  with  the  University  of 
Stuttgart  those  undesirable  effects  could  be  avoided.  The  task  was  to  find  the 
optimal  shape  for  a  given  volume  under  any  (given)  flow  conditions.  Some 
results  obtained  from  an  early  version  of  that  CFD  programme  were 
published  [33].  Meanwhile,  the  programme  could  be  improved  further. 
However,  based  on  the  calculation  methods  implemented  as  yet,  multiple 
curvature  effects  did  simply  not  occur  even  in  these  simulations.  In  a 
numerical  evaluation  of  the  penguin-like  body,  the  shape  of  the  drag  curve 
(see  Fig.  4  and  5)  could  be  confirmed.  The  curve  was,  however,  shifted  to 
drag  coefficients  ca.  20  %  higher  than  those  obtained  experimentally. 
Validation  experiments  are  in  preparation  to  find  out  whether  the 
measurements  were  incorrect  or  the  turbulence  model  used  in  the  calculation 
was  insufficient  for  the  this  particular  application. 

Nevertheless,  since  most  of  the  higher  evolved  flying  and  swimming 
animals  show  wavy  body  contours,  comparative  studies  on  the  curvature 
development  with  size  progression  seem  to  be  promising.  Fig.  16  shows  a 
comparison  of  the  outlines  from  three  different  sized  penguin  species. 

In  these  three  species,  the  body  length  (in  the  swimming  posture) 
changes  at  a  ration  of  ca.  1  :  2  :  3,  and  -  considering  that  they  swim  at 
different  speeds,  and  the  kinematic  viscosity  in  their  marine  environment 
varies  with  temperature  and  salinity  -  the  preferably  used  Reynolds  numbers 
vary  at  a  ratio  of  about  1:2:4,  respectively.  The  Little  penguin  has  a 


slender  beak  and  a  relatively  big  head,  whereas  the  contour  wave  in  the 
forebody  of  the  Emperor  is  more  extended,  and  its  amplitude  increases  with 
length.  The  shape  of  the  Gentoo  seems  to  be  an  intermediate  stage  between 
these  two  examples.  The  superimposition  of  the  contours  shows  that  where  the 
one  curve  has  a  maximum,  the  next  one  has  a  minimum,  and  so  on..  This 
comparison  suggests  that  there  might  be  some  distinct  (“harmonic”)  solutions 
to  that  kind  of  shape  adaptation. 


Fig.  16  Comparison  of  the  body  contours:  Little,  Gentoo  and  Emperor 
penguin,  above:  side  view,  below:  top  view. 

Considering  further,  that  a  certain  dorso-ventral  asymmetry  is  evident 
in  the  body  shape  of  mostly  all  animals  adapted  to  fast  sustained  swimming, 
the  understanding  of  the  wave-like  curvature  concept  in  a  three  dimensional 
way,  may  eventually  lead  to  completely  new  and  even  more  “organic” 
designs  in  engineering.  To  find  the  “composition  rules”  (the  author  believes 
that  they  exists)  will  be  particularly  useful  for  example  to  better  integrate 
cockpits  etc.  into  the  shape  of  the  fuselage. 


DC  ACKNOWLEDGEMENT 

The  studies  on  Antarctic  penguins  were  supported  by  grants  from  the 
Deutsche  Forschungsgemeinschaft  (MZ-AD  24/11,  BA  1291/3  1-4).  We 
thank  also  the  Alfred-Wegener-Institut  ftir  Polar-  und  Meeresforschung, 
Hanseatic  Cruises,  Plancius-Oceanwide,  and  Quark  Expeditions  for  the 
logistic  support  of  our  expeditions.  The  experiments  with  the  body  of 
rotation  were  enabled  by  a  grant  from  the  Volkswagen-Stiftung.  Thanks  to 
all  participants  of  the  INTAS  project  94-3737  for  the  many  useful 
discussions. 

X.  REFERENCES: 

1.  J.  Videler  “Comparing  the  cost  of  flight:  Aircraft  designers  can  still 
learn  from  nature”  In:  W.  Nachtigall  (ed.):  BIONA-report  8  (1. 
Bionik-Kongress,  Wiesbaden),  Akad.Wiss.  u.  Lit.,  Mainz:  G.Fischer, 
Stuttgart,  New  York,  1992:  53-72. 

2.  H.  Hertel  “Struktur  -  Form  -  Bewegung”  Krausekopf:  Mainz,  1 963 . 

3.  H.  Hertel  “Biologic-technical  research  on  structure,  form  and 
movement”  In:  G.Bugliarello  (ed.):  Bioengeneering  -  an  engeneering 
view.  Proc.  Symp.  Engin.  Signif.  Biol.  Sci.,  San  Francisco,  1968:  07- 
143.. 

4.  J.  Gray  “Studies  in  Animal  Locomotion.  VI  The  Propulsive  power  of 
the  Dolphin”  J.  exp.  Biol.  13, 1936:  192-199. 

5.  F.E.  Fish  and  C.A.  Hui  “Dolphin  swimming  -  a  review”.  Mamm.  Rev. 
21, 1991:  181-195. 

6.  F.E.  Fish  “Power  output  and  propulsive  efficiency  of  swimming 
bottlenose  dolphins  (Tursiopstruncatus)”, /£>/#,  1993, 185:  179-193. 

7.  E.V.  Romanenko  “Hydrodynamics”,  In  V.E.  Sokolov  and  E.V. 
Romanenko  (eds.)  The  Black  Sea  Bottlenose  Dolphin ,  Nauka, 

Moscow,  1997:  621-649  (in  Russian). 

8.  M.O.  Kramer  “Boundary  layer  stabilization  by  distributed  damping”  J. 
Am.  Soc.  Nav.  Eng.  Febr.  1960:  25-33. 

9.  P.W.  Carpenter  “Status  of  transition  delay  using  compliant  walls”  In: 
D.M.  Bushnell  and  J.N.  Heftier,  (eds.):  Viscous  drag  reduction  in 
boundary  layers.  AIAA,  New  York,  1990:  79-113. 

10.  V.  V.  Babenko,  M.  V.  Kanarskij  and  V.  I.  Korobov  “The  boundary 
layer  in  elastic  plates”  Naukova  Dumka,  Kiew,  1993  (in  Russian). 


441 


11.  E.T.  Uskova,  V.  C.  Raevskij,  L.I.  Momot  and  I.  A.  Uskov  (1975) 
“Comparative  studies  on  the  hydrodynamic  efficiency  of 
polyethylenoxid  suspensions  and  skin  secrets  of  marine  animals” 
Bionika  9,  Naukova  Dumka,  Kiew,  1975:  90-92  (in  Russian). 

12.  W.-E.  Reif  “Squamation  and  ecology  of  sharks”  Courier  Forschungs- 
institut  Senckenberg,  Frankfurt/M Nr.  78, 1985. 

1 3 .  W.-E.  Reif  and  A.  Dinkelacker  “Hydrodynamics  of  the  squamation  in 
fast  swimming  harks”  Neues  Jahrbuch  fur  Geologie  und 
Palaontologie.  Abhandlungen  Band  164,.  E.  Schweizerbart’sche 
Verlagsbuchhandlung,  Stuttgart,  1982:  184-187. 

14.  M.  Bruse,  D.W.  Bechert,  J.G.Th.  van  der  Hoeven,  W.  Hage  and  G. 
Hoppe  “Experiments  with  conventional  and  with  novel  adjustable 
drag-reducing  surfaces”  In:  R.M.C.  So,  C.G.  Speziale  and  B.E. 
Launder  (eds.):  Near-wall  turbulent  flow.  Elsevier  Science  Publishers 
B.V.  1993:719-738. 

15.  Y.G.  Aleyev  “Nekton”  The  Hague:  Dr.  W.  Junk  b.v.,  1977. 

16.  B.  D.  Clark  and  W.  Bemis  “Kinematics  of  swimming  of  penguins  at 
Detroit  Zoo’ V.  Zool,  Lond.,  188,  1979: 411-428. 

17.  W.  Nachtigal!  and  D.  Bilo  “Stromungsanpassung  des  Pinguins  beim 
Schwimmen  unter  Wasser”  J.  Comp.  Physiol  137,  1980:  17-26. 

18.  C.A.  Hui  “Swimming  in  Penguins”  Diss.  Univ.  Calif.,  Los  Angeles, 
1983. 

19.  B.M.  Culik  “Energy  expenditur  of  Adelie  penguins”  In:  P.  Dann,  I. 
Norman  and  P.  Reilly  (eds.):  The  Penguins.  Surrey  Beatty  &  Sons  Pty 
Limited,  Chipping  Norton,  Australia,  1995:  177-195. 

20.  B.M.  Culik,  R.P.  Wilson  and  R.  Bannasch  “Under-water  swimming  at 
low  energetic  cost  by  Pygoscelid  penguins”  J.  exp.  Biol  197, 1994: 
65-78. 

21.  R.  Bannasch  “Schwimm-  und  Tauchleistungen  der  Pinguine”  Milu  6, 
1985:295-308. 

22.  R.  Bannasch  “Hydrodynamics  of  penguins  -  an  experimental 


approach”  In:  P.  Dann,  I.  Norman  and  P.  Reilly  (eds.):  The  Penguins. 
Surrey  Beatty  &  Sons  Pty  Limited,  Chipping  Norton,  Australia,  1995: 
141-171. 

23.  R.  Bannasch  “Widerstandsarme  StrOmungskOrper  -  Optimalformen 
nach  Patenten  der  Natur”  In:  W.  Nachtigall  &  A.  Wisser  (eds.): 
BIONA-report  10,  Akad.  Wiss.  u.  Lit.,  Mainz:  G.  Fischer,  Stuttgart, 
Jena,  New  York,  1996:  151-176. 

24.  R.  Bannasch  and  J.  Fiebig  “Herstellung  von  Pinguinmodellen  fur 
hydrodynamische  Untersuchungen”  Der  Praparator,  Bochum  38(1), 
1992: 1-5. 

25.  S.F.  Hoerner  “Fluid-dynamic  drag”  2nd  edition.  Bricktown  New  Jersy. 
Hocmer,  S.  F.,  1965. 

26.  H.  Schlichting  “Grenzschicht-Theorie”  Verlag  G.  Braun.  Karsruhe, 
1982. 

27.  P.R.  Bandyopadhyay  “Viscous  drag  reduction  of  a  nose  body”  A1AA  J. 
27, 1989: 274-282. 

28.  P.R.  Bandyopadhyay  “Convex  curvature  concept  of  viscous  drag 
reduction”  In:  D.M.  Bushnell  and  J.N.  He&er  (eds.):  Viscous  drag 
reduction  in  boundary  layers.  Vol.  123,  1990:  285-324. 

29.  P.R.  Bandyopadhyay  and  A.  Ahmed  “Turbulent  boundary  layers 
subjected  to  multiple  curvatures  and  pressure  gradients”  J.  Fluid  Mech. 
246, 1993: 503-527. 

30. 1.  Rechenberg  “Evolutionsstrategie”  Problemata,  Frommann-Holzboog. 
Stuttgart,  1973. 

31.1.  Rechenberg  “Evolutionsstrategie  ‘94”  Problemata,  Frommann- 
Holzboog,  Stuttgart,  1994. 

32.  W.E.  Pinebrook  “Drag  minimization  on  a  body  of  revolution” 
Dissertation.University  of  Houston,  1982. 

33.  Th.  Lutz,  H.  Schweyher,  S.  Wagner  and  R.  Bannasch  “Shape 
optimization  of  axisymmetric  bodies  in  incompressible  flow”.  Proc.  2nd 
Int.  Airship  Conf,  Stuttgart  / Friedrichshafen,  3.-4.Juli  1996:  211- 
224. 


442 


Imaginative  solutions  by  marine  organisms  for  drag  reduction 

Frank  E.  Fish 

Department  of  Biology,  West  Chester  University,  West  Chester,  PA  19383  USA 

Both  machines  and  animals  must  contend  with  the  same  physical  laws  that  regulate  their  design  and  behavior. 
Many  animals  demonstrate  high  levels  of  performance  with  respect  to  movement  through  water,  and 
therefore,  may  be  useful  as  model  systems  to  analyze  novel  mechanisms  for  drag  reduction  that  are  superior 
to  engineered  solutions.  A  survey  of  various  animals  demonstrates  that  they  have  evolved  a  number  of 
morphological  and  behavioral  drag-reducing -mechanisms.  Although  more  complex,  these  mechanisms  act 
similarly  to  analogous  engineered  solutions  for  movement  when  submerged  and  across  the  air-water 
interface. 


We  were  lying  upon  the  back  of  a  sort  of  submarine  boat,  which 
appeared  (as  far  as  I  could  judge)  like  a  huge  fish  of  steel.  (Jules 
Verne,  Twenty  Thousand  Leagues  Under  The  Sea) 

INTRODUCTION 

The  idea  that  new  technologies  can  be  developed  from 
observation  of  nature  has  been  long  standing.  Indeed,  nature  has 
served  as  the  inspiration  for  various  technological  developments 
including  flight  and  robotics  [1,  2,  3].  Copying  nature  by  the  biomimetic 
approach  attempts  to  seek  common  solutions  from  engineering  and 
biology  for  increased  efficiency  and  specialization  [4].  It  is  no 
accident  that  the  shape  of  modern  submarines,  fish,  and  marine 
mammals  are  so  closely  matched.  Parallels  between  natural  and 
engineered  designs  occur  because  both  are  selected  for  a  range  of 
performance  constrained  by  the  same  physical  forces. 

Analysis  of  locomotor  specializations  in  animals  holds  for 
engineers  die  possibility  that  animals  can  .be  used  as  solutions  to  design 
problems  for  reduction  in  energy  input,  whether  in  their  construction  or 
in  the  performance  of  work.  Any  mechanism  that  allows  for  increased 
energy  economy  use  can  provide  an  important  advantage  to  the 
survival  of  an  animal.  It  is  viewed  that  evolution  (descent  with 
modification)  through  the  Darwinian  process  of  "natural  selection"  has 
fostered  improvements  in  design  which  have  culminated  in  adaptations 
for  high  speed  and  efficiency  [4,  5].  Because  natural  selection  chooses 
from  a  wide  range  of  design  and  performance  possibilities  as  dictated 
through  the  genetic  code  and  functional  demand  of  the  environment,  a 
variety  of  possible  solutions  to  engineering  problems  may  be 
investigated.  The  diverse  morphological  specializations  exhibited  by 
animals  may  be  targeted  by  engineers  for  technology  transfer  and 
effectively  reduce  the  time  of  development  of  innovative  technological 
solutions. 

However,  the  use  of  animal  models  for  design  improvements  is 
not  without  criticism.  Strict  adherence  to  biological  designs  is 
considered  to  rarely  produce  any  practical  results  and  can  impede  the 
development  of  engineered  systems  [6,  7].  Airplanes  do  not  flap  their 
wings  like  birds  for  lift  and  ships  do  not  undulate  like  fish  for 
propulsion.  The  reason  that  the  duplication  of  biological  systems  has 
been  limited  is  due  to  evolutionary  and  material  constraints. 

Animals  are  functionally  multifaceted  (i.  e.,  they  move,  feed, 
reproduce)  and  must  compromise  optimal  solutions  for  specialized 
functions  to  perform  adequately  rather  than  maximally  [8,  9].  The 
biotic  and  abiotic  environments  of  the  time  that  a  new  design  evolves 
dictates  its  selection  without  anticipation  for  potential  future  purpose 
and  effectiveness.  Both  superior  and  poor  designs  with  respect  to 
present  time  may  be  lost  if  they  did  not  function  adequately  in  past 
environments  or  if  they  were  accidentally  lost  due  to  chance  events.  In 
addition,  animals  have  evolved  along  lines  of  common  descent  with 
shared  developmental  patterns  which  restricts  possible  solutions. 
Radical  redesigns  are  not  permitted  to  expedite  enhancing 
performance;  instead,  it  is  existing  designs  which  are  modified. 
Although  swimming  in  whales  would  be  more  efficient  if  these  animals 
remained  submerged  like  fish  (see  below),  their  common  evolutionary 
history  with  other  air-breathing  mammals  requires  that  they 
periodically  return  to  the  water  surface  to  fill  their  lungs  despite 
increased  energy  cost. 

Animals  are  further  limited  by  the  variety  of  structural  materials 
available.  Animals  are  composed  of  either  fibers,  such  as  collagen, 
chitin,  and  keratin,  or  composites,  such  as  bone  and  cartilage  [10]. 
Compared  to  manufactured  materials,  like  metals,  ceramics  and 
glasses,  biological  materials  are  generally  weaker  and  less  stiff. 
Furthermore,  movements  are  generated  through  forceful  contraction  of 


the  muscles  transmitted  to  a  jointed  skeleton  by  tendonous  connections. 
The  arrangement  of  the  contractile  machinery  precludes  the  use  of 
rotational  movements  so  ubiquitous  in  engineered  systems  [8]. 
Therefore,  biological  systems  suffer  lower  efficiency  due  to  periodic 
accelerations  over  a  propulsive  cycle. 

Despite  these  concerns,  the  realization  of  new  and  superior 
designs  to  reduce  drag  based  on  animal  systems  has  been  tantalizing, 
although  elusive  [7,  11,  12].  Aquatic  animals  are  considered  superior  in 
their  capabilities  to  technologies  produced  from  nautical  engineering 
[2].  Speeds  over  11  m/s  (>21  kts)  have  been  attained  by  dolphins  [13], 
whereas  fish  display  speeds  as  high  as  20  m/s  (39  kts)  and  can 
accelerate  at  40-50  m/s^  [11,  14].  Such  high  levels  of  performance 
were  assumed  to  be  dependent  on  adaptations  which  reduced  drag. 

This  report  explores  the  specialized  adaptations  used  by  aquatic 
animals  for  drag  reduction.  These  adaptations  are  compared  with 
analogous  engineered  solutions.  Comparison  of  biological  and 
mechanical  systems  can  provide  insight  into  the  effectiveness  of  each 
system  and  help  direct  engineers  toward  innovative  applications  of 
biological  systems.  For  a  full  appreciation  of  the  topic,  this  survey 
includes  discussion  of  mechanisms  which  are  considered  valid, 
fallacious,  and  speculative. 

DRAG  COMPONENTS 

A  previous  review  of  biological  drag  reduction  by  Bushnell  and 
Moore  [5]  examined  three  types  of  drag  (form  drag,  skin-friction  drag, 
and  drag-due-to-lift)  for  organisms  totally  immersed  in  a  fluid,  whether 
air  or  water.  The  present  review  examines  how  organisms  reduce  their 
drag  in  an  aqueous  environment  for  fully  submerged  bodies  and  bodies 
operating  at  the  air-water  interface. 

The  primary  component  of  drag  experienced  by  aquatic  animals 
varies  in  accordance  with  (1)  flow  conditions  around  the  animal  and  in 
its  boundary  layer,  (2)  proximity  to  the  air-water  interface,  and  (3)  the 
relative  predominance  of  inertial,  gravitational,  and  viscous  forces. 
Because  of  the  interest  in  rapid  motion  in  water  and  application  of 
biological  designs  to  large  structures,  the  discussion  will  focus  on 
conditions  encompassing  high  Reynolds  numbers  (Re),  expressed  as: 

Re  =  U  L  /  \)  (1) 

where  U  is  the  velocity,  L  is  a  characteristic  linear  distance  (e.g.,  body 
length),  and  u  is  kinematic  viscosity,  which  is  equal  to  1. 044x1 0"^  m^/s 
for  sea  water  at  20°C.  At  high  Re,  inertial  forces  predominate  over 
viscous  forces.  Of  particular  interest  is  the  range  of  Re  >  10^,  where 
transition  from  laminar  to  turbulent  flow  conditions  can  occur. 
Gravitational  forces  predominate  when  animals  swim  near  or  pierce 
the  water  surface.  The  ratio  of  inertial  forces  to  gravitational  forces 
experienced  by  a  body  moving  at  or  close  to  a  fluid/fluid  interface  is 
given  by  the  dimensionless  Froude  number,  Fl,  as: 

FL  =  U/(gLw)1/2  (2) 

where  g  is  the  gravitational  acceleration,  9.8  m/s  ,  and  Lw  is  the 
waterline  length  along  the  longitudinal  axis  of  the  body. 

For  submerged  bodies,  minimum  drag  is  associated  with  purely 
frictional  drag  with  laminar  boundary  conditions  (Fig.  1).  To  maintain  a 
laminar  boundary  layer,  the  surface  of  the  body  should  be  smooth  and 
the  configuration  of  the  body  should  promote  a  large  favorable 
(negative)  pressure  gradient  [15].  This  gradient  occurs  when  the 
pressure  is  decreasing  along  the  streamline  from  the  leading  edge 
toward  the  trailing  edge  by  gradually  increasing  the  thickness  of  the 


443 


□  pressure  drag 
|  frictional  drag 


laminar  partly  turbulent  laminar  partly  turbulent 
_ laminar _ laminar _ 


Attached  Separated 

Boundary  Conditions 

Fig.  1.  Relative  drag  associated  with  boundary  conditions.  Redrawn 
from  [11]. 

body.  A  large  region  with  a  favorable  pressure  gradient  is  achieved  by 
positioning  the  maximum  thickness  of  the  body  posteriorly.  However  at 
high  Re  (>  10^),  transition  from  laminar  to  turbulent  boundary 
conditions  can  occur.  The  result  of  this  transition  is  an  increase  in  the 
frictional  drag  due  to  an  increase  in  boundary  layer  thickness. 

Pressure  or  form  drag  is  produced  from  pressure  difference  in 
the  flow  outside  the  boundary  layer  arising  from  changing  flow 
velocities  around  the  body.  The  pressure  differential  from  leading  to 
trailing  edges  of  the  body  is  the  source  of  the  force  [11].  Streamlining 
minimizes  drag  by  reducing  the  magnitude  of  the  pressure  gradient 
over  the  body  [7]. 

Pressure  drag  is  also  dependent  on  the  interaction  of  the  boundary 
layer  and  pressure  gradient.  Boundary  layer  separation  generally 
occurs  in  the  region  posterior  of  the  maximum  thickness  of  the  body.  In 
this  region  an  adverse  pressure  gradient  develops  with  high  pressure 
located  posteriorly.  At  a  point  along  the  gradient,  fluid  in  the  boundary 
layer  does  not  have  sufficient  momentum  to  overcome  the  increasing 
pressure  and  separation  occurs.  Premature  separation  along  the  body 
as  opposed  to  near  the  trailing  edge  will  produce  a  broad  wake  with 
substantial  energy  loss.  Separation  is  more  likely  to  occur  with  laminar 
boundary  conditions.  This  results  in  higher  drag  with  laminar  conditions 
than  with  a  turbulent  boundary  layer  (Fig.  1).  Separation  is  delayed  in  a 
turbulent  boundary  layer,  because  momentum  is  transferred  vertically 
due  to  increased  mixing  within  the  layer  [15]. 

Wave  drag  occurs  when  an  animal  swims  at  or  near  the  water 
surface  acting  as  a  displacement  hull  [16,  17,  18],  Kinetic  energy  from 
the  animal's  motion  is  transferred  into  potential  energy  in  the  upward 
displacement  of  water  in  the  formation  of  surface  waves.  This  energy 
loss  can  be  substantial  at  a  maximum  of  five  times  the  frictional  drag 
when  the  body  is  at  a  relative  depth  of  50%  of  the  maximum  diameter 
of  the  body  and  Fl  =  0.5  [17,  19,  20]. 

Speed  at  the  water  surface  is  constrained  by  the  formation  of 
surface  waves  [18,  21,  22],  As  an  animal  swims  faster,  constructive 
interference  from  bow  and  stern  waves  trap  it  in  a  trough,  ultimately 
limiting  further  increases  in  speed  [23,  24].  To  move  faster,  the  animal 
would  have  to  literally  swim  uphill,  which  is  energetically  very  costly. 
This  effective  speed  limit  for  a  conventional  displacement  hull,  such  as 
a  ship  or  duck,  is  called  the  hull  speed,  [21].  Hull  speed  depends  on 
Lw  with  longer  bodies  having  higher  hull  speeds.  Ufo  is  calculated  as: 

Uh  =  teLw/2  7t)1/2  (3). 

Spray  drag  or  surface  interference  drag  is  created  by  water  piled 
up  along  the  forebody  of  a  surface-piercing  strut  or  foil  and  being  shot 
into  the  air  [19].  At  high  Fj^  spray  drag  is  approximately  26%  of  total 
drag  for  a  surface-piercing  flat  plate  and  30%  for  a  strut  with  a  blunt 
trailing  edge  [19].  The  best  design  to  reduce  spray  drag  is  a  pointed 
leading  edge  and  long  forebody  region  relative  to  the  maximum 
thickness  (Fig.  2). 


FOREBODY  THICKNESS  RATIO  (T/X) 


Fig.  2.  Relationship  between  spray  drag  and  forebody  thickness  ratio 
based  on  [19], 

The  induced  drag  component  is  produced  from  vorticity 
generated  by  lifting  hydrofoils  (e.g.,  fins,  flippers,  flukes).  When  the 
hydrofoil  is  canted  at  an  angle  to  the  water  flow  (i.e.,  angle  of  attack), 
a  lift  is  generated  due  to  deflection  of  the  fluid  and  pressure  difference 
between  the  two  surfaces  of  the  hydrofoil  [5,  11],  The  pressure 
difference  induces  the  formation  of  longitudinal  tip  vortices  resulting  in 
energy  dissipation  [7,  11],  The  induced  drag  coefficient  (C^i)  is 
determined  as: 

CD.  =  CL2/7tAR  (4) 

where  CL  is  the  coefficient  of  lift  and  AR  is  the  aspect  ratio.  AR  is  an 
indicator  of  the  geometry  of  the  hydrofoil  and  is  calculated  as: 

AR  =  S2/A  =  S/C  (5) 

in  which  S  is  the  hydrofoil  span,  A  is  the  maximum  projected  area  of 
the  hydrofoil,  and  C  is  the  chord.  As  AR  increases,  the  hydrofoil 
planform  becomes  long  and  narrow.  Equation  4  suggests  that  hydrofoils 
with  high  AR  will  experience  a  low  induced  drag. 

BIOLOGICAL  SOLUTIONS  FOR  DRAG  REDUCTION 

A  variety  of  engineered  solutions  and  possible  animal 
mechanisms  for  drag  reduction  exist  for  each  of  the  drag  components 
presented  above.  Animals  reduce  drag  by  utilizing  secreted  materials, 
anatomical  features,  and  behavioral  patterns. 

Friction  Drag 

Mucus 

The  addition  of  dilute  solutions  of  long-chain  polymers  into  flow  is 
well  established  as  a  means  of  drag  reduction  [25],  The  conditions 
necessary  are  (1)  turbulent  or  pulsed  laminar  flow  in  the  boundary 
layer,  (2)  the  polymer  is  linear  and  soluble,  (3)  the  polymer  has  a 
molecular  weight  of  50,000  or  more,  and  (4)  the  density  and  viscosity 
of  the  fluid  from  the  surface  outwards  must  be  constant  [25,  26],  The 
mucus  secreted  by  fish  over  the  body  surface  is  considered  to  meet 
these  conditions.  The  mucus  is  a  combination  mucopolysaccharides, 
nucleic  acids,  proteins,  and  surfactants  in  the  form  of  lipids, 
phospholipids  and  lipoproteins  [5]. 

The  undulatory  or  oscillatory  movements  of  fish  during  swimming 
indicates  turbulent  or  pulsed  flow  for  which  mucus  could  be  effective 
in  reducing  drag  [25,  26].  Measurements  of  dilute  solutions  of  fish 
mucus  in  turbulent  pipe  flow  exhibited  as  much  as  66%  reduction  in 
friction  drag  [25,  27].  The  mucus  is  believed  to  reduce  the  velocity 
gradient  over  the  fish  and  thus  decrease  viscous  shear  stress  and 
reduce  the  rate  of  momentum  transfer  from  the  free-stream  flow  to  the 
surface  of  the  fish  [26].  The  mucus  also  may  fill  in  irregularities  to 
improve  streamlining  [28].  However,  no  association  was  found 
between  amount  of  drag  reduction  and  species  of  fish  which  swim  at 
high  speeds.  Even  snails,  which  are  not  noted  for  speed,  produce  a 
mucus  that  reduces  drag  [25]. 

Secretions  from  dolphins  have  been  examined  also  for  drag 
reducing  abilities,  although  with  no  success.  Secretions  from  the 


444 


dolphin  eye  fail  to  produce  any  drag-reducing  effect  [29].  Likewise, 
the  high  density  of  epidermal  cells  shed  from  dolphin  skin  have  little 
effect,  although  the  composition  of  these  cells  is  considered  similar  to  a 
mucopolysaccharide  [29,  30].  High  rates  of  skin  sloughing  may  aid  in 
minimizing  drag  by  preventing  fouling  by  encrusting  organisms  [31]. 

Riblets 

The  development  of  riblets  to  reduce  turbulent  skin  friction  came 
in  part  from  the  study  of  shark  scales  or  dermal  denticles  [32].  Riblets 
are  streamwise  microgrooves  that  act  as  fences  to  break  up  spanwise 
vortices,  and  reduce  the  surface  shear  stress  and  momentum  loss.  Fast 
swimming  sharks  have  scales  that  are  different  from  other  sharks. 
These  scales  have  flat  crowns  and  sharp  ridges  oriented  longitudinally 
with  rounded  valleys  [33,  34,  35,  36].  Although  the  ridges  are 
discontinuous  due  to  the  distribution  of  the  scales,  a  7-8%  drag 
reduction  is  possibly  as  measured  for  continuous  riblets  [32,  37],  The 
streamwise  surface  grooves  of  scallop  shells  also  indicate  the  use  of 
riblets  [38].  The  optimal  riblet  spacing  is  present  in  those  scallops 
demonstrating  the  greatest  swimming  ability.  Small  ridges  on  the 
epidermis  of  dolphins  had  been  hypothesized  to  stabilize  longitudinal 
vortices  [39,  40],  but  the  geometry  of  the  ridges  with  rounded  edges 
does  not  suggest  an  effective  analogy  with  riblets  [12]. 

Viscous  dampening 

By  far,  arguments  surrounding  the  investigation  and  application  of 
mechanisms  for  viscous  dampening  by  dolphins  have  been  the  most 
contentious  [7,  12].  The  controversy,  known  as  Gray's  Paradox,  was 
the  result  of  an  estimation  of  the  power  output,  based  on  calculation  of 
drag  with  turbulent  boundary  conditions,  for  a  rapidly  swimming 
dolphin.  The  estimated  drag  power  could  not  be  reconciled  with  the 
available  power  generated  by  the  muscles  [41].  Gray's  resolution  to  the 
problem  was  that  the  drag  on  the  dolphin  would  have  had  to  be  lower 
by  maintenance  of  a  fully  laminar  boundary  layer,  despite  Re  above 
transition.  Gray  proposed  a  mechanism  to  laminarize  the  boundary 
layer  by  accelerating  the  flow  over  the  posterior  half  of  the  body  (see 
boundary  layer  acceleration  below).  However,  the  basic  premise  of 
Gray’s  Paradox  was  flawed,  because  the  observation  of  the  dolphin 
swimming  speed  was  for  a  sprint  (7  sec)  and  Gray  used  measurements 
of  muscle  power  output  for  sustained  performance  of  human  oarsmen, 
which  are  lower  than  power  outputs  for  burst  activities  [12]. 

Gray's  Paradox,  however,  endured  and  was  invigorated  by  the 
work  of  Max  Kramer  [42,  43,  44].  Kramer  claimed  that  a  laminar 
boundary  layer  without  separation  could  be  achieved  at  high  Re  by 
coating  a  torpedo  with  an  artificial  skin  based  on  the  skin  of  a  dolphin. 
The  dolphin  integument  is  composed  of  a  smooth,  hairless  epidermal 
surface  forming  an  elastic  membrane  [45]  and  is  anchored  to  the 
underlying  dermis  by  longitudinal  dermal  crest  with  rows  of  papillae, 
which  penetrate  the  lower  epidermis  [29,  40,  43,  44,  45].  Kramer's 
analogous  skin  was  composed  of  a  heavy  rubber  diaphragm  supported 
by  rubber  studs  with  the  intervening  spaces  filled  with  a  viscous 
silicone  fluid  [42].  It  was  hypothesized  that  the  coating  would  dampen 
out  perturbations  in  the  flow  and  prevent  or  delay  transition.  When  a 
portion  of  a  towed  body  anterior  of  the  maximum  thickness  was  coated, 
a  59%  reduction  in  drag  was  achieved  at  Re=15xl0^  compared  to  a 
rigid  reference  model  with  fully  turbulent  flow.  These  results  suggested 
the  "dolphin's  secret"  and  a  resolution  to  Gray's  Paradox  [43]. 

In  what  has  been  characterized  as  "enthusiastic  optimism"  and 
"Pentagon  and  Kremlin  paranoia"  [7],  research  on  dolphin 
hydrodynamics  and  compliant  coatings  was  accelerated  during  the 
1960s  [12,  45,  46].  Attempts  to  verify  Kramer's  results  subsequently 
failed  [46,  47],  although  some  success  in  reducing  skin  friction  was 
possible  with  other  compliant  coatings  [48,  49].  It  was  suggested  that  a 
compliant  coating  would  reduce  drag  by  controlling  turbulence  in  the 
boundary  layer  rather  than  delaying  transition  [46].  It  would  be  more 
important  in  minimizing  total  drag  by  delaying  separation  than  to  delay 
transition  in  the  boundary  layer. 

The  structure  of  the  skin  and  blubber  layer  of  dolphins  is  highly 
organized  and  complex  [40,  50];  thus,  the  analogy  with  the  compliant 
skin  proposed  by  Kramer  may  be  only  superficial  and  have  little 
functional  similarity.  When  swimming  at  high  speed  or  for  bursts, 
dolphins  exhibit  prominent  skin  folds  [51].  Similar  speed-induced  skin 
folds  were  shown  to  add  to  drag  when  observed  on  naked  women 
swimming  or  towed  at  2-4  m/s  [45].  The  possession  of  a  thick  skin, 
which  could  make  the  induced  folds,  is  attributed  also  to  turbulent 


boundary  conditions  for  the  beluga  whale  (Delphinapterus  leucas) 
[36]. 

Drag  measurements  of  gliding  dolphins  and  rigid  models  indicated 
that  the  boundary  layer  was  largely  turbulent  [13,  16,  36,  39,45,  52], 
This  was  verified  by  low -speed,  flow  visualization  studies  on  dolphins 
using  dye  or  bioluminescence  [53,  54,  55].  The  fluid  layer  against  the 
body,  inferred  to  represent  the  boundary  layer,  thickened  anterior  of 
the  dorsal  fin.  The  inferred  transition  anterior  to  the  dorsal  fin 
corresponded  with  a  local  Re  of  about  3x1 0^,  and  was  confirmed  from 
measurements  of  turbulent  pulsations  on  a  live  dolphin  [45].  The 
boundary  layer  remained  attached  up  to  the  flukes  for  gliding  animals 
[55],  but  separated  anterior  of  the  flukes  for  an  actively  swimming 
dolphin  [53].  Similar  observations  were  made  on  seals  swimming 
through  bioluminescence  [56].  Seals  swim  in  a  matter  analogous  to 
dolphins  [57]. 

As  indicated  from  flow  visualization  experiments  on  dolphins, 
differences  in  boundary  layer  flow  occur  between  actively  swimming 
and  gliding  animals.  This  implies  that  viscous  dampening  may  be  under 
active  control  when  the  animal  is  oscillating  its  flukes.  Experiments 
using  remote  pressure  sensors  in  the  boundary  layer  of  an  actively 
swimming  dolphin  indicated  that  although  agitated  the  boundary  layer 
did  not  become  completely  turbulent  [58],  Although  the  degree  of 
turbulence  and  the  pressure  were  determined  to  decrease  over  the 
posterior  portion  of  the  body,  these  results  may  not  be  associated  with 
viscous  dampening  as  has  been  hypothesized  [36,  59].  Indeed  there  is 
no  evidence  to  suggest  that  viscous  dampening  of  the  skin  should  be 
any  more  likely  when  the  animal  is  oscillating  its  flukes  as  opposed  to 
gliding  [12].  A  substantial  amount  of  time  during  swimming  may  be 
occupied  by  gliding  when  low  drag  would  be  beneficial. 

As  originally  proposed  by  Gray  [41],  acceleration  of  the 
boundary  layer  due  to  propulsive  fluke  actions  could  account  for  the 
results  of  flow  visualization  and  pressure  studies  [53,  58].  Estimates  of 
drag  on  actively  swimming  dolphins  based  on  kinematics  and 
hydrodynamic  models  have  indicated  turbulence  due  to  high  drag 
values  [11,  52,  60,  61],  Such  high  drags  are  consistent  with  estimates 
for  actively  swimming  animals  which  can  be  2-5  times  the  greater  than 
drag  values  of  equivalent  rigid  bodies  [62]. 

Dynamic  dampening 

The  network  of  subdermal  canals  and  pores  in  the  skin  of  fish 
suggests  use  of  a  suction  mechanism  to  stabilize  the  boundary  layer  and 
prevent  separation  [63,  64].  In  the  trachipterid  fish,  Desmodema ,  the 
placement  of  maximum  thickness  is  at  7%  of  total  length.  This  will 
result  in  a  negative  pressure  gradient  over  the  majority  of  the  body. 
The  pore  and  canal  system  is  believed  to  redistribute  fluid  from  high  to 
low  pressure  regions.  Engineered  systems  using  boundary  layer  suction 
achieved  66-100%  laminar  flow  [65]. 

Boundary  layer  acceleration 

Injection  of  high  momentum  fluid  into  the  boundary  layer  has  the 
capacity  to  delay  both  transition  and  separation  [11].  The  effluent  from 
the  gills  of  fish  could  potentially  introduce  kinetic  energy  into  the 
boundary  layer  [28,  66].  Flow  visualization  in  fish,  however,  has  shown 
the  pulsed  flow  during  active  respiration  increases  turbulence  [45,  66]. 
The  location  of  the  gill  slits  anterior  of  the  maximum  thickness  of  fish 
(i.e.,  position  of  lowest  pressure)  would  enhance  respiratory  flow 
rather  than  surface  flow.  During  passive  or  ram  ventilation  in  scombrid 
fish,  the  mouth  and  gill  coverings  are  kept  open  so  that  water  can 
continuously  flow  over  the  gills  without  pumping.  The  constant 
swimming  motion  of  the  fish  maintains  the  flow.  Ram  ventilation  does 
not  prevent  turbulence,  but  it  appears  to  extend  the  laminar  region  of 
the  boundary  layer  by  13-100%  [45]. 

Re-acceleration  of  the  boundary  layer  as  fluid  was  accelerated 
from  the  oscillating  flukes  of  dolphins  was  proposed  originally  as  the 
resolution  to  Gray's  Paradox  [41].  Calculations  of  the  dynamic  pressure 
distribution  over  an  actively  swimming  dolphin  indicate  the  extension  of 
a  favorable  pressure  gradient  over  the  total  body  with  a  steep  pressure 
reduction  in  the  region  of  the  peduncle  and  flukes  [59].  This 
mechanism  seems  to  have  greater  potential  for  boundary  layer 
stabilization  in  the  dolphin  than  maintenance  of  laminar  flow  with 
viscous  dampening.  A  similar  mechanism  may  operate  in  cephalopods 
(e.g.,  squid,  octopus).  Water  flowing  into  the  inlet  of  the  mantle  cavity 
during  inhalation  and  during  exhalation  through  the  siphon  when  jetting 
could  accelerate  the  boundary  layer  [45]. 


445 


Fig.  3.  Representative  body  shapes  of  marine  mammals.  From  top  to 
bottom:  minke  whale  ( Balaenoptera  acutorostrata ),  right  whale 
(Eubalaena  glacialis),  harbor  porpoise  ( Phocoena  phocoena),  Florida 
manatee  ( Trichechus  manatus),  and  harp  seal  (Phoca  groenlandica). 


Boundary  layer  heating 

Warm-bodied  animals,  such  as  marine  mammals,  scombrid  fishes, 
and  laminid  sharks,  have  the  capacity  to  use  heat  conducted  from  the 
body  surface  to  decrease  water  viscosity  [66,  67].  Dolphins  exhibit  a 
temperature  differential  between  the  water  and  skin  surface  of  9°C 
which  would  reduce  viscosity  by  11%  [12].  A  maximum  temperature 
difference  of  15°C  for  tuna  would  provide  a  14%  decrease  in  friction 
drag  as  long  as  the  boundary  layer  was  heated  instantaneously  [11]. 
Although  plausible,  this  method  of  drag  reduction  is  unlikely  due  to  the 
short  amount  of  time  (0.1  s)  that  the  water  would  be  in  contact  with  the 
body  [66], 

Pressure  Drag 

Fusiform  shape 

It  is  surprising  that  although  G.  Cayley  (circa  1800)  considered 
the  fusiform  design  of  the  dolphin  to  be  a  body  of  least  resistance,  this 
design  was  not  embraced  for  submarine  hulls  until  the  USS  Albacore  in 
1953.  Drag  is  minimized  primarily  by  streamlining  the  shape  of  the 
body  and  the  appendages.  The  streamlined  profile  of  these  structures  is 
characterized  by  a  rounded  leading  edge  and  a  slowly  tapering  tail 
(Fig.  3).  This  design  delays  separation  which  occurs  closer  to  the 
trailing  edge,  resulting  in  a  smaller  wake  and  reduced  pressure  drag. 

An  indication  of  the  streamlining  of  a  body  is  the  Fineness  Ratio 
(FR  =  ratio  of  maximum  length  to  maximum  thickness)  [1 1].  Bodies  of 
rotation  demonstrate  minimum  drag  in  a  range  of  FR  of  3-7  [17,  68, 
69].  Based  on  airship  design,  the  optimal  FR  is  4.5  which  provides  the 
minimum  drag  for  the  maximum  volume  [68].  Fast  swimming  fishes, 
penguins  and  aquatic  mammals  are  well  streamlined  with  body 
dimensions  within  the  optimal  range  of  FR  [11,  57,  70,  71]. 

In  engineered  'laminar'  profiles,  the  position  of  the  maximum 
thickness  is  located  posteriorly  to  reduce  drag  by  maintenance  of  an 
extended  favorable  pressure  gradient  and  laminar  boundary  flow  [11]. 
The  shape  of  a  dolphin  and  a  sea  lion  have  been  likened  to  a  NACA 
66-018  airfoil  [17,  72],  whereas,  tuna  display  similarities  with  the 
NACA  67-021  [17].  Indeed,  most  rapidly  swimming  aquatic  animals 
have  displaced  the  maximum  thickness  posteriorly  [17,  45].  The 
maximum  thickness  of  fast  swimming  fish  and  marine  mammals  is 
located  at  0.3-0. 7  of  the  body  length  [12,  17,  45,  66,  72]. 

Abrupt  departures  from  a  streamlined  shape  are  avoided  through 
use  of  integumentary  structures.  Blubber  in  marine  mammals  contours 
the  body  along  its  longitudinal  axis  [56,  71].  In  addition,  blubber 
streamlines  the  caudal  peduncle  in  dolphins  to  reduce  its  drag  in  the 
flukes'  plane  of  oscillation  [12]  and  provides  a  streamlined  shape  to  the 
appendages  [73,  74],  Hair  and  feathers  also  can  be  used  with  their 
entrapped  air  layers  to  contour  the  body  [70,  75,  76].  The  lack  of 
arrector  pili  muscles  in  seals  and  sea  otters  permits  the  pelage  to  lie  flat 
in  water,  minimizing  resistance  to  swimming  [77].  When  models  of  a 
seal  with  and  without  hair  covering  were  compared,  a  reduction  in 
drag  with  the  hair  covering  occurred  at  velocities  of  8-10  m/s  [78]. 
However,  it  was  noted  that  these  speeds  are  not  normal  for  seals  and 
the  results  may  not  be  ecologically  relevant  [79]. 

Despite  the  presumption  of  the  teardrop,  fusiform  shape  as  the 
optimal  design  for  drag  reduction,  a  number  of  aquatic  animals  have 
anterior  projecting  beaks,  bills,  and  rostrums.  In  part,  the  departure 


from  a  smoothly  rounded  head  in  these  animals  may  be  a  function  of 
their  feeding  morphology  requiring  grasping  jaws.  However,  the 
alternating  concave  and  convex  profile  of  the  forebody  may  induce  a 
stepwise,  gradual  pressure  change  which  can  reduce  skin  friction  in 
animals  [70,  80,  81].  The  relatively  small  surface  area  of  the  anterior 
projection  in  conjunction  with  a  reduced  pressure  gradient  [45,82]  can 
decrease  drag. 

Redirection  of  flow  about  dorsal  spines  of  some  sharks  would  aid 
in  preventing  flow  separation  and  increased  pressure  drag.  The  spines 
are  found  on  the  leading  edge  of  the  dorsal  fins.  Because  there  is  a  gap 
between  the  spines  and  the  fins,  the  combination  could  act  in  a  manner 
analogous  to  slotted  wings  as  the  body  laterally  undulates  during 
swimming,  canting  the  dorsal  fins  at  an  angle  to  the  flow  [83]. 

Burst-and-coast  swimming  is  a  behavioral  strategy  that  exploits 
the  lower  drag  of  a  rigid,  non-flexing  animal  compared  to  when  it  is 
actively  swimming  [62].  Animals  rarely  swim  steadily.  Many  animals 
swim  intermittently  using  a  two-phase  periodic  behavior  of  alternating 
accelerations  (burst  phase)  interspersed  with  periods  of  glides  (coast 
phase)  [84,  85].  Estimates  of  energy  savings  were  projected  from  24% 
to  over  50%  for  fish  using  this  behavior  [86,  87], 

Vortex  generators 

Large-scale  vortices  can  be  generated  around  the  bodies  and 
appendages  of  animals  to  influence  flow  and  reduce  drag  [5,  11]. 
Alternate  vortices  shed  from  around  the  head  of  swimming  fish  were 
postulated  to  act  as  rigid  pegs  [88].  The  Vortex  Peg  Hypothesis 
suggested  that  the  fish  pushed  off  the  vortices  reducing  swimming 
effort  and  that  the  drag  was  virtually  zero  by  reclaiming  energy  from 
the  vortices  [11,  53,  88],  This  hypothesis  was  considered  unlikely, 
because  the  velocity  difference  between  the  fish  and  vortices  was  too 
great  to  make  the  system  efficient  [11]. 

However,  anteriorly  generated  vortices  and  vortices  generated 
from  the  undulation  of  the  caudal  fin  can  interfere  with  each  other  to 
increase  locomotor  efficiency  [53,  89,  90],  The  opposing  rotations  of 
the  anterior  vortices  generated  as  a  K&rm&n  vortex  street  and  the 
thrust-type  vortices  (reverse  Karm&n  vortex  street)  can  destructively 
interfere  [90].  This  interference  produced  enhanced  efficiency  when 
the  sites  of  vortex  generating  were  optimally  spaced. 

Leading  edge  bumps  were  identified  as  possible  drag  reducing 
devices  [5].  Leading  edge  bumps  are  found  on  the  head  of 
hammerhead  sharks  and  pectoral  flipper  of  humpback  whales,  which 
are  used  as  lifting  surfaces  during  maneuvers  [91,  92]..  On  the 
humpback  whale  flipper,  the  bumps  are  evenly  spaced  over  the 
majority  of  the  span  [91].  These  bumps  were  hypothesized  to  generate 
vorticity  to  postpone  stall  at  high  angles  of  attack.  This  function  may  be 
analogous  to  strakes  which  change  the  stall  characteristics  of  aircraft 
wings  by  generating  vorticity  [19,  93].  Vortex  generators  are  most 
effective  for  increasing  lift  and  reducing  drag  when  the  boundary 
layer  has  been  tripped  [94],  Turbulent  boundary  conditions  would  be 
likely  for  humpback  whale  flippers  which  operate  near  Re  =  2x10^ 
[91]- 

Turbulizers 

Induction  of  turbulence  by  roughness  and  surface  projections 
within  the  boundary  layer  can  ultimately  reduce  total  drag  by  delaying 
boundary  layer  separation  [11].  Sculpturing  on  the  shells  of 
cephalopods  (ammonoids  and  nautiloids)  had  a  positive  hydrodynamic 
effect  when  immersed  in  the  boundary  layer,  but  sculpturing  which 
extended  outside  of  the  boundary  layer  had  a  negative  effect  [95],  For 
fish,  the  presence  of  scales,  rough  surfaces,  and  spiny  projections  has 
been  likened  to  a  tripping  device  to  stabilize  the  boundary  layer  [5,  11, 
45,  6496].  In  mullet,  Mugil  saliens ,  scale  development  is  correlated 
with  body  size  and  Re  [45,  96].  At  Re  less  than  10^,  the  fish  has  no 
scales;  whereas  at  3x10^,  rough  ctenoid  scales  appear  on  the  body 
behind  the  head.  The  ctenoid  scales  have  a  comblike  edge,  these  scales 
are  believed  to  produce  microturbulence.  Ctenoid  scales  are  replaced, 
however,  with  smoother  cycloid  scales  above  10*\  where  transition 
would  normally  occur. 

The  elongate  rostrum  of  the  swordfish,  Xiphias  gladius ,  has  a 
rough  surface  with  craters  and  bumps  [82].  Because  the  sword  can 
reach  a  length  of  40-45%  of  body  length,  at  high  swimming  speeds,  the 
critical  Re  for  transition  would  be  reached  before  the  head.  Thus, 
separation  would  be  avoided  from  the  body  of  the  fish,  despite  the 
anterior  position  of  the  maximum  thickness  which  is  just  posterior  of  the 
head  [45,  82]. 


446 


Drafting 

Various  animals  travel  in  highly  organized  formations.  This 
behavior  has  been  hypothesized  to  reduce  drag  and  enhance  locomotor 
performance  of  individuals.  Formation  movement  generally  is  accepted 
for  automotive  and  cycling  competitions  [97,  98,  99],  which  use  the 
techniques  of  "drafting”  or  "slipstreaming".  Wind  tunnel  measurements 
on  cars  demonstrated  a  37-48%  reduction  in  drag  when  following 
closely  behind  another  vehicle  [97,  100].  Trailing  cyclists  in  a  pace  line 
experience  a  38%  reduction  in  wind  resistance  [98]  and  an  energy 
savings  of  62%  when  drafting  behind  a  more  massive  body,  such  as  a 
truck  [99]. 

For  animals,  formation  swimmers  influence  the  flow  of  water 
around  adjacent  individuals.  Vorticity  generated  by  anterior  individuals 
provides  momentum  to  the  water.  If  a  trailing  animal  is  oriented 
parallel  and  is  moving  in  the  same  direction  to  the  tangential  velocity  of 
the  vortex,  the  body  will  experience  a  reduction  in  its  relative  velocity. 
Because  the  drag  is  directly  proportional  to  the  velocity  squared,  a 
decrease  in  the  relative  velocity  can  decrease  drag  and  the  associated 
energy  expenditure.  Vorticity  is  shed  into  the  wake  of  a  passive  body 
as  two  rows  of  counter-rotating  vortices  (i.e.,  K&rm£n  vortex  street) 
where  the  optimal  position  for  drag  reduction  is  directly  behind  another 
body  [101].  Although  similar  in  pattern  to  the  K&rm£n  vortex  street,  a 
thrust-type  vortex  system  has  the  opposite  rotation  of  the  vortices.  In 
this  system  which  is  generated  by  an  oscillating  foil,  the  optimal 
orientation  is  diagonally  [102]. 

Queues  of  spiny  lobsters  (Panulirus  argus)  in  water  were  shown 
to  sustain  less  drag  per  individual  than  a  single  lobster  traveling  at  the 
same  speed  [103],  The  reduction  in  energetic  cost  per  individual  in  a 
queue  was  a  direct  function  of  queue  size.  Ducklings  which  swim 
behind  the  mother  in  single-file  experience  a  7.8-43.5%  decrease  in 
energy  cost  with  increased  savings  for  larger  groups  [101).  In  addition, 
the  duckling  at  the  end  of  the  formation  appears  to  received  the  largest 
energetic  savings  [Fish,  1995].  Drag  reduction  in  single-file  formation 
is  associated  with  small  spacings  between  individuals  (<  one  body 
length)  [97,  100,  104], 

Thrust-type  vortices  produced  by  fish  provide  drag  reduction  in 
diamond-shaped  formations  [86,  102].  Trailing  fish  experience  a 
relative  velocity  40-50%  of  the  free  stream  velocity  and  a  reduction  of 
the  force  generated  for  swimming  by  a  factor  of  4  to  6.  However,  the 
decrease  in  relative  velocity  is  not  maintained  with  each  successive 
row  of  trailing  fish  due  to  destructive  interference. 

Wave  Drag 

Bow  structure 

Bulbous  bows  on  displacement  hulls  reduce  wave  drag  by  60%  by 
canceling  most  of  the  wave  pattern  created  at  the  bow  and  avoiding 
energy  loss  by  wave  breaking  [105,  106],  Semiaquatic  mammals  (e.g., 
beaver,  muskrat,  water  opossum)  swim  on  the  water  surface  while 
holding  their  forelimbs  under  the  chin  [22,  107].  Such  as  configuration 
of  the  limbs  may  effectively  act  like  a  bulbous  bow,  although  this  has 
not  been  examined. 

Hydroplaning 

Relatively  few  animals  swim  at  the  water  surface  for  extended 
periods.  As  a  displacement  hull,  surface  swimming  animals  encounter 
high  energy  costs  and  limitations  to  speed  from  wave  drag.  Despite  the 
small  size  of  ducklings  which  places  severe  limitations  on  swimming 
velocity  due  to  hull  speed,  speeds  above  hull  speed  are  accomplished 
by  replacing  the  displacement  hull  configuration  with  a  planing  hull 
[18].  The  motion  of  a  planing  hull  has  been  described  as 
"hydroplaning”  or  "skimming"  [108].  With  the  hull  inclined  with  a 
positive  angle  of  trim,  a  positive  pressure  develops  under  the  hull 
creating  a  vertical  "dynamic  lift"  component  which  at  high  speeds  may 
be  greater  than  buoyancy  [105,  109]. 

Several  factors  contribute  to  the  relatively  low  drag  of  planing. 
(1)  The  increase  in  trim  angle  raises  the  bow  from  the  water 
decreasing  the  amount  of  wetted  surface  area  reducing  skin  friction 
[108,  109].  (2)  Above  hull  speed  water  does  not  have  time  to  respond 
to  the  pressure  disturbance  and  the  water  surface  is  effectively 
smoothed  [105,  108,  110].  (3)  Wave  drag  is  largely  eliminated  by 
lifting  the  hull,  although  spray  drag  will  increase  [19,  105,  109]. 

At  Fl  =  0.6- 1.0,  a  hull  is  semiplaning  such  that  it  is  supported  by 
both  hydrodynamic  (dynamic  lift)  and  hydrostatic  (buoyant  lift)  forces 
[105,  109].  Above  Fl  =  1,  the  hull  is  supported  entirely  by  dynamic  lift 


(planing).  Mallard  ducklings  {Anas  platyrhynchos)  can  burst  at  Fl  >  1 
effectively  planing  on  the  water  surface  [18].  Steamer  ducks 
( Tachyeres  spp.)  include  three  large,  flightless  species  which 
hydroplane  continuously  over  distances  of  1  km  and  at  speeds  up  to 
6.67  m/s  (Fl  =  3)  over  the  water  surface  using  their  feet  and  wings 
[18,111]. 

Spray  Drag 

Two  bat  species  ( Noctilio  leporinus,  Pizonyx  vivesi)  are  adapted 
for  catching  and  eating  fish  [1 12,  1 13].  The  bats  use  their  echolocation 
to  detect  fish  by  ripples  or  breaks  on  the  water  surface  and  then  drag 
their  feet  through  the  water  to  gaff  the  fish  with  their  claws.  To  reduce 
drag,  the  toes  and  claws  are  laterally  compressed  with  a  reversed 
fusiform  cross-section  [114].  Although  a  typical  fusiform  shape  works 
effectively  for  fully  immersed  bodies,  this  shape  should  be  avoided  at 
the  air-water  interface  [20].  At  high  Froude  numbers  (Fl  <  0.5),  spray 
drag  can  be  a  significant  proportion  of  the  total  drag,  whereas  wave 
drag  is  insignificant  [19].  For  the  fishing  bats,  where  Fl  >  270,  the 
reversed  fusiform  design  with  a  long  forebody  region  relative  to  the 
claw  thickness  can  reduce  spray  drag  [19,  114].  An  analogous  design 
is  observed  in  the  lower  mandible  of  the  black  skimmer  {Rhyncops 
nigra),  which  catches  fish  at  the  water  surface  with  its  beak  [115], 
Application  of  this  mechanism,  however,  is  limited  to  linear  motion, 
because  the  reversed  fusiform  design  will  incur  premature  separation 
with  increased  drag  and  loss  of  lift  during  turning  maneuvers. 

Induced  Drag 

The  design  of  the  appendages  (e.g.,  fins,  flukes,  flippers) 
determines  the  magnitude  of  the  induced  drag.  Well-performing 
appendages  maximize  the  ratio  of  lift  (L)  to  drag  (D)  generated  by 
their  action  [11].  An  increase  in  the  maximum  L/D  with  increasing 
size  is  achieved  by  increasing  span  more  rapidly  than  the  square-root 
of  planar  area,  thereby  increasing  AR  [68,  116,  117,  118,  119].  High 
AR  and  tapering  of  the  appendages  reduces  tip  vorticity  and  induced 
drag  [11,  119,  120,  121].  The  fastest  swimming  fish  and  marine 
mammals  have  propulsors  with  AR  ranging  from  3.4-8. 7  [57].  AR 
above  8-10  provides  little  further  advantage  and  may  be  structurally 
limited  [11]. 

Induced  drag  also  is  limited  by  the  sweep  angle  of  the  appendage. 
A  tapered  wing  with  sweptback  or  crescent  design  could  reduce  the 
induced  drag  by  8.8%  compared  to  a  wing  with  an  elliptical  planform 
[117].  Induced  drag  can  be  reduced  with  a  swept  wing  planform  with  a 
root  chord  greater  than  the  chord  at  the  tips  giving  a  triangular  shape 
[122,  123].  This  optimal  shape  approximates  the  planform  of  animals 
which  swim  with  a  lunate  propulsor,  including  scombrid  fishes,  laminid 
sharks,  extinct  ichthyosaurs,  cetaceans,  and  phocid  seals  [11,  57,  62, 
118]. 

Flight 

A  behavioral  strategy  to  minimize  drag  is  to  leave  the  water 
entirely.  Many  aquatic  animals  leap  clear  of  the  water  to  travel  through 
the  air  to  reduce  the  energy  required  for  locomotion  and  avoid 
predation.  In  certain  cases  the  animals  take  a  ballistic  trajectory,  such 
as  dolphins,  seals,  sea  lions,  penguins,  and  fish  [124,  125,  126], 
whereas  others  have  modified  lifting  surfaces  to  extend  the  flight  over 
long  distances,  such  as  flying  squid  and  flying  fish  [127,  128]. 

Porpoising  consists  of  rhythmic,  serial  leaps  in  which  the  animal 
leaves  and  re-enters  the  water  nose-first  during  continuous  swimming. 
Models  of  porpoising  predict  that  at  high  velocities  the  energy  to  leap  a 
given  distance  is  lower  than  the  energy  to  swim  [124,  129].  Below 
some  critical  speed,  however,  the  opposite  is  assumed.  As  obligate  air- 
breathers,  marine  mammals  and  penguins  must  swim  in  close  proximity 
to  the  surface  despite  increased  drag  [17,  71],  Porpoising  permits  these 
animals  to  breath  while  simultaneously  reducing  locomotor  energy 
costs  [125,  130]. 

CONCLUDING  REMARKS 

Progress  in  technologies  concerned  with  drag  reduction  comes 
from  the  discovery  and  refinement  of  new  designs.  A  diversity  of  drag 
reducing  mechanisms  are  exhibited  by  aquatic  animals  in  association 
with  their  habits  and  restrictions  on  body  design.  Both  machines  and 
animals  must  contend  with  the  same  physical  laws  that  regulate  their 
design  and  behavior.  Although  animal  mechanisms  have  been 
recognized  mainly  after  an  engineered  solution  was  developed,  the 
analogy  simply  demonstrates  functional  similarity  and  close 


447 


examination  of  the  biological  mechanism  may  indicate  possible 
pathways  for  improvements  in  engineered  designs.  In  comparison  to 
engineers  who  can  limit  variables  in  their  systems,  the  problem  for 
biologists  has  been  that  the  systems  they  study  are  complex.  More  than 
two  hundred  years  ago,  the  British  philosopher  David  Hume  pondered 
the  complexity  of  biological  organisms  as: 

All  these  various  machines,  and  even  their  most  minute  parts,  are 
adjusted  to  each  other  with  an  accuracy  which  ravishes  into  admiration 
all  men  who  have  ever  contemplated  them.  The  curious  adapting  of 
means  to  ends,  throughout  all  nature,  resembles  exactly,  though  it  much 
exceeds,  the  productions  of  human  contrivance. 

As  matters  of  energy  economy  and  greater  speeds  are  desired  in 
engineered  systems  [5],  imaginative  solutions  for  drag  reduction  from 
nature  may  serve  as  the  inspiration  for  new  technologies.  The  union 
between  biologists  and  engineers  and  use  of  modern  computational 
approaches  [131,  132]  promise  an  understanding  of  biological  systems 
and  modifications  fitted  to  an  engineered  application. 

ACKNOWLEDGMENTS 

I  would  like  to  express  my  appreciation  to  the  organizers  of  this 
symposium  for  their  invitation  to  attend.  This  review  is  based  in  part  on 
research  performed  with  support  from  National  Science  Foundation 
grant  number  DCB-9 117274  and  the  Office  of  Naval  Research  grant 
number  N00014-95-1-1045. 

REFERENCES 

1.  Jakab,  P.  L.  1990.  Visions  of  a  flying  machine.  Smithsonian 
Institution  Press,  Washington. 

2.  Triantafyllou,  G.  S.  and  Triantafyllou,  M.  S.  1995.  An  efficient 
swimming  machine.  Sci.  Amer .,  272:64-70. 

3.  Bandyopadhyay,  P.  R.  and  Donnelly,  M.  J.  1997.  The  swimming 
hydrodynamics  of  a  pair  of  flapping  foils  attached  to  a  rigid 
body.  Tenth  Internal.  Symp.  Unmanned  Untethered  Submersible 
Tech.:  Proc .  Sp.  Ses.  Bio-Eng  Res.  Related  to  Autonomous 
Underwater  Vehicles.  Pp.  27-43. 

4.  Vincent,  J.  1990.  Structural  biomaterials.  Princeton  Univ.  Press, 
Princeton. 

5.  Bushnell,  D.  M.  and  Moore,  K.  J.  1991.  Drag  reduction  in 
nature.  Ann.  Rev.  Fluid Mech.,  23:65-79. 

6.  Harris,  J.  S.  1989.  An  airplane  is  not  a  bird.  Invention  & 
Technology,  5:  18-22. 

7.  Vogel,  S.  1994.  Life  in  moving  fluids.  Princeton  University 
Press,  Princeton. 

8.  Katz,  S.  L  and  Jordan,  C.  E.  1997.  A  case  for  building  integrated 
models  of  aquatic  locomotion  that  couple  internal  and  external 
forces.  Tenth  Internat.  Symp.  Unmanned  Untethered 
Submersible  Tech.:  Proc.  Sp.  Ses.  Bio-Eng  Res.  Related  to 
Autonomous  Underwater  Vehicles.  Pp.  135-152. 

9.  Webb,  P.  W.  1997.  Designs  for  stability  and  maneuverability  in 
aquatic  vertebrates:  What  can  we  learn.  Tenth  Internat.  Symp. 
Unmanned  Untethered  Submersible  Tech.:  Proc.  Sp.  Ses.  Bio- 
Eng  Res.  Related  to  Autonomous  Underwater  Vehicles.  Pp.  85- 
108. 

10.  Alexander,  R.  McN.  1985.  The  ideal  and  the  feasible:  physical 
constraints  on  evolution.  Biol.  J.  Linn.  Soc.,  26:345-358. 

11.  Webb,  P.  W.  1975.  Hydrodynamics  and  energetics  of  fish 
propulsion.  Bull.  Fish.  Res.  Bd.  Can.,  190:1-158. 

12.  Fish,  F.  E.  and  Hui,  C.  J.  1991.  Dolphin  swimming  -  a  review. 
Mamm.  Rev.,  21:181-195. 

13.  Lang,  T.  G.  1975.  Speed,  power,  and  drag  measurements  of 
dolphins  and  porpoises.  In  T.  Y.  Wu,  C.  J.  Brokaw  and  C. 
Brennen  (eds.),  Swimming  and  flying  in  nature,  Vol.  2,  pp.  553- 
571.  Plenum  Press,  New  York. 

14.  Magnuson,  J.  J.  1978.  Locomotion  by  scombrid  fishes: 
hydrodynamics,  morphology  and  behaviour.  In  W.  S.  Hoar  and 
D.  J.  Randall  (eds.),  Fish  physiology,  vol.  7,  pp.  239-313. 
Academic  Press,  London. 

15.  Katz,  J.  and  Plotkin,  A.  1991.  Low-speed  aerodynamics:  from 
wing  theory  to  panel  methods.  McGraw-Hill,  New  York. 

16.  Lang  ,  T.  G.  and  Daybell,  D.  A.  1963.  Porpoise  performance 
tests  in  a  seawater  tank.  Nav.  Ord.  Test  Sta.  Tech.  Rep.  3063. 

17.  Hertel,  H.  1966.  Structure,  form,  movement.  Reinhold,  New 
York. 


18.  Aigeldinger,  T.  L.  and  Fish,  F.  E.  1995.  Hydroplaning  by 
ducklings:  Overcoming  limitations  to  swimming  at  the  water 
surface.  J.  Exp.  Biol.,  198:1567-1574. 

19.  Hoerner,  S.  F.  1965.  Fluid-Dynamic  Drag.  Published  by 
author,  Brick  Town,  New  Jersey. 

20.  Marchaj,  C.  A.  1991.  Aero-hydrodynamics  of  sailing. 
International  Marine  Publishing,  Camden,  Maine. 

21.  Prange,  H.  and  Schmidt-Nielsen,  K.  1970.  The  metabolic  cost  of 
swimming  in  ducks.  J.  Exp.  Biol.,  53:763-777. 

22.  Fish,  F.  E.  1982.  Aerobic  energetics  of  surface  swimming  in  the 
muskrat  Ondatra  zibethicus.  Physiol.  Zool .,  55:180-189. 

23.  Vogel,  S.  1988.  Life’s  devices.  Princeton  University  Press, 
Princeton. 

24.  Denny,  M.  W.  1993.  Air  and  water.  Princeton  University  Press, 
Princeton. 

25.  Hoyt,  J.  W.  1975.  Hydrodynamic  drag  reduction  due  to  fish 
slimes.  In  T.  Y.  Wu,  C.  J.  Brokaw,  and  C.  Brennen  (eds.), 
Swimming  and  flying  in  nature,  Vol.  2,  pp.  653-672.  Plenum 
Press,  New  York. 

26.  Daniel,  T.  L.  1981.  Fish  mucus:  In  situ  measurements  of  polymer 
drag  reduction.  Biol.  Bull,  160:376-382. 

27.  Rosen,  M.  W.  and  Cornford,  N.  E.  1971.  Fluid  friction  of  fish 
slimes.  Nature,  234:49-51. 

28.  Breder,  C.  M.  1926.  The  locomotion  of  fishes.  Zoologica  (N.Y.), 
4:159-256. 

29.  Sokolov,  V.,  Bulina,  I,  and  Rodionov,  V.  1969.  Interaction  of 
dolphin  epidermis  with  flow  boundary  layer.  Nature,  222:267- 
268. 

30.  Harrison,  R.  J.  and  Thurley,  K.  W.  1972.  Fine  structural  features 
of  delphinid  epidermis.  J.  Anat.,  Ill:  498-499. 

31.  Gucinski,  H.  and  Baier,  R.  E.  1983.  Surface  properties  of 
porpoise  and  killer  whale  skin  in  vivo.  Amer.  Zool.,  23:959. 

32.  Walsh,  M.  J.  1990.  Riblets.  Prog.  Astro.  Aero.,  123:203-261. 

33.  Pershin,  S.  V.,  Chernyshov,  L.  F.,  Kozlov,  L.  F.,  Koval,  A.  P., 
and  Zayets,  V.  A.  1976.  Patterns  in  the  integuments  of  fast¬ 
swimming  fishes.  Bionika,  10:3-21. 

34.  Reif,  W.-E.  1978.  Protective  and  hydrodynamic  function  of  the 
dermal  skeleton  of  elasmobranchs.  Neues  Jahrb.  Geol.  Palaotol, 
157:133-141. 

35.  Reif,  W.-E.  and  Dinkelacker,  A.  1982.  Hydrodynamics  of  the 
squamation  in  fast  swimming  sharks.  Neues  Jahrb.  Geol. 
Palaotol,  164:184-187. 

36.  Pershin,  S.  V.  1988.  Fundamentals  of  hydrobionics. 
Sudostroyeniye  Publ.,  Leningrad. 

37.  Reidy,  L.  W.  1987.  Flat  plate  drag  reduction  in  a  water  tunnel 
using  riblets.  NOSC  Tech.  Rep.  1169. 

38.  Anderson,  E.  J.,  MacGillivray,  P.  S.,  and  DeMont,  M.  E.  1997. 
Scallop  shells  exhibit  optimization  of  riblet  dimensions  for  drag 
reduction.  Biol.  Bull.  192:341-344. 

39.  Purves,  P.  E.,  Dudok  van  Heel,  W.  H.,  and  Jonk,  A.  1975. 
Locomotion  in  dolphins  Part  I:  Hydrodynamic  experiments  on  a 
model  of  the  bottle-nosed  dolphin,  Tursiops  truncatus,  (Mont.). 
Aqu.  Mamm.,  3:5-31. 

40.  Yurchenko,  N.  F.  and  Babenko,  V.  V.  1980.  Stabilization  of  the 
longitudinal  vortices  by  skin  integuments  of  dolphins.  Biophysics, 
25:309-315. 

41.  Gray,  J.  1936.  Studies  in  animal  locomotion  VI.  The  propulsive 
powers  of  the  dolphin.  J.  Exp.  Biol,  13:192-199. 

42.  Kramer,  M.  O.  1960.  Boundary  layer  stabilization  by  distributed 
damping.  J.  Amer.  Soc.  Nav.  Eng.,  72:25-33. 

43.  Kramer,  M.  O.  1960.  The  dolphins'  secret.  New  Sci.,  7:1118- 
1120. 

44.  Kramer,  M.  O.  1965.  Hydrodynamics  of  the  dolphin.  In  V.  T. 
Chow  (ed.),  Advances  in  Hydroscience,  Vol.  2  .,  pp.  111-130. 
Academic  Press,  New  York. 

45.  Aleyev,  Yu.  G.  1977.  Nekton .  Junk,  The  Hague. 

46.  Riley,  J.  J.,  Gad-el-Hak,  M.  and  Metcalfe,  R.  W.  1988. 
Compliant  coatings.  Ann.  Rev.  Fluid  Mech.,  20:393-420. 

47.  Landahl,  M.  T.  1962.  On  stability  of  a  laminar  incompressible 
boundary  layer  over  a  flexible  surface.  J.  Fluid  Mech.,  13:609- 
632. 

48.  Blick,  E.  F.  and  Walters,  R.  R.  1968.  Turbulent  boundary-layer 
characteristics  of  compliant  surfaces.  J.  Aircraft,  5:11-16. 

49.  Gad-el-Hak,  M.  1987.  Compliant  cpatings  research:  A  guide  to 
the  experimentalist.  J.  Fluid.  Struct'.,  1:55-70. 


448 


50.  Toedt,  M.  E.,  Reuss,  L.  E.,  Dillaman,  R.  M.,  and  Pabst  D.  A. 
1997.  Collagen  and  elastin  arrangements  in  the  blubber  of 
common  dolphin  ( Delphinus  delphis).  Amer.  Zool. ,  37:56A. 

51.  Essapian,  F.  S.  1955.  Speed-induced  skin  folds  in  the  bottle¬ 
nosed  porpoise,  Tursiops  truncatus.  Breviora  Mus.  Comp.  Zool , 
43:1-4. 

52.  Lang,  T.  G.  and  K.  Pryor.  1966.  Hydrodynamic  performance  of 
porpoises  (Stenella  attenuata).  Science ,  152:531-533. 

53.  Rosen,  M.  W.  1961.  Experiments  with  swimming  fish  and 
dolphins.  Amer.  Soc.  Mech.  Eng.  Paper  61-WA-203. 

54.  Latz,  M.  I.,  Rohr,  J.  and  Hoyt,  J.  1995.  A  novel  flow 
visualization  technique  using  bioluminescent  marine  plankton  - 
Part  I:  Laboratory  studies.  IEEEJ.  Ocean.  Eng.,  20:144-147. 

55.  Rohr,  J.,  M.  I.  Latz,  E.  Hendricks,  and  J.  C.  Nauen.  1995..  A 
novel  flow  visualization  technique  using  bioluminescent  marine 
plankton  -  Part  II:  Field  studies.  IEEE  J.  Ocean.  Eng.,  20:147- 
149. 

56.  Williams,  T.  M.  and  Kooyman,  G.  L.  1985.  Swimming 
performance  and  hydrodynamic  characteristics  of  harbor  seals 
Phoca  vitulina.  Physiol.  Zool.,  58:576-589. 

57.  Fish,  F.  E.,  Innes,  S.,  and  Ronald,  K.  1988.  Kinematics  and 
estimated  thrust  production  of  swimming  harp  and  ringed  seals. 
J.Exp.  Biol. ,  137:157-173. 

58.  Romanenko,  E.  V.  1976.  Acoustics  and  hydrodynamics  of 
certain  marine  animals.  Sov.  Phys.  Acoust.,  22:357-358. 

59.  Romanenko,  E.  V.  1981.  Distribution  of  dynamic  pressure  over 
the  body  of  an  actively  swimming  dolphin.  Sov.  Phys.  Dokl, 
26:1037-1038. 

60.  Videler,  J.  and  Kamermans,  P.  1985.  Differences  between 
upstroke  and  downstroke  in  swimming  dolphins.  J.  Exp.  Biol, 
119:265-274. 

61.  Fish,  F.  E.  1993.  Power  output  and  propulsive  efficiency  of 
swimming  bottlenose  dolphins  ( Tursiops  truncatus).  J.  Exp.  Biol. , 
185:179-193. 

62.  Lighthill,  J.  1975.  Mathematical  biofluiddynamics.  Soc.  Ind. 
Appl.  Math.,  Philadelphia. 

63.  Walters,  V.  1963.  The  trachipterid  integument  and  an  hypothesis 
on  its  hydrodynamic  function.  Copeia,  1963:260-270. 

64.  Bone,  Q.  1972.  Buoyancy  and  hydrodynamic  functions  of 
integument  in  the  castor  oil  fish,  Ruvettus  pretiosus  (Pisces: 
Gempylidae).  Copeia,  1972:78-87. 

65.  AbdulNour,  B.  S.  and  Mueller,  M.  K.  1993.  Hybrid  laminar  flow 
over  wings  enhanced  by  continuous  boundary-layer  suction. 
SAE  Tech.  Paper  931386. 

66.  Walters,  V.  1962.  Body  form  and  swimming  performance  in 
scombrid  fishes.  Am.  Zool,  2:143-149. 

67.  Lang,  T.  G.  1966.  Hydrodynamic  analysis  of  cetacean 
performance.  In  K.  S.  Norris  (ed.),  Whales,  Dolphins  and 
Porpoises ,  pp.  410-432.  Univ.  of  California  Press,  Berkeley. 

68.  von  Mises,  R.  1945.  Theory  of  flight.  Dover,  New  York. 

69.  Hess,  J.  L.  1976.  On  the  problem  of  shaping  an  axisymmetric 
body  to  obtain  low  drag  at  large  Reynolds  numbers.  J.  Ship  Res., 
20:51-60. 

70.  Bannasch,  R.  1995.  Hydrodynamics  of  penguins  -  an 
experimental  approach.  In  P.  Dann,  I  Norman,  and  P.  Reilly 
(eds.),  The  penguins :  Ecology  and  management,  pp.  141-176. 
Surrey  Beatty  and  Sons,  Norton,  NSW. 

71.  Fish,  F.  E.  1993.  Influence  of  hydrodynamic  design  and 
propulsive  mode  on  mammalian  swimming  energetics.  Aust.  J. 
Zool,  42:79-101. 

72.  Feldkamp,  S.  D.  1987.  Swimming  in  the  California  sea  lion: 
Morphometries,  drag  and  energetics.  J.  Exp.  Biol,  131:117-135. 

73.  Felts,  W.  J.  L.  1966.  Some  functional  and  structural 
characteristics  of  cetaceans  flippers  and  flukes.  In  K.  S.  Norris 
(ed.),  Whales,  Dolphins  and  Porpoises ,  pp.  255-276.  University 
of  California  Press,  Berkeley. 

74.  Lang,  T.  G.  1966.  Hydrodynamic  analysis  of  dolphin  fin  profiles. 
Nature,  209:1-1 10-1  111. 

75.  Sokolov,  W.  1962.  Adaptations  of  the  mammalian  skin  to  the 
aquatic  mode  of  life.  Nature,  195:464-466. 

76.  Mordvinov,  Yu.  E.  and  Kurbatov,  B.  V.  1972.  Influence  of  hair 
cover  in  some  species  of  Phocidae  upon  the  value  of  general 
hydrodynamic  resistance.  Zool.  Zh.,  51:242-247. 

77.  Ling,  J.  K.  1970.  Pelage  and  molting  in  wild  mammals  with 
special  reference  to  aquatic  forms.  Quart.  Rev.  Biol,  45:16-54. 


78.  Romanenko,  E.  V.,  Sokolov,  V.  E.,  and  Kalinichenko,  N.  M. 
1973.  Hydrodynamic  patterns  of  hair  cover  in  Phoca  sibirica. 
Zool.  Zh.,  52:1537-1542. 

79.  Kooyman,  G.  L.  1989.  Diverse  divers:  physiology  and  behavior. 
Springer-Verlag,  Berlin. 

80.  Bandyopadhyay,  P.  R.  1989.  Viscous  drag  reduction  of  a  nose 
body.  AIAA  Journal,  27:274-282. 

81.  Bandyopadhyay,  P.  R.  and  Ahmed,  A.  1993.  Turbulent  boundary 
layers  subjected  to  multiple  curvatures  and  pressure  gradients.  J. 
Fluid  Mech.,  246:503-527. 

82.  Videler,  J.  J.  1995.  Body  surface  adaptations  to  boundary-layer 
dynamics.  In  C.  P.  Ellington  and  T.  J.  Pedley  (eds.),  Biological 
fluid  dynamics,  pp.  1-20.  Soc.  Exp.  Biol.,  Cambridge. 

83.  Maisey,  J.  G.  1979.  Finspine  morphogenesis  in  squalid  and 
heterodontid  sharks.  Zool  J.  Linn .  Soc.,  66:161-183. 

84.  Videler,  J.  J.  and  Weihs,  D.  1982.  Energetic  advantages  of 
burst-and-coast  swimming  of  fish  at  high  speeds.  J.  Exp.  Biol., 
97:169-178. 

85.  Weihs,  D.  and  Webb,  P.  W.  1983.  Optimization  of  locomotion. 
In  P.  W.  Webb  and  D.  Weihs  (eds.),  Fish  biomechanics,  pp. 
339-371.  Praeger,  New  York. 

86.  Weihs,  D.  1974.  Energetic  advantages  of  burst  swimming  of 
fish.  J.  Theor.  Biol,  48:215-229. 

87.  Fish  FE,  Fegely,  J,  Xanthopoulos  CJ.  1991.  Burst-and-coast 
swimming  in  schooling  fish  ( Notemigonus  crysoleucas)  with 
implications  for  energy  economy.  Comp.  Biochem.  Physiol. , 
100A:633-637. 

88.  Rosen,  M.  W.  1959.  Water  flow  about  a  swimming  fish.  U.S. 
Nav.  Ord.  TestSta  Tech.  Publ.  2298:1-96. 

89.  Triantafyllou,  G.  S.,  Triantafyllou,  M.  S.,  and  Gosenbaugh,  M. 
A.  1993.  Optimal  thrust  development  in  oscillating  foils  with 
application  to  fish  propulsion.  J.  Fluids  Struct.,  7:205-224. 

90.  Gopalkrishnan,  R.,  Triantafyllou,  M.  S.,  Triantafyllou,  G.  S.,  and 
Barrett,  D.  1994.  Active  vorticity  control  in  a  shear  flow  using  a 
flapping  foil.  J.  Fluid  Mech.,  274:1-21. 

91.  Fish,  F.  E.  and  Battle,  J.  M.  1995.  Hydrodynamic  design  of  the 
humpback  whale  flipper.  J.  Morph.,  225:51-60. 

92.  Nakaya,  K.  1995.  Hydrodynamic  function  of  the  head  in  the 
hammerhead  sharks  (Elasmobranchii:  Sphrynidae).  Copeia , 
1995:330-336. 

93.  Shevell,  R.  S.  1986.  Aerodynamic  anomalies:  Can  CFD  prevent 
or  correct  them?  J.  Aircraft ,  23:641-649. 

94.  Bragg,  M.  B.  and  Gregorek,  G.  M.  1987.  Experimental  study  of 
airfoil  performance  with  vortex  generators.  J.  Aircraft,  24:305- 
309. 

95.  Chamberlain,  J.  A.,  Jr.  and  Westermann,  G.  E.  G.  1976. 
Hydrodynamic  properties  of  cephalopod  shell  ornament. 
Paleobiology,  2:316-331. 

96.  Videler,  J.  1993.  Fish  swimming.  Chapman  and  Hall,  London. 

97.  Romberg,  G.  F.,  Chianese,  F.,  Jr.,  and  Lajoie,  R.  G.  1971. 
Aerodynamics  of  race  cars  in  drafting  and  passing  situations. 
Soc.  Auto.  Eng.  Paper  710213. 

98.  Kyle,  C.  R.  1979.  Reduction  of  wind  resistance  and  power  output 
of  racing  cyclists  and  runners  traveling  in  groups.  Ergonomics, 
22:387-397. 

99.  Hagberg,  J.  M.  and  McCole,  S.  D.  1990.  The  effect  of  drafting 
and  aerodynamic  equipment  on  energy  expenditure  during 
cycling.  Cycling  Sci.,  2:19-22. 

100.  Zabat,  M.,  Frascaroli,  S.,  and  Browand,  F.  K.  1994.  Drag 
measurements  on  2,  3  and  4  car  platoons.  Soc.  Auto.  Eng.  Paper 
940421. 

101.  Fish,  F.  E.  1994.  Energy  conservation  by  formation  swimming: 
metabolic  evidence  from  ducklings.  In  L.  Maddock,  Q.  Bone, 
and  J.  M.  V.  Rayner  (eds.),  Mechanics  and  physiology  of  animal 
swimming,  pp.  193-204.  Cambridge  University  Press, 
Cambridge. 

102.  Weihs,  D.  1973.  Hydromechanics  of  fish  schooling.  Nature 4 
241:290-291. 

103.  Bill,  R.  G.  and  Herrnkind,  W.  F.  1976.  Drag  reduction  by 
formation  movement  in  spiny  lobsters.  Science,  193:1 146-1 148. 

104.  Fish,  F.  E.  1995.  Kinematics  of  ducklings  swimming  in  formation: 
Energetic  consequences  of  position.  J.  Exp.  Zool,  272:1-11. 

105.  Saunders,  H.  E.  1957.  Hydrodynamics  in  ship  design.  Soc.  Nav. 
Arch.  Mar,  Eng.,  New  York. 


449 


106.  Wehausen,  J.  V.  1973.  The  wave  resistance  of  ships.  In  C.  S. 
Yih  (ed.),  Advances  in  applied  mechanics ,  Vol.  13,  pp.  93-245. 
Academic  Press,  New  York. 

107.  Fish,  F.  E.  1993.  Comparison  of  swimming  kinematics  between 
terrestrial  and  semiaquatic  opossums.  J.  Mamm .,  74:275-284. 

108.  Hammitt,  A.  G.  1975.  Technical  yacht  design.  Van  Nostrand 
Reinhold,  New  York. 

109.  Marchaj,  C.  A.  1964.  Sailing  theory  and  practice.  Dodd,  Mead 
and  Co.,  New  York. 

110.  Taylor,  D.  W.  1933.  The  speed  and  power  of  ships.  Ransdell  Inc., 
Washington,  D.  C. 

111.  Livezey,  B.  C.  and  Humphrey,  P.  S.  1983.  Mechanics  of 
steaming  in  steamer-ducks.  Auk ,  100:485-488. 

112.  Bloedel,  P.  1955.  Hunting  methods  of  fish-eating  bats, 
particularly  Noctilio  leporinus.  J.  Mamm.,  36:390-399. 

113.  Suthers,  R.  1965.  Acoustic  orientation  by  fish-catching  bats.  J. 
Exp.  Biol.,  158:319-348. 

114.  Fish,  F.  E.,  Blood,  B.  R.,  and  Clark,  B.  D.  1991.  Hydrodynamics 
of  the  feet  offish-catching  bats:  Influence  of  the  water  surface 
on  drag  and  morphological  design.  J.  Exp.  Zool. ,  258:164-173. 

115.  Withers,  P.  C.  and  Timko,  P.  L.  1977.  The  significance  of  ground 
effect  to  the  aerodynamic  cost  of  flight  and  energetics  of  the 
black  skimmer  ( Rhyncops  nigra).  J.  Exp.  Biol,  70:13-26. 

1 16.  Lighthill,  J.  1977.  Introduction  to  scaling  of  aerial  locomotion. 
In  T.  J.  Pedley  (ed.),  Scale  effects  in  animal  locomotion,  pp.  365- 
404.  Academic  Press,  London. 

117.  van  Dam,  C.  P.  1987.  Efficiency  characteristics  of  crescent¬ 
shaped  wings  and  caudal  fins.  Nature ,  325:435-437. 

118.  Bose,  N.,  Lien,  J.,  and  Ahia,  J.  1990.  Measurements  of  the 
bodies  and  flukes  of  several  cetacean  species.  Proc.  Roy.  Soc. 
Bond.  B,  242:163-173. 

119.  Daniel,  T.,  Jordan,  C.,  and  Grunbaum,  D.  1992.  In  R.  McN. 
Alexander  (ed.),  Advances  in  comparative  &  environmental 
physiology  11:  Mechanics  of  animal  locomotion,  pp.  17-49. 
Springer-Verlag,  Berlin. 

120.  Rayner,  J.  M.  V.  1985.  Vorticity  and  propulsion  mechanics  in 
swimming  and  flying  animals.  In  J.  Riess  and  E.  Frey  (eds.), 
Konstruktionsprinzipen  lebender  und  ausgestorbener  Reptilien , 
pp.  89-1 18.  University  of  Tubingen,  Tubingen,  F.R.G. 

121.  Webb,  P.  W.,  and  Buffr6nil,  V.  de.  1990.  Locomotion  in  the 
biology  of  large  aquatic  vertebrates.  Trans.  Amer.  Fish.  Soc., 
119:629-641. 

122.  Kilchermann,  D.  1953.  The  distribution  of  lift  over  the  surface 
of  swept  wings.  Aero.  Quart.,  4:261-278. 

123.  Ashenberg,  J.  and  Weihs,  D.  1984.  Minimum  induced  drag  of 
wings  with  curved  planform.  J.  Aircraft,  21:89-91. 

124.  Au,  D.  and  Weihs,  D.  1980.  At  high  speeds  dolphins  save  energy 
by  leaping.  Nature x  284:548-550. 

125.  Hui,  C.  A.  1987.  The  porpoising  of  penguins:  an  energy- 
conserving  behavior  for  respiratory  ventilation?  Can.  J.  Zool. , 
65:209-211. 

126.  Williams,  T.  M.  1987.  Approaches  for  the  study  of  exercise 
physiology  and  hydrodynamics  in  marine  mammals.  In  A.  C. 
Huntley,  D.  P.  Costa,  G.  A.  J.  Worthy,  and  M.  A.  Castellini 
(eds.),  Approaches  to  marine  mammal  energetics,  pp.  127-145. 
Spec.  Publ.  Soc.  Mar.  Mamm.  No.  1. 

127.  Fish,  F.  E.  1990.  Wing  design  and  scaling  of  flying  fish  with 
regard  to  flight  performance.  J.  Zool,  Bond.,  221:391-403. 

128.  Azuma,  A.  1992.  The  biokinetics  of  flying  and  swimming. 
Springer-Verlag,  Tokyo. 

129.  Blake,  R.  W.  1983.  Energetics  of  leaping  in  dolphins  and  other 
aquatic  animals.  J.  Mar.  Biol.  Assoc.  UK.,  63:61-71. 

130.  Hui,  C.  A.  1989.  Surfacing  behavior  and  ventilation  in  fr,ee- 
ranging  dolphins.  J.  Mamm.,  70:833-835. 

131.  Liu,  H.,  Wassersug,  R.  J.,  and  Kawachi,  K.  1996.  A 
computational  fluid  dynamics  study  of  tadpole  swimming.  J.  Exp. 
Biol. ,  199:1245-1260. 

132.  Moin,  P.  and  Kim,  J.  1997.  Tackling  turbulence  with 
supercomputers.  Sci.  Amer.,  276:62-68. 


450 


ON  BIOLOGICAL  FOUNDATIONS  OF  DOLPHIN’S  CONTROL  OF  HYDRODYNAMIC  RESISTANCE 

REDUCTION 


V.  Babenko,  A.  A.  Yaremchuk 
Professor,  Dr. Tech. Sc.,  Head. of  Department 
Department  of  Hydrobionics  and. Boundary  Layer  Control 
8/4,  Zheliabov  str.,  252057,  Kiev,  Ukraine 
E-mail:  vb@b ionics Jcieviua 


Abstract  -  The  comparative  analysis  of  the  heat  emission. rating  of  a  man. and. a  dolphin. has  been  carried,  out.  Deficiencies  in 
biopower  estimation  on  the  basis  of  oxygen  consumption  are  shown.  The  comparative  analysis  of  microvibration  ,  components  of  the 
skin  of  man  and  dolphin  is  carried  out. 


In  the  course  of  comparative  analysis  of  human’s  and.  dolphin’s 
skin,  surface  microvibrations  the  authors  calculated .  microvibration 
velocity  as  the  product  of  the  circular  frequency  and  amplitude, 
according  to  the  records  of  microvibrations  of  swimmer  skin  and.  of 
dolphin’s  (namely,  Tursiops  truncatus)  skin,  listed,  in  the  work.  [1]. 
Average  velocity  values  thus  obtained  are:  for  human,  body  - 
0,35  mm/s,  for  dolphin  in  water  -  1,88  mm/s,  for  dolphin  in  the  air  - 
1,13  mm/s.  Dolphin’s  vibration  velocity  in. the  air  is  3,2  times  greater 
than. that  of  human’s,  and.  in. the  water  -  5,4  times.  As  long  as  mean, 
power  of  vibration. process  is  proportional  to  the  square  of  velocity, 
corresponding  power  relation  looks  even  more  impressive:  10.2  times 
in  the  air  and. 29.2  times  in. the  water.  The  reason,  for  such,  excess  of 
vibration  power  is,evidently,  the  quality  of  dolphin’s  skin. surface.  But 
there  is  something  else  here  -  it  should  be  noted,that  vibrations  of 
dolphin’s  skin  in  the  water  have  higher  frequency  and  greater  velocity 
than  vibrations  in  the  air.  From  the  pure  mechanical  point  of  view  the 
fact  looks  incredible:  a  transition  of  vibrating  surface  from  the  low- 
viscosity  medium  (air)  to  the  high-viscosity  medium  (water)  should. not 
expand,  the  frequency  range  of  vibrations.  The  explanation,  of  the 
phenomenon  may  be  an  adaptive  electromagnetic  control  of  vibrations. 

Results  of  electric  potentials  distribution,  measurements  for  the 
skin,  surface  of  a  dolphin,  are  listed,  in.  the  work.  [2].  The  average 
potential,  calculated,  on.  the  basis  of  this  distribution,  is  170  mV.  For 
human,  body  similar  technique  of  measurements  gives  18  mV  for 
common  points  and  .57  mV  for  bioactive  points.  Such  evident  excess  - 
about  9.4  times  -  of  dolphin’s  average  potential  over  human’s  one  has 
morphological  explanation  -  more  powerful  peripheral  nervous  system 
of  a  dolphin  However,  there  is  a  supposition,  about  very  good  heat 
insulation  of  a  dolphin  by  adipose  tissue.  In  .  such  case  the  skin  ,  surface 
must  be  lean. in. heat  energy,that  makes  nervous  system  control  highly 
problematic,  due  to  well-known  sharp  decline  of  nerve-pulse 
propagation,  speed  in.  case  of  heat-leaning.  To  check,  the  latter, 
comparative  analysis  of  dolphin’s  and  swimmer’s  skin,  heat  emission 
was  carried  .out.  Thermal  losses  analysis  was  based,  on.  Sirle  technique 
for  cylindrical  model  of  heat  source.  With  such  a  model  for  the 
boundary  surface  there  was  found: 


■  L,.  =  t(. 


.  .B—hfl 
nykv  +  X2) 


(1) 


where  t°p  ,  Dp  -  temperature  and.  diameter  of  the  boundary  surface, 
respectively,  t°c  ,  Dv  -  temperature  and  diameter  of  heat-emitting 
cylinder,  tV  -  surrounding  medium  temperature  ,  pi  -  heat  power  line 
density,  Zi  ,  Z2- thermal  conductivities  of  the  source  medium  and. 
surrounding  medium,  respectively. 

Dolphin  skin  thermal  conductivity  is  known  to  be  [3] 
Xn«0.209  Wiri'K'1.  Remarkable,  that  human nonvascular  skin,  as  well 
as  adipose  tissues  thermal  conductivity  have  just  the  same  value  - 
0.209  W  m‘l  K'1  [4],  while  for  muscular  tissues  at  normal  blood  flow 
Xn«0.532W  m’1  K  \  Conseguently,  thermal  conductivity  of  adipose 
tissues  is  only  2.5  times  less  than  that  of  muscular  tissues  and  .  equal  to 
the  skin,  conductivity.  Therefore  ,  wide-spread,  suppo s i ti on, regarding 
heavy  heat  insulation. of  a  dolphin  by  adipose  tissues  is  incorrect.  For 
Dc,  that  corresponds  underskin  adipose  tissue  boundary,  and  Dp=0.3  m, 
t°P-tooc=0.54oC,  t°c=37°C  from  (1)  we  get  p,=246W/m,  that  fits  the 
value  of  heat  flux  density  about  390  W/m2  ,  thus  disproving  the 
existence  of  dolphin  skin  heat  leaning. 

To  compare  heat  emission  capacity  of  dolphin,  and  that  of 
swimmer,  let  us  analyse  the  known  records  of  investigations  of  human 
heat  emission.  Results  of  investigations  of  heat  emission  of  various  parts 
of  human  body "at  rest  both  for  radiant  and  .  convective  constituents  are 
listed  in  the  work  [5].  By  averaging  the  results  for  various  body  parts, 
one  can  get  average  heat  flux  density  about  62  W/m ,  that 


corresponds  to  overall  power  of  the  whole  skin  surface  about  250  W. 
Furtermore,  results  of  investigations  of  swimmer  body  heat  emission 
are  listed. in  the  work  . [6].  These  results  show  that  in  unsteady-state  heat 
exchange  in  water  temperature  range  from  15°C  up  to  27°C  thermal 
losses  of  swimmer  are  proportional  to  the  temerature  difference 
between. skin  and. water  andin.some  cases  exceed  10  kW.  Transition  to 
a  steady-state  heat  exchange  takes  7-10  min,  the  heat  flux  density  of  a 
steady  state  being  in  the  range  from  250  W/m2  up  to  800  W/m,  that 
yields  total  losses  for  the  whole  skin  surface  from  1  kW  to  3.2  kW.  The 
average  value  of  this  power  is  just  2.1  kW.  Therefore,  heat  flux 
density  of  a  dolphin,  calculated  previously,fits  the  range  of  swimmer’s 
skin  heat  flux  density. 

Estimation  of  power  of  basic  methabolysm  N0  as  well  as 
active  methabolysm  ,Na  for  warm-blooded  animals  and  humans  is 
known  [1,  7]  to  be  based. on  oxygen  consumption  either  of  the  organism 
as  a  whole  or  that  reduced  to  the  unit  of  weight.  By  such  estimation, 
values  of  No=100  W  and.Na=2.2kW  were  obtained. in. the  work.  [1]. 
Comparison,  of  methabolysm  power  estimations,  based,  on.  oxygen, 
consumption,  and .  previously  calculated,  power  losses  for  just  one 
constituent  (heat  emission)  shows  evident  underestimation,  of  power 
losses  in.  calculations,  based  ,  on.  oxygen  consumption  data.  Such  result 
is  hardly  unexpected, takting  into  account  the  following: 

1. The  main  process  of  energy  transformation  -  the  oxidizing  cycle  (e. 

g.  tricarboxylic  acid,  cycle)  of  warm-blooded,  animals  goes  on 
without  oxygem  The  latter  takes  part  in  reaction  only  on  final 
stages  of  phosphorylization  [7]. 

2 . According  to  well-known  hypothesis,  thermal  energy  that  is 

released,  on.  a  final  stage  of  the  phosphrylization  is  spent  on 
maintainence  of  body  thermal  conditions.  There  is  a  remarkable 
correspondence  of  active  methabolysm  power  (2.2  kW),  derived 
from  oxygen,  consumption,  and  average  power  of  thermal  losses 
of  a  swimmer,  that  equals  2.1  kW. 

3. Q02  has  nothing  to  do  with  oxygen  methabolysm  of  separate  organs 

and.  tissues  of  an.  organism.  Table  1  shows  data  from  [7], 
concerning  oxygen  supply  of  human’s  organs  and.  tissues, 
wherefrom  one  can.  see  that,  muscles,  for  instance,  having  the 
largest  relative  mass,  consume  rather  small  portion  of  oxygen. 

Summing  up  all  stated,  above,  we  may  conclude,  that,  on.  our 
opinion,  it  is  incorrect  to  use  oxygen  consumption  in.  a  quantitative 
estimation,  of  bioenergetics  of  the  whole  being.  Such  estimates 
should  be  used-  for  comparison  of  separate  bioenergetic  processes 
only. 

According  to  experimental  data,  the  frequency  of  dolphin, 
skin  vibrations  occupies  the  range  from  11  Hz  to  16  Hz.  On  the  other 
hand,  analysis  of  change  of  mucles  contraction,  force  as  a 
function  of  electrostimulation  pulses  frequency  [8]  shows  just  that 
range  as  a  range  of  rather  high  speed,  of  increase  of  muscle 
contraction. force  with  increase  of  stimulation  frequency.  Increase  of 
stimulation,  frequency  above  20  Flz  results  in  eventual  halting  of 
contraction,  force  increase,  while  muscle  fatiguability  intensifies 
quickly.  Thus  micrvibrations  frequency  range  corresponds  to  optimal 
one  from  the  point  of  view  of  energetical  output  of  muscle  tissue. 

Field  force  analysis  of  electromagnetic  interaction  between 
dolphin  skin  and  surrounding  water  medium  was  based  on  Maxwell  - 
Tamm  equation. for  non-unifofm  medium  [9,10].  In.  accordance  with 
the  equacti  on  volume  density  of  electric  forces  f0  is 

fo  =  P^c  “  — grads  +ig-rarf^E^t^-j  (2), 

wherein  p  -  charge  volume  density,  Ec  -  electric  field,  intensity,  s  - 
dielectric  constant,  ,  5C  -  medium  density. 


451 


To  analyse  the  contribution  of  the  equation.  [2]  second 
component  an  order  of  dielectric  constant  gradient  intensity  has  to  be 
evaluated.  The  said  gradient  has  to  be  considered  on  the  interface  of 
water  medium  and  dolphin  skin  surface.  Considering  the  direction,  of 
normal  to  the  boundary,  approximation  can  be  used. 

(3) 

12 

wherein  so  -  dielectric  constant,  s2 it  fit  -  absolute  dielectric  constants 
of  dolphin  ,  skin  and  water  medium  respectively,  li2  -  transition  ,  zone 
width. 

Results  of  examinations  of  absolute  dielectric  constants  of 
skin,musscle  and  other  tissues  are  listed  in  [4,1 1,12].  Approximation  of 
these  records  for  frequency  range  below  10  kHz  yields  a  frequency 
funcion 

e2  *7,91  106  /{' 'a  (4) 

Extremely  high  level  of  s2  for  low  frequencies  has  biophysical 
explanation.  [11,12],  and. substances  with,  such  level  of  e2  are  called 
energetically  saturated,  ones.  At  the  same  time,  such  level  of 
dielectric  constant  of  artificial  substanses  may  be  the  end  of  a  very 
long  technological  road.  For  water  medium  at  low  frequencies 
dielectric  constant  st  «  80,  i.e.  e2  »  s(. 

To  estimate  the  value  of  li2  in. (3),  two  premises  may  be  used.: 
firstly,  external  layer  of  epidermis  hinder  water  molecules,  and, 
secondly,  to  form  such  medium  factor  as  dielectric  constant,  at  least 
one  layer  of  water  molecules  is  necessary.  That  defines  the  choice 
of  lj2  value  as  a  figure  that  equals  to  maximal  size  of  water 
moleculae,  i.  e.  0,138  nm  [13,  14]. 

Surface  electric  field  intensity  in  regions  of  heightened 
hydrodynamic  resistance  can  be  as  high,  as  E  -  1  mV/mm.  Then  for  f 
=  10  Hz  modulus  of  the  second  component  of  (2)  |  f0'  I  =80  kH/m  ,  and 
for  f=20  Hz  we  get  |  ff  |  =57  kH/m3.  Such  force  action  causes 
changes  in  water  moleculaes  construction  structure  in  the  near 
proximity  of  dolphin,  skin,  that,  consequently,  leads  to  decline  of 
hydrodynamic  resistance. 

When  a  dolphin  is  transfered  .from  the  air  into  sea  water,  that  has 
low  conductivity,  leveling  of  different  areas  of  skin,  surface  occurs, 
and,  on  the  other  hand,  there  is  an.  increase  of  field  intensity  due  to 
appearence  of  crumples  on.  the  boundary  lines.  That  explains 
paradoxal  increase  of  frequency  range  of  microvibrations,  noted 
previously. 

Analysis,  thus  carried,  out,  makes  the  basis  for  entire 
explanation,  of  mechanism  of  electromagnetic  control  of  a  dolphin 
skin  surface. 


REFERENCES 

1.  S.  V.  Per  shin  «Basis  of  a  hydrobionics».  -  Leningrad: 
Sudostroenie,  1988.  -  264  pp. 

2.  O.  V.  Nechaeva,  V.  N.  Plehanov,  V.  G.  Hadzginski  «Peculiarity 
of  potentials  distribution  ,  on  skin  surface  of  dolphins))  Bionica.  - 
1973.  7,  -p.  79-83. 

3.  D.  A.  Parry  «The  Structure  of  Whale  Blubber,  and  a  Discussion, 
of  its  Thermal  Properties»  Quart.  J.  Microsc.  Sc.  -1949.  -Nl.  -P. 
273-1279. 

4.  «Biophysical  characteristics  of  human's  tissues)).  The  reference 
book  /  V.  A.  Berezovski,  N.  N.  Kolotilov  -  Kiev:  Naukova  dumka, 
1990  -224  pp. 

5.  M.  A.  Arakelan  «Device  for  determination,  of  radiant  and 
convective  components  of  heat  exchange  in  the  industrial 
environment))  Heat  measurement,  energy-  and.  resources  saving. 
-  Kiev:  Institute  of  energy  saving  problems,  1989.  -p.  17-27. 

6.  O.  A.  Geraschenko  «Basis  of  heat  measurement)).  -  Kiev: 
Naukova  dumka,  1971-  -191  pp. 

7.  L.  D.  Lukyanova,  B.  S.  Balmuhanov,  A.  T-  Ugolev  «Depended. 
on.  oxygen  processes  in  a  cell  and.  its  functional  condition)).  - 
Moskwa:  Nauka,  1982.  -301  pp. 

8.  R.  Plonsy,  R.  Barr  «Bioelectricity:  Quantative  approach)). - 
Moskva:  Mir, 1964.  366  pp. 

9.  K.  Shimoni  «Electro engineering  theory)).  -  Moskva:  Mir,  1964. 
773  pp. 

10.  I.  E.  Tamm  «Basics  of  electrical  theory)).  -  Moskva: 
Nauka,  1989.-504  pp. 

11.  W.  R.  Adey  «Frequency  and  energetic  windows  in  weak 
electromagnetic  fields  influence  on  a  living  tisssue))  TIIER.- 
1980. -Nl.-pp.  140-148. 

12.  H.  P.  Schwan,  K.  P.  Foster  «Influence  of  high-firequency  fields  on 
biological  systems))  TIIER.-1980.-N1.  -pp.  121-132. 

13.  V.  I.  Klasssen  «Water  systems  magnetization)).  -  Moskva: 
Himia,1982.  -  pp. 

14.  U.  I.  Ergin  «Electro  lytic  solutions  structure  and 

magneticproperties)).  -Moskva:  Nauka,  1983.  -  183  pp. 


Table 


Tissues 

Skeletal 

muscle 

Skin 

Digestive 

organs 

Liver 

Brain 

Heart 

Kidney 

Lungs 

Weight  of  organ,  in  %  from 
the  total  body  weight 

40 

10 

4 

2 

4 

0,4 

0,4 

1,4 

Consumption  of  02  at  rest  in 
%  from  Q02 

25 

2 

19 

20 

15 

9 

5 

4 

452 


HYDROBIONICS  PRINCIPLES  OF  DRAG  REDUCTION 

Viktor  V.  Babenko 


Department  of  Hydrobionics  and  Boundary  Layer  Control,  Professor,  Dr.Tech.Sc.,  Head  of 
Department,  8/4,  Zheliabov  str.,  252057,  Kiev,  Ukraine,  E-mail:  vb@bionics.kiev.ua 


The  principles  of  hydrodynamical  drag  reduction  based  on  insight  to  drag-reduction  adaptations  of 
Nectons  were  developed.  Presented  are  the  two  methods  used  in  nature.  The  first  is  based  on 
adaptations  in  skin  cover.  It  is  an  analog  of  viscous-elastic  active  coating  for  friction  drag 
reduction.  The  second  consists  in  use  of  swordfish  sword  with  polymer  feed. 


It  was  demonstrated  for  the  first  time  in  [3]  and  then 
confirmed  in  [6,  9],  on  the  basis  of  a  set  biological  and 
hydrodynamic  experimental  and  theoretical  studies,  with  use  of 
modeling,  that  the  cetacean  integument  has  self-adjusting 
properties  during  active  swimming  with  regard  to  damping 
perturbations  in  the  boundary  layer,  and  that  it  effectively 
performs  the  function  of  a  hydrodynamically  active  cover  that 
diminishes  drag  reduction  appreciably.  This  effect  is  attributable 
to  change  in  physicomechanical  parameters  of  a  specially  [or 
particularly]  developed  integument,  with  papillary  and  ridged 
microstructure  of  one  layer  and  other  layers,  with  profuse  blood 
supply  and  innervation.  The  mechanical  characteristics  of  the 
functionally  specific  integument  of  cetaceans  are  regulated  by 
means  of  the  vascular  system,  as  well  as  change  in  the  animal's 
metabolism  in  different  modes  of  nonstationary  swimming,  in 
connection  with  the  function  of  the  bendeng  and  oscillatory 
propulsion  complex.  Let  us  note  that  live  dolphins  are 
characterized  by  a  wide  range  of  vasomotor  variability-dilation 
and  constriction  of  blood  vessels. 

A  model  of  the  delphinid  integument  was  constructed  on  the 
basis  of  a  mehanical  model  of  a  skin  section  rendered  in  the  form 
of  a  Voigt-Kelvin  viscoelastic  element  with  additional  links  and  a 
corresponding  differential  equation  for  oscillation  dynamics.  The 
dimensionless  parameters  of  modeling  were  established,  which 
take  into  consideration  such  extremely  important  features  of  the 
skin  as  active  oscillating  mass,  oscillation  frequency  and  related 
damping  [3,  4].  Some  of  these  characteristics  were  determined 
from  measurements  of  live  ^dolphins,  which  made  it  possible  to 
conduct  a  numerical  analysis  of  modeling  parameters  and 
demonstrate  their  optimum  values  with  an  expernal  load  in  the 
boundary  layer  conforming  to  specific  speeds  of  swimming.  A 
comprehensive  study  was  made  of  the  question  of  actively 
oscillating  mass  of  the  delphinid  integument,  and  a  reltionship 
was  demonstrated  between  thickness  of  skin  layers  and  typical 
thicknesses  of  boundary  layer  [2]. 

A  conprehensive  study  was  also  made  of  elasticity  of  the 
integyment  of  live  dolphins  [1].  Measurements  of  elasticity  of  the 
skin  of  three  Black  Sea  dolphin  species-common  dolphin, 
bottlenosed  dolphin  and  porpoise-revealed  that  the  modulus  of 
elasticity  depends  on  the  dolphin  species,  its  conditioning  and 
condition  of  the  animal  during  the  experiment.  Experiments  have 
showm  that,  by  tensing  the  cutaneous  muscle  dolhhins  can  alter 
integumental  elasticity  by  almost  two  times.  The  distribution  of 
values  for  the  elasticity  modulus  of  the  skin  over  the  body  of  two 
dilphinid  species  in  different  states  is  illustrated  in  Figure  1 . 

The  coefficients  of  absorption  of  disturbance  energy 
[perturbation  energy]  by  the  delphinid  integument  were  measured 
and,  for  comparison, sheets  of  different  materials.  The  value  of  the 
coefficient  was  determined  according  to  relative  height  of 
bouncing  of  solid  spheres  differing  in  mass.  It  was  found  that,  in 
live  dolphins,  the  coefficient  of  absorption  of  disturbance  energy 
by  the  integument  depends  on  the  magnitude  of  this  energy,  and  it 
has  a  maximum  of  95%  in  the  area  of  disturbance  energies 
^-corresponding  to  the  order  of  energy  of  turbulent  pulsations  in 
the  boundary  layer.  The  absorption  coefficient  is  lower  in  a  sick 
dolphin  and  does  not  exceed  80%,  it  is  no  more  than  70%  in  a 
dolphing  right  after  death.  The  absorption  coefficient  is  about 
80%  for  elastomers  [elastoplastic]  and  only  40-50%  for 
construction  materials,  where  the  pattern  of  relative  energy  of 
perturbation  changes  to  the  opposite. 

Self-regulation  of  skin  damping  in  ceraceans  during  active 
swimming  has  the  reverse  effect  on  the  hydrodynamic  boundary 
later,  with  change  in  nature  of  pulsations,  speed  and  pressure. 
Measurements  of  pulsation  of  velocities  in  the  dolphin's  boundary 
layer,  at  Reynolds  numbers  Re>2.7*106  .  revealed  that  there  is 
extension  of  the  transitional  mode  of  flow  [current]  and  pulsations 
drop  virtually  to  a  level  that  in  close  to  streamline  mode.  It  has 


been  demonstrated  that  there  are  different  degrees  of  turbulence 
in  the  boundary  layer  of  the  dolphin  and  rigid  model  (Figure  2), 
which  increases  all  the  more  with  some  increase  invelocity  and 
Reynolds  number  alogues  of  integument  were  developed  for 
comprehensive  laboratory  studies  and  explanation  of  physical 
patterns  in  the  boundary  layer  with  flow-around  [7,  8,  10,  13]. 
There  was  experimental  confir  mation  of  the  possibility  of 
encrease  in  hydrodynamic  stability  of  flow  in  a  streamline 
boundary  layer  of  water  by  use  of  viscoelastic  damping  surfaces. 

It  was  found  that  there  was  a  decrease  in  build-up  of  perturbed 
motion, increase  in  Reynolds  number  for  loss  of  stability, 
increased  length  of  transient  zone,  as  compared  to  a  hard  surface. 
The  Gertlerian  vortices  formed  in  the  transitional  zone  become 
more  stable.  Enlargement  of  the  viscous  sublayer,  decrease  in 
maximum  pulsation  rates  and  redistribution  of  these  parameters 
over  the  thickness  of  the  boundary  layer,  decrease  in  local 
Reynolds  shear  stresses  were  found  on  elastic  surfaces  in  the 
turbulent  boundary  layer.  This  is  indicative  of  substantisl 
structural  change  in  flow  in  the  boundary  layer  on  an  elastic 
surface,  such  as  (and  more  effectively)  the  integument  of 
cetaceans.  Bioenergetic  calculations  of  drag  reduction  (Figure  3) 
were  made  for  four  delphinid  species:  porpoese-smallest  of  the 
delphinids  with  moderate  speed,  common  dolphinaverage  in  size 
and  swift,  killer  whalelargest  high-speed  species-  and  white  whale, 
which  is  swift,  killer  whalelargest  high-speed  species-and  white 
whale,  which  is  a  large,  slowswimming  delphinid.  Maximum 
decline  of  drag  reduction  was  determined,  according  to  the 
calculations,  for  the  common  dolphin.  Taking  hydrodynamic 
distinctions  of  the  gill  system  of  swordfish  into  consideration,  a 
model  was  developed  to  experimentally  check  interaction  of  gills 
with  the  rostrum  [5].  Its  construction  and  methods  of 
investigation  in  the  biohydrodynamic  unit,  as  well  as  results  of 
testing  models  with  xiphoid  [sword-shaped]  tips  differing  in 
length,  without  simulating  the  function  of  the  gill  system,  are 
described  in  [9].  We  first  filled  the  disposable  container  with 
waterm  which  flowed  under  compressed  air  pressure  through  the 
slit  in  the  model,  turning  on  an  electric  stopwatch  [timer]. 
Duration  of  fluid  injection  was  determined  when  interpreting  the 
oscillograms,  in  addition  to  timer  reading.  Similarly,  injections  of 
other  types  of  fluids  were  made  through  the  nose  slits  with  attach 
ment  to  the  model  of  an  ogive-shaped  (OT),  short  (SXT)  and 
elongated  (LXT)  xiphoidshaped  tips.  The  oscillograms  of  model 
drag  reduction  were  interpreted  by  means  of  calibration  lines.  In 
addition,  the  results  of  fluid  injection  into  stationary  water  were 
also  recorded  on  the  oscillograms. 

Figure  4  illustrates  the  results  of  measu  ring  drag  reduction 
in  models  with  different  tips  using  aqeuous  solutions  of  polyethy 
lene  oxide  (PEO)  through  the  slit.  Without  injection  of  PEO 
solution,  the  coefficient  of  model  drag  reduction  with  Cx  a  sword 
shaped  tip  increased,  as  compared  to  OT,  although  there  was 
insignificant  increase  in  size  if  wet  surface.  These  experiments 
simulated  flow-around  of  swordfish  with  the  mouth  closed  and 
gill  slits  open.  When  the  gill  slits  are  also  closed,  it  is  possible  to 
lower  drag  reduction  by  10-12%,  according  to  the  results  of  tests 
on  the  model  [9].  Positions  7  and  9  in  Figures  4  and  5, 
respectively,  indicate  injection  of  a  PEO  solution  prepared  before 
the  experiments  at  an  average  rate  of  Q=59  cc/s,  while  8  and  10  in 
Figures  2  and  3,  respectively,  show  injection  of  solution  prepared 
7  days  before  the  tests,  with  Q=49  cc/s.  As  compared  to  the  OT, 
the  efficacy  of  injection  of  PEO  solution  increases  with  increase  in 
size  of  the  ensiform  tip  and  it  depends  less  on  Q  (curves  in  Figure 
2  with  SXT,  Q=34  cc/s,  and  with  LXT,  Q=45  cc/s).  These 
experiments  simulate  dissolution  of  slime  in  the  gill  system  of 
swordfish,  regulation  of  flow  through  the  gill  slits,  as  well  as  the 
case  of  a  broken  sword  or,  shorter  one  as,  for  example,  in  a 
sailfish. 


453 


Subsequently,  analysis  of  the  obrained  results  was  made 
with  consideration  of  subtraction  from  model  drag  reduction  of 
hydrodynamic  characteristics  measured  in  stationary  flow  (Figure 
5).  The  results  of  experiments  on  a  model  with  OT  revealed  that 
injection  of  freshly  prepared  polymer  solution  with  concentration 
C=0. 1%  (curve  9)  had  the  greatest  effect  on  lowering  drag 
reduction. 

Maximum  decrease  in  drag  reduction  was  obtained  with 
Reynolds  numbers  where  the  rate  of  injection  was  commensurate 
with  free-stream  velocity  (the  region  of  minimum  curves  in  Figure 
5).  Beyond  this  range  of  Reynolds  numbers,  an  increase  in  rate 
[outlay]  was  a  secondary  factor  and  did  not  affect  the  value  of  Cv 

Replacement  of  PEO  solution  (curve  13)  with  synthetic  glue 
solution  in  the  same  concentration  (curve  12)  led  to  appreciable 
decrease  in  efficacy  of  injection  through  the  slit.  Let  us  not  that 
the  nature  of  the  curves  is  determined  by  the  fact  that,  at  different 
flow-around  velocities,  air  pressure  in  the  system  of  injection  of 
polyner  solytion  underwent  virtually  no  change,  which  produced 
an  inconsistency  between  velocities  of  injection  and  free  stream 
How.  with  increase  in  the  latter  parameter  and  decrease  in  efficacy 
of  injection. 

Experiments  on  a  model  with  SXT  and  LXT  revealed  that 
injection  of  the  polymer  was  the  most  effective  with  SXT  at 
C=0. 15%,  and  with  LXT  at  Re<IO'’  with  C=0.l%,  and  with 
Rc<IOf>  with  C=0.05%.  Unlike  the  experiments  with  an  OT,  the 
inconsistency  between  rate  of  injection  and  free-stream  flow  did 
not  have  such  a  strong  influence  on  efficacy  of  injection,  while  the 
range  of  efTecaey  extended  and  shifted  to  the  range  of  high 
Reynolds  numbers.  As  compared  to  OT.  SXT  and  LXT  led  to 
increase  in  absolute  value  of  decline  of  C\,  as  well  as  reduction  of 
Cs,  at  which  better  results  are  observed. 

REFERENCES 

I  BABENKO  ^Investigation  of  Elasticity  of  Live  Dolphinid 
Skin^BIONIKA,  No  13.  1979.  pp  43-52. 


2.  ldem,wVibrating  Mass  of  Delphinid  Integument?  Ibid,  No  14, 
1980,  pp  21-27. 

3.  BABENKO  V.,  KOZLOW  L.  and  PERSHIN  S«Variable 
Damping  of  Dolphin  Skin  at  Different  Swimming  Speeds? 
Ibid,  No  6,  1972,  pp  42-52. 

4  BABENKO  V.,  KOZLOW  L.,  PERSHIN  S.  et.ai“Self- 
Regulation  of  skin  damping  in  cetaceans  during  active 
swimming?BIONICA,  No  16,  1986,  pp  3-10. 

5.  BABENKO  V.,  KOZLOW  L”  Hydrodynamic  functions  of 
swordfish  gill  system?  Ibid,  pp  11-15. 

6.  BABENKO  V  "Hydrobionics  principles  of  drag  reduction?  in 
«High  speed  body  motion  in  water»,  AGARD  report  827,  1988, 
pp  3-1 -3-14. 

7.  KANARSKIY  M.,  BABENKO  V.,  KOZLOW  L. 
“Experimental  Investigation  of  Turbulent  Boundary  Layer  on 

Elastic  Surface?  in  "Stratifitsirovannyye  i  turbulentnyye 
techeniya"  [Stratified  and  Turbulent  Flow],  Kiev,  Naukova 
dumka,  1979,  pp  59-67. 

8.  KOZLOW  L.,  BABENKO  V.  “Experimental  Studies  of 
Boundary  Layei?Kiev,  Naukova  Dumka,  1978,  1 84  pages. 

9.  KOZLOV  L.,  BABENKO  V.,  PERSHIN  S.«Self- Adjustment 
of  Skin  Damping  During  Active  Swimming  of  Some 
Cetaceans”  BIONICA,  Nd2,  1978,  pp  55-58. 

10.  KOZLOV  L„  SHAKALO  V.«Some  Results  of  Measuring 
Velocity  Pulsations  in  Delphinid  Boundary  Layer? 
BIONICA,  No  7,  1973,  pp  50-52. 

11.  KAYAN  V.,  PYATETSKIY  V.  “Hydrodynamic 
Characteristics  of  Bottlenosed  Dolphin  in  Different  Modes  of 
Acceleration?! bid,  No  12,  1978,  pp  48-55. 

12.  ROMANENKO  Ye.  ^Fundamentals  of  Statistical 
Biohydrodynamics? Moscow,  Nauka,  1976,  167  pages. 

13.  YURCHENKO  N.,  BABENKO  V.,  KOZLOV  L. 
^Experimental  Study  of  Gertlerian  Instability  in  Boundary 

Layer?  in"Stratifitsirovanyye  i  turbulentnyye  techeniya", 
Kiev,  Naukova  dunka,  1979,  pp  50-59. 


Figure  2.  Comparative  turbulence  in  boundary  layer  of  swimming 
bottlenosed  dolphin  (I)  and  towed  rigid  model  of  solid  of  revolution 
(2)  in  function  of  Reynolds  numder 


Figure  I.  Distribution  of  values  for  modulus  of  elasticity  of 
dolphin  skin  along  body,  measured  in  different  longitudinal 
sections  [  1 1 
a  -  common  dolphin; 
b  -  bottlenosed  dolphin; 

I  -  just  caught  and  excited  dolphin; 

II  -  trained  and  calm  dolphin  (same  animals) 


454 


Figure  3.  Coefficients  of  hydrodynamic  drag  as  a  function  of 
Reynolds  number  for  dolphins  and  solidsf  1 1.12]:  1  -  common 
porpoise  towing  carcasses;  2  -  porpoise;  3  -  common  dolphin;  4  - 
killer  whale:  5  -  white  whale-bioenergetic  calculations  for  active 
swimming  at  sea;  6  -  rigid  model  of  doltlenoseddolphin. 
hydrodynamic  calculations  made- on  computer;  7,  8  -  Bottlenosed 
dolphin,  experiment-passive  swimming  by  inertia  in  tank  (a- 
positivc  acceleration,  b  -  negative);  9  -  surfacing  of  streamled  rigid 
"Dolphin"  model;  L  -  laminar,  Tr  -  transitional  and  T  -  turbulent 
flowing  around  the  rigid  plate 


Figure  4.  Value  Cx  as  a  function  of  Reynolds  number  with 
different-shaped  rostral  parts  of  model.  1,  2,  3  -  drag  of  smooth 
longitudinally  streamlined  Hat  plate,  with  laminar,  transitional 
and  turbulent  boundary  layers,  respectively  [9];  4,  5,  6  -  model 
drag  with  OT,  SXT.  LXT  [9];  with  injection  of  aqueous  PEO  in 
concentration  of  0.1%;  7,  8  -  with  OT;  9  -  with  SXT;  10  -  with 
LXT 


Figure  5.  Effect  of  injection  of  PEO  on  drag  on  model  with  OT 
(a),  with  SXT  and  LXT  (b).  a:  I.  2.  3  -  same  as  in  Figure  2;  4  - 
standard  [8];  injection  of  water  at  average  rale:  5  -  57.6  cc/s;  6-71 
cc/s;  7  -  73  cc/s;  injection  of  PEO  concentration  &  rate:  8  -  0.05%, 
54  cc/s;  9-0. 1%,  59  cc/s;  10-0.1%,  49  cc/s;  II  -0.15%.  54  cc/s;  12 
-  0. 1  •  80  cc/s  13-0.1  %,  84  cc/s;  14-0,1”  1 00  cc/s; 


b:  model  with  SXT:  15  -  standard  [8];  16  -  water  injection,  51  cc/s; 
PEO  injection:  17)  0.05%,  47  cc/s;  18  -  0.1%,  34  cc/s;  19  -  0. 15%, 
28  cc/s;  model  with  LXT:  20  -  standard  [8];  21  -  water  injection,  51 
cc/s;  22  -  "  -  "  70  cc/s;  PEO  injection:  23  -  0,05%,  50  cc/s;  25  - 
0.15%,  38  cc/s 


455 


PHASED  VORTEX  SEEDING  FOR  THRUST  MODULATION  IN  A  RIGID  CYLINDER  WITH 

FLAPPING  FOIL  THRUSTERS 


Promode  R.  Bandyopadhyay 
John  M  Castano, 

William  Nedderman  and 
Daniel  Thivierge 

Naval  Undersea  Warfare  Center 
Newport,  RI 02841 

bandyopadhyay@c80.npt.nuwc.navy.mil 


ABSTRACT 

A  biologically  inspired  approach  to  the  propulsion  of  a  rigid 
cylinder  is  taken.  Here,  thrust,  drag  and  precision  maneuvering  of  the 
entire  cylinder  are  viewed  in  an  integral  generic  framework.  The 
dynamics  in  such  an  approach  is  controlled  by  deterministic  unsteady 
vortex  dynamics.  Recently,  it  has  been  demonstrated  experimentally 
that  such  vortex  dynamics  can  be  used  to  produce  vectored  jets  which 
can  provide  thrust,  drag  or  maneuvering  cross-stream  forces  and 
moments  to  a  rigid  cylinder.  In  the  present  work,  it  is  further  shown 
experimentally  that,  a  phased  vortex  seeding  from  the  nose  of  the 
cylinder  can  be  used  to  finely  modulate,  within  ±  5-10%,  the  thrust 
produced  by  a  pair  of  flapping  foils  mounted  at  the  tail  of  a  rigid 
cylinder. 

INTRODUCTION 

NUWC  is  engaged  in  the  study  of  aquatic  locomotion  with  a  goal 
to  apply  the  knowledge  to  underwater  vehicles.  While  the  works  of 
Lighthill,  Wu,  Webb,  Ellington,  Bainbridge  and  Triantafyllou,  to  name 
only  a  few,  have  contributed  to  the  understanding  of  the  mechanism  of 
fish  propulsion,  the  application  to  engineering  remains  a  serious 
challenge  (see  citations  in  Ref.  3). 

The  NUWC  work  is  described  in  Refs.  1-6.  The  following 
summarizes  the  experience:  the  biologically  based  mechanisms  need 
to  be  applied  to  rigid  bodies  as  opposed  to  flexible  bodies;  the  emphasis 
should  be  on  precision  maneuvering  and  low  speed  application,  rather 
than  the  production  of  pure  axial  propulsion;  production  of  all  forces, 
viz.,  thrust,  drag  and  cross-stream  maneuvering  forces  should  be 
viewed  in  an  integral  manner  because  they  have  a  common  production 
mechanism.  The  NUWC  work  has  also  led  to  the  exploration  of  a  new 
area,  viz.,  biologically-inspired  maneuvering  of  small  underwater 
bodies.  The  studies  indicate  that  the  maneuvering  and  control  of  man 
made  vehicles  like  aircraft  are  based  on  moments,  while  those  of 
biologically  based  engineering  vehicles  would  be  force  based.  In  the 
latter,  this  makes  brisk  maneuvering,  which  has  a  low  time  constant, 
feasible. 

A  remarkable  feature  of  the  locomotion  of  a  fish  like  aquatic  animal  is 
the  production  of  large  unsteady  forces.  This  can  be  seen  by 
comparing  Figs.  1  and  7.  In  the  former,  the  steady  drag  levels  at  20 
cm/s  are  less  than  1/100  th  of  the  peak  unsteady  forces  due  to  a  pair  of 
flapping  foils  attached  to  a  rigid  cylinder,  shown  in  the  latter  figure. 
The  drag  values  in  Fig.  1  are  1/50  th  of  the  time  mean  thrust  values 
shown  in  Fig.  7.  Although  these  biologically  based  mechanisms  give  us 
an  impressive  level  of  force,  their  necessity  in  an  aquatic  animal  is 
probably  due  to  the  amenability  of  their  origin,  viz.,  an  unsteady 
deterministic  vortex  shedding,  to  active  control.  This  makes  precision 
maneuvering,  defined  as  quick  acceleration  and  deceleration,  and 
rapid  turning  compared  to  body  length,  feasible. 

The  development  of  a  biologically  based  dual  flapping  foil  device 
attached  to  a  rigid  body,  for  the  generation  of  axial  and  cross-stream 
forces  on  a  rigid  cylinder  at  low  speeds  is  described  in  Refs.  1  and  3. 
In  these  works,  the  hydrodynamics  of  the  flapping  motion  of  the  tail 
fins  is  reproduced  in  an  engineering  rigid  bodied  cylindrical  model. 
The  present  is  a  follow  on  work.  Here,  the  motivation  has  been  to 
understand  the  role  of  the  head  movement  of  a  fish  and  to  apply  again 
in  the  context  of  a  rigid  cylinder.  In  the  literature,  Lighthill  and  others 
have  speculated  on  the  drag  reducing,  or  thrust  enhancing  role  of 


vortices  shed  due  to  the  head  movement  of  a  fish.  It  is  less  ambiguous 
to  carry  out  this  investigation  in  a  rigid  cylinder,  because  therein  it  is 
possible  to  isolate  the  head  movement  from  the  effects  of  the  sinuous 
motion  of  the  body  of  a  fish. 

The  hydrodynamic  foundation  of  the  dual  flapping  foil  device  attached 
to  the  tail  of  a  rigid  cylinder  is  given  in  Bandyopadhyay  &  Donnelly 
(1997).  The  dynamic  measurements  of  axial  forces  and  cross-stream 
moments,  as  well  as  the  detailed  phase-matched  measurements  of 
vorticity -velocity  vectors  of  the  vortex  shedding  process  have  been 
reported.  The  results  are  compared  with  theories  and  others’ 
measurements.  Two  modes  of  flap  oscillation  are  considered:  waving 
and  clapping.  In  the  waving  mode,  the  flaps  move  in  phase,  and  in  the 
clapping  mode,  they  are  out  of  phase.  In  the  present  work,  a  new  set 
of  tiny  vortices  are  shed  from  the  nose  area  and  they  are  allowed  to 
convect  downstream  and  interact  with  those  being  shed  by  the  flapping 
foils  in  waving  mode  (Fig.  2).  Dynamic  balance  measurements  are 
then  carried  out  to  determine  the  modulating  influence  of  the  nose 
vortex  seeding. 


Figure  1.  Estimated  steady  state  drag  on  the  basic  cylinder  model 
shown  in  Fig.  2. 

EXPERIMENTS: 

The  model  is  shown  schematically  in  Fig.  2.  Figure  3  is  a  photograph  of 
the  model.  The  model  is  76  mm  in  diameter  and  about  1  m  in  length. 
The  tail  has  a  circular  to  flat  transition  section  at  the  end  of  which  two 
76  mm  x  76  mm  flaps  are  attached.  There  is  a  fixed  divider  plate  in 
between.  The  entire  cylinder  floats  and  the  model  is  strut  mounted.  A 
six  component  dynamic  balance  is  mounted  at  the  strut  cylinder 
junction.  The  balance  (ATT  Inc.)  measures  the  strain  in  a  monolithic 
structure  containing  three  symmetrically  placed  beams.  Temperature 
compensation  and  water  proofing  are  provided.  A  balance  with  high 
moment  range  had  to  be  chosen.  The  axial  force  resolution  is  0.24  N. 
Data  collected  with  the  balance  in  the  past  has  compared  favorably 
with  theories  (Bandyopadhyay  &  Donnelly  1997;  Bandyopadhyay  et  al. 
1997c).  Two  magnetic  actuators  are  used  to  oscillate  the  tail  flaps  and 
two  LVDTs  are  used  to  measure  their  phase.  A  third  actuator  is  used 
to  oscillate  a  1  mm  thin  plate  near  the  nose. 

This  nose  slider  protrudes  out  of  the  cylinder  surface  alternately 
at  port  and  starboard  sides.  Figure  4  shows  the  distribution  of  nose 


457 


slider  protrusion  against  actuator  voltage.  The  maximum  protrusion  is 
3-4  mm  in  the  working  range  of  12  V.  This  is  probably  of  the  order  of 
the  local  thickness  of  the  boundary  layer  which  is  presumably  laminar 
at  flow  speeds  of  around  20  cm/s.  At  a  nose  slider  frequency  of  3.65 
Hz  and  speeds  of  20  -  40  cm/s,  a  Strouhal  number  based  on  the  slider 
protrusion  of  3  -  4  mm  varies  between  0.274  and  0.73.  The  nose  slider 
vortex  shedding  is  probably  optimum  in  this  Strouhal  number  range 


(Fig.  9a). 


Actuator:  Pha»® 


FLOATING 

AXISYMMETRIC 

CYLINDER 

Diameter:  d  «  7S.2  mm 


SIX-COMPONENT 
DYNAMIC 
LOAD  CELL 


OSCILLATING 
FLAP  #2  (dxd): 
Operating  In  Phase 
With  #1 


Figure  2.  Schematic  of  Model.  A  software  operated  digital  controller 
is  used  to  select  the  phase  lag  of  the  nose  slider  actuator  relative  to  the 
two  flap  actuators  which  operate  in  phase,  called  waving  mode  here 
(as  opposed  to  clapping  mode  where  they  operate  in  anti-phase). 


Figure  3.  Photograph  of  model  and  digital  controller  of  actuators. 


Slider  Displacement  from  Cylinder  Surface 


Figure  4.  Variation  of  nose  slider  depth  with  actuator  voltage 
(horizontal  axis:  Volts)  and  frequency. 

PRELIMINARY  EXPERIMENTS: 

Preliminary  measurements  of  axial  forces  are  shown  in  Fig.  5  where 
the  ensemble  averaged  traces  are  compared  for  nose  slider  on/off 
cases.  The  time  lag  in  the  on-case  is  zero  with  respect  to  the  tail  flaps. 
Mainly  the  peak  levels  of  thrust,  and  to  a  lesser  extent  the  drag  values 
as  well,  are  enhanced  by  the  nose  vortex  seeding.  The  time  integrated 
values  increase  in  the  on-case,  but  they  are  still  barely  above  zero  and 
are  within  the  uncertainties  of  measurements.  The  effect  of  a  lag  in 
nose  vortex  shedding  is  shown  in  Fig.  6.  Particularly  the  thrust  peaks 
are  highest  at  a  lag  of  300  degrees  and  lowest  at  120  degrees.  The 
difference  between  the  two  lags  is  180  degrees  which  suggests  that  an 
exquisitely  phase-dependent  mechanism  is  involved. 


2.C  Hz  041 


The  experiments  were  carried  out  at  flap  frequencies  between  2.6  and 
6.2  Hz  and  flow  speeds  of  upto  1.5  m/s.  A  computer  driven  controller 
was  built  to  operate  the  actuators  (Fig.  3).  All  three  actuators  were 
operated  at  the  same  frequency.  The  phase  of  the  nose  actuator  was 
digitally  shifted  with  respect  to  the  flaps  by  means  of  a  software.  The 
flap  actuators  operated  in  phase.  The  drag  balance  was  operated  by  a 
second  computer.  A  third  computer  was  used  to  monitor  the  tunnel 
characteristics  in  real  time  and  for  acquisition  of  all  data,  namely  the 
balance  output,  flap  phase,  actuator  currents  and  voltages  and  their 
phase,  and  flow  speed.  The  balance  signals  were  digitized  at  250  Hz 
and  the  other  signals  at  8Khz.  The  balance  trace  was  ensemble 
averaged  over  5  cycles  of  flap  oscillations  and  then  a  three-point 
averaging  was  performed  to  further  filter  out.  The  flow  speed  was 
measured  both  by  a  Pitot  tube  located  in  the  test  section  near  the  tail  of 
the  model  and  also  from  the  pressure  drop  along  the  tunnel  nozzle. 
The  experiments  were  carried  out  in  the  NUWC  Low  Speed  Water 
Tunnel.  The  test  section  is  30  cm  x  30  cm  in  cross-section  and  the 
length  is  about  3  m.  The  tunnel  is  noisy  at  low  speeds.  Close  tracking 
of  flow  speed  with  a  sensitive  Pitot  tube  mounted  in  the  test  section  is 
required  for  accuracy.  This  is  particularly  in  view  of  the  fact  that  the 
mechanism  on  hand  is  exquisitely  Strouhal  number  dependent.  A 
perforated  metal  plate  was  placed  in  the  latter  experiments 
downstream  of  the  test  section  to  improve  the  flow  steadiness  at  low 
speeds. 


Figure  5.  Ensemble  averaged  trace  of  axial  force  on  the  model.  Tail 
flap  St  -  0.25  -  0.35.  Nose  slider:  (a)  off,  (b)  on. 


458 


(a) 

4.2  Hz  120  D«g 


1.1  Hi  D*f 


Figure  6.  Effect  of  phase  lag  of  nose  slider  on  axial  force.  Tail  flap  St 
=  0.13.  Lag:  (a)  120  deg,  (b)  300  deg. 

RESULTS  AND  DISCUSSION: 

The  preliminary  results  suggested  that  the  nose  vortex  seeding  did 
have  a  temporal  effect  on  the  axial  forces.  However,  it  was  necessary 
to  repeat  the  experiments  at  a  Strouhal  number  where  the  net  axial 
force  was  clearly  a  thrust.  Also,  a  perforated  plate  was  installed  in  the 
downstream  end  of  the  test  section  to  steady  the  low  speed  streams. 
These  later  results  are  shown  in  Figs.  7  &  8.  Figure  7  shows  the 
temporal  effects  of  phase  lag  of  nose  vortex  seeding.  The  thrust  peak 
is  highest  at  300  deg  and  lowest  at  120  deg.  The  effects  of  phase  lag 
on  the  time  integrated  thrust  levels  are  shown  in  Fig.  8  at  three  Strouhal 

fA 

numbers.  The  Strouhal  number  St  is  defined  as  — ,  where /and  A  are 

U 

frequency  and  amplitude  of  oscillation  of  the  tips  of  the  flapping  foils 
and  U  is  the  freestream  speed.  A  sinusoidal  effect  of  lag  on  net  thrust 
is  present.  The  net  thrust  is  enhanced  around  120  deg  and  reduced  at 
300  deg.  The  integrated  effect  is  opposite  to  the  effects  on  peak  values 
of  thrust  and  drag. 

Because  the  mechanism  on  hand  is  exquisitely  dependent  on  Strouhal 
number,  care  had  to  be  taken  in  tracking  the  freestream  speed.  Recall 
that  a  perforated  plate  was  installed  in  the  test  section  to  achieve  steady 
freestream  speeds  in  the  later  runs.  The  speeds  and  Strouhal  numbers 
are  16.2  -  21.0  cm/s  and  0.6  -  0.46  in  Fig.  8a,  27.4  -  30.5  cm/s  and  0.375 
-  0.337  in  Fig.  8b,  and  36.0  -  37.8  cm/s  and  0.276  -  0.263  in  Fig.  8c, 
respectively.  The  speed  variation  between  runs,  thus  was  within  5%  at 
a  nominal  speed  of  40  cm/s,  which  increased  to  20%  at  lower  speeds  of 
20  cm/s.  The  measurements  reported  in  Fig.  8  are  for  those  runs  where 
the  freestream  speed  remained  nearly  constant  over  several  successive 
runs.  At  that  condition,  the  Phot  readings  were  at  worst,  within  5% 
from  that  obtained  from  the  nozzle  pressure  drop.  The  scatter  can 
probably  be  reduced  by  holding  the  freestream  speed  more  accurately. 

The  data  has  a  considerable  amount  of  scatter,  but  Fig.  8a  still  indicates 
that  the  net  thrust  is  slightly  enhanced  compared  to  the  off  case.  No 
attempt  has  been  made  to  optimize  the  protrusion  of  the  nose  slider  for 
thrust  enhancement,  but  the  possibility  of  further  enhancement  remains. 


0  D*g  Lbs 


(a) 


Lag  110  0*0 


Lag  040  Dag 


459 


U«  >00  0*9 


Figure  7.  Ensemble  averaged  time  trace  of  axial  force  on  the  model, 
(a)  Nose  slider  phase  lag:  0  deg;  (b)  60  deg;  (c)  120  deg;  (d)  180  deg; 
(e)  240  deg;  (f)  300  deg. 


MECHANISM  OF  THRUST  MODULATION: 

Several  questions  arise:  (1)  what  is  the  mechanism  of  thrust 
modulation?  (2)  is  there  any  viscous  drag  reduction  over  the  cylinder 
involved?  (3)  how  are  the  presumably  tiny  nose  vortices  surviving  a 
distance  of  1  m?  (4)  how  relevant  are  the  results  to  fish  locomotion?  A 
hypothesis  of  flow  mechanism  given  below  attempts  to  provide 
qualitative  answers  to  these  questions. 

A  starting  point  would  be  the  question:  what  is  the  trajectory  of  the 
shed  nose  vortex?  Earlier  dye  flow  visualization  and  phase-matched 
laser  doppler  measurements  of  vorticity  and  velocity  vectors  of  the 
vortex  shedding  from  the  flapping  foils  at‘  the  tail  is  instructive 
(Bandyopadhyay  &  Donnelly  1997).  They  indicated  that  the  shed 
vortices  do  not  propagate  along  the  tangent  at  the  trailing  edge.  In  a 
similar  manner,  in  Fig.  9a,  it  is  hypothesized  that  the  shed  vortices  from 
an  oscillating  surface-normal  plate  would  track  at  a  higher  elevation 
than  that  from  a  non-moving  obstruction  would.  This  would  allow  the 
vortices  not  to  interact  with  the  cylinder  boundary  layer  and  to  survive 
longer.  As  sketched  in  Fig.  9b,  the  vortices  might  undergo  a  pairing 
process  increasing  their  spacing  and  survivability.  The  seed  vortices 
then  interact  with  those  formed  by  the  oscillating  flaps.  Further  pairing 
could  ensue.  Negative  vortices  marked  A,  B  &  C  on  the  port  side  could 
have  a  common  induction  due  to  proximity  with  the  positive  vortex  D 
and  give  rise  to  a  downstream  vectored  jet  over  the  phase  0-180  deg. 
This  could  be  followed  by  an  agglomerated  induction  of  similar  but 
negative  vortices  from  the  starboard  side.  The  net  interaction  results  in 
the  modulation  of  the  vector  of  the  jets  between  pairs  of  vortices  which 
is  the  source  of  the  axial  force.  The  mechanism  is  thus  primarily 
rotational  and  inviscid. 


(a) 


(b)  2.0i 


1.2 


1,00  60  120  1«0  240  300  360 

Pa®#  Lag  (Dag) 


Figure  8.  Variation  of  time-averaged  axial  thrust  with  phase  lag  of 
nose  slider.  Speed,  Frequency  &  Tal  Flap  St:  (a)  16.2  -  21.0  cm/s,  3.77 
Hz  &  0.6  -  0.46;  (b)  27.4  -  30.5  cm/s;  3.64  Hz  &  0.375  -  0.337;  (c)  36  - 
38  cm/s;  3.65  Hz  &  0.276  -  0.263. 

The  present  work  suggests  that  if  the  head  movement  of  a  fish  truly 
sheds  vortices,  then  the  body  waving  may  be  a  mechanism  to  ensure 
the  survivability  of  these  vortices  in  the  presence  of  cross  currents  so 
that  eventually  they  become  available  to  modulate  the  thrust  produced 
by  the  caudal  fins.  If  the  propulsion  of  novel  underwater  bodies  is 
based  on  the  jets  produced  by  discrete  deterministic  vortex  shedding, 
then  that  would  open  up  the  possibility  of  exquisite  maneuverability  via 
phase-matched  vortex  seeding  from  other  appendages.  Further  work  is 
necessary  to  determine  if  the  vortex  seeding  can  be  optimized  for 
significant  enhancement  of  net  thrust. 

CONCLUDING  REMARKS: 

The  dual  flapping  foil  maneuvering  device  for  small  cylinders  has  been 
demonstrated  earlier  in  the  laboratory.  A  reasonable  documentation 
and  understanding  of  the  mechanism  of  production  of  axial  and  cross¬ 
stream  forces  and  moments  have  been  reported.  In  the  present  work, 
the  effect  of  a  phased  vortex  seeding  from  the  nose  on  axial  forces  is 
studied.  It  is  shown  that  such  vortex  seeding  can  modulate  the  axial 
force  in  a  fine  range,  within  ±  5-10%,  if  operated  at  the  correct 
Strouhal  numbers. 


(a) 


* 

; 


i 


460 


Phased  Vortex  Leading  to  Vortex  Interaction: 

Seeding  Survival  and  Modulation  of  Thrust 

Strengthening 

Figure  9.  Schematics  of  mechanism:  (a)  effect  of  unsteadiness  of  a 
vorticity  source  on  vortex  trajectory,  and  (b)  mechanism  of  thrust 
modulation. 

Future  work  needs  to  be  carried  out  to  determine  the  optimizing  effects 
of  increasing  nose  slider  protrusion  over  the  cylinder  surface  and  the 
upstream  location  of  the  nose  slider  with  respect  to  the  flapping  foils 
and  Strouhal  number.  The  measurements  need  to  be  verified  in  a 
water  tunnel  where  the  low  speeds  are  more  accurately  held  constant, 
the  effects  of  environmental  disturbances  determined  and  the 
modulation  effects  need  to  be  verified  in  an  unbounded  surrounding. 
Perhaps,  much  can  be  learned  by  simulating  the  vortex  interactions 
numerically. 

The  viscous  drag  reduction  of  a  turbulent  boundary  layer  involves 
phenomena  that  are  only  partly  deterministic;  the  vortices  involved  are 
rather  small  physically  and  a  great  deal  of  randomness  in  space  and 
time  is  present.  Bodies  with  flapping  foil  mechanism,  on  the  other  hand 
do  not  have  these  as  primary  limitations  -  force  modulation  is  largely  an 
inviscid  process.  The  optimization  process  appears  to  be  more 
tractable  when  an  inviscid  phenomena  of  large  deterministic  vortices  is 
involved.  Biologically  based  thrust  modulation  is  an  alternative  to 
conventional  approaches  to  the  drag  reduction  of  turbulent  boundary 
layers.  Conventional  propulsors  also  involve  an  inviscid  mechanism, 
deterministic  vortex  shedding  and  the  production  of  jets,  much  as 
flapping  foils  do.  It  might  be  worth  treating  the  propulsion  and  drag  of 
a  conventional  underwater  vehicle  in  an  integral  manner.  Then, 
upstream  seeding  of  large  deterministic  vortices  to  supplant  the 
turbulent  boundary  layer  structures  and  achieve  an  overall 
enhancement  of  thrust  in  presence  of  the  propulsor  is  worth  exploring. 
In  other  words,  integrating  certain  cylinder  drag  reduction 
methodologies  with  rotating  in-situ  propulsors,  is  a  new  twist  to  drag 
reduction  research  that  can  be  learned  from  bilocomotion. 

ACKNOWLEDGMENTS 

The  support  of  ONR  (Dr.  T.  McMullen)  and  NUWC  IR  (Dr.  S. 
Dickinson)  is  gratefully  acknowledged. 

REFERENCES 

1.  Bandyopadhyay,  P.  R.,  Castano,  J.  M.,  Nedderman,  W., 
Donnelly,  M.  Zeiger.  M  1996  "A  Small  Maneuvering  Device  for 
Energetic  Environment,"  (edited  and  captioned;  6  minutes)  Video, 
NUWC  Newport,  RI. 

2.  Bandyopadhyay,  P.  R.,  Castano,  J.  M.,  Rice,  J.  Q.  Philips,  R. 
B.,  Nedderman,  W.  H.  &  Macy,  W.  K.  1997a  "Low-speed 
Maneuvering  Hydrodynamics  of  Fish  and  Small  Underwater  Vehicles" 
ASME  Jou.  Fluids  Engrg.,  V119,  pp.  136-144. 

3.  Bandyopadhyay,  P.  R.  &  Donnelly,  M.  J.  1997  “The 
Swimming  Hydrodynamics  of  a  Pair  of  Flapping  Foils  Attached  to  a 
Rigid  Body”,  AGARD  Meeting  on  High-Speed  Underwater  Bodies ,  to 
be  held  at  Kiev,  Ukraine,  Sept.  1-3,  1997,  pp.  1.1-1.17. 

4.  Bandyopadhyay,  P.  R.,  Nedderman,  W.  H.,  Castano,  J.  M.  & 
Thivierge,  D.  1997b  “Phased  Vortex  Shedding  for  Enhancement  of 
Thrust  of  a  Cylinder,”  (edited  and  captioned;  7  minutes)  Video,  NUWC 
Newport,  RI.. 

5.  Bandyopadhyay,  P.  R.,  Nedderman,  W.  H.,  Dick,  J.  & 
Castano,  J.  M.  1997c  “Loads  on  Biologically- Inspired  Winged  Bodies 
Under  Surface  Waves“,  ASME  Jou.  FI.  Engrg.,  (submitted). 


6.  Bandyopadhyay,  P.  R.,  Singh,  S.  &  Chockalingam,  F.,  1998 

“A  Theoretical  Control  Study  of  the  Biologically- Inspired  Maneuvering 
of  a  Small  Vehicle  Under  a  Free  Surface  Wave,”  Jou.  Fluids  Engrg. 
(subjudice). 


461 


Drag  Reduction  and  Turbulence  Control  in  Swimming  Fish-like  Bodies 


M.J.  Wolfgang1,  S.W.  Tolkoff1,  A.H.  Techet1,  D.S.  Barrett1,  M.S.  Triantafyllou1 
D.K.P.  Yue1,  F.S.  Hover1,  M.A.  Grosenbaugh2,  &  W.R.  McGillis2 

1  Department  of  Ocean  Engineering 
Massachusetts  Institute  of  Technology 
Cambridge,  Massachusetts  02139 

2  Department  of  Applied  Ocean  Physics  and  Engineering 
Woods  Hole  Oceanographic  Institution 
Woods  Hole,  Massachusetts  02543 


Experimental  measurements  on  the  RoboTuna  demonstrate  that  the  power  required  to  propel  a  swimming  streamlined, 
fish-like  body  is  smaller  than  the  power  needed  to  tow  the  body  at  the  same  speed.  The  lateral  motion  of  the  swimming 
body  is  a  traveling  wave  with  wavelength  A  and  amplitude  varying  quadratically  along  the  length.  Parametric  studies  show 
sensitivity  of  drag  reduction  to  the  principal  parameters,  most  importantly  the  Strouhal  number  and  the  phase  speed  of  the 
body  wave.  Numerical  power  estimates  using  an  inviscid  boundary-integral  numerical  scheme  are  in  good  agreement  with 
the  experimental  data.  Wake  flow  visualization  and  near-body  digital  particle  image  velocimetry  (DPIV)  reveal  mechanisms 
contributing  to  the  observed  drag  reduction. 


1  Introduction 

Unsteady  flow  control  offers  the  possibility  of  advancing  the  ef¬ 
ficiency  of  marine  propulsion  technology  by  shifting  the  paradigm  of 
conventional  propulsion  methods.  Unsteady  propulsion  techniques 
offer  several  distinct  advantages  over  conventional  steady  propul¬ 
sion  methods:  unsteady  foil  motion  can  achieve  high  lift  coefficient 
[1]  and  is  an  efficient  thrust  production  mechanism  [2,3].  Addition¬ 
ally,  oscillating  foils  can  effectively  manipulate  oncoming  vorticity 
[4]  and  recapture  energy  from  these  disturbances  [5]. 

Ffowcs-Williams  &  Zhao  [6]  and  Tokomaru  Sz  Dimotakis  [7] 
have  shown  that  efficient  flow  control  can  be  achieved  by  unsteady 
motion  of  a  body  in  the  fluid.  In  addition,  periodic  forcing  of  a  flow 
has  been  studied  by  several  investigators,  with  important  implica¬ 
tions  on  efficient  propulsion.  Imposing  harmonic  rotary  oscillations 
of  a  cylinder  in  an  oncoming  stream  can  result  in  a  reduction  in  wake 
width  [8],  with  maximum  influence  on  the  flow  when  the  frequency 
is  close  to  the  Strouhal  frequency  [7].  Boundary  layer  turbulence 
suppression  was  observed  by  [9]  in  the  flow  around  a  flexible  plate 
in  an  oncoming  stream,  as  long  as  the  phase  speed  of  the  plate’s 
traveling  wave  cv  exceeds  the  free  stream  velocity  U. 

The  swimming  motions  of  a  fish  are  rhythmic  hence  causing 
unsteady  flow.  They  have  evolved  over  millions  of  years,  and  as 
a  result,  fish  swimming  dynamics  provide  an  ideal  framework  to 
investigate  drag  reduction  and  vorticity  control  mechanisms,  in  ad¬ 
dition  to  the  implications  on  innovative  marine  vehicle  design.  Out¬ 
standing  maneuvering  and  propulsive  performance  by  fish  has  been 
reported  [10,11],  causing  interest  in  fish  swimming  dynamics.  Stud¬ 
ies  by  Light  hill  [12]  and  Wu  [13,14]  have  shed  light  to  the  inviscid 
hydromechanics  of  fish-like  propulsion.  In  this  paper,  we  investigate 
the  effects  of  unsteady  propulsion  and  flow  control  on  drag  reduc¬ 
tion  in  streamlined  bodies.  Gray  [15]  first  reported  a  discrepancy 
between  the  power  required  to  propel  a  rigid  dolphin  and  the  avail¬ 
able  muscular  power  which  is  smaller  by  a  factor  of  seven  ( Gray’s 
paradox).  However,  Gray’s  conclusions  have  remained  controversial 
for  over  sixty  years  due  to  the  difficulty  in  obtaining  reliable  force 
measurements  from  live  fish. 

We  chose  to  develop  a  robotic  mechanism,  which  can  emulate 
very  closely  the  swimming  of  the  tuna  [16,17].  Measurements  of 
the  hydrodynamic  forces  and  the  swimming  kinematics  on  the  flex¬ 
ible  robot  have  shown  that  at  Reynolds  number  of  about  106,  drag 
can  be  reduced  by  50%  or  more.  Dye  visualization  techniques  are 


utilized  in  experiments  with  the  robotic  tuna,  in  order  to  elucidate 
mechanisms  of  vorticity  control  by  the  tail  in  the  wake.  Boundary 
layer  modification  along  the  length  of  the  swimming  fish  is  stud¬ 
ied  quantitatively  using  digital  particle  image  velocimetry  (DPIV) 
[18,19].  Additionally,  an  inviscid  numerical  method  has  been  devel¬ 
oped  to  model  the  fish  swimming  dynamics,  based  on  a  boundary- 
integral  approach.  The  numerics  provide  reasonable  estimates  of 
the  power  needed  for  fish-like  swimming,  which  indeed  compare  well 
with  the  experimental  robotic  fish  data  for  the  power  expended  by 
the  motors. 

2  Experimental  Apparatus 

2.1  Robotic  design  and  construction 

The  hull  of  the  RoboTuna  has  the  shape  of  a  bluefin  tuna  ( thun - 
nus  thynnus),  including  the  tail  fin.  The  length  of  the  robot  is 
L  =  1.25m.  The  mechanism  is  attached  to  a  carriage  in  the  Ocean 
Engineering  Testing  Tank  Facility  at  MIT  in  a  water  tank  with  di¬ 
mensions  35  m  by  2.5  m  by  1.25  m.  The  robot  is  submerged  at  mid¬ 
depth  of  the  tank  to  avoid  free  surface  and  bottom  interference.  The 
body  sections  of  the  RoboTuna  are  approximately  elliptical,  and  the 
maximum  transverse  dimensions  are:  height  0.30  m  and  width  0.21 
m.  A  set  of  eight  anodized  aluminum  links  support  the  structure 
shown  in  Figure  1,  showing  the  basic  outline  of  the  mechanism.  The 
eight  rigid  links  are  capable  of  rotating  about  a  single  axis.  Flexing 
of  the  hull  is  achieved  by  affixing  sets  of  densely-packed  plastic  ribs 
transversely  on  stainless  steel  backbones  running  between  the  ends 
of  adjacent  links.  An  impermeable  skin  structure,  one  inch  thick, 
consisting  of  layers  of  filter  foam  and  tensioned  thin  latex  sheets  is 
used,  contained  on  both  sides  by  conformal  Lycra  skin. 

The  links  are  activated  by  six  brushless  motors,  3  HP  each. 
The  second  link  is  rigidly  attached  to  the  carriage  and  the  first  and 
third  links  are  coupled  to  move  in  anti-phase,  hence  there  are  six 
degrees  of  freedom.  Strings  and  pulleys  transmit  the  motion  to  in¬ 
dividual  links.  Pairs  of  cables  (or  tendons)  are  channeled  down  the 
centerline  of  the  frame,  one  set  per  motor.  The  first  two  links  use  a 
block  and  tackle  mechanism  which  allows  developing  high  torque. 
The  remaining  four  links  use  direct  drive  actuation  because  of  space 
limitations.  We  will  refer  to  six  joints ,  numbered  sequentially  from 
the  front  joint  0  (activating  the  coupled  first  and  third  links)  to  the 
tail  joint  5  (activating  the  tail-fin). 


463 


Figure  1:  Lateral  schematic  view  of  the  robotic  fish-like  mechanism  and  the  supporting  streamlined  strut  which  attaches  to  the  tow 
carriage.  Skin  cutaways  reveal  the  bulkhead  and  framing  structure. 


Load  cells  ( Entran  elf-tc500)  are  mounted  on  the  twelve  ac¬ 
tuating  strings  to  measure  the  transmitted  forces.  Displacement 
sensors  ( ETI  servomount  precision  potentiometers)  provide  accu¬ 
rate  link  motion  measurements.  These  measurements  allow  detailed 
evaluation  of  the  power  transmitted  to  the  mechanism.  Also,  the 
axial  force  transmitted  by  the  streamlined  strut  on  the  carriage 
is  measured  by  two  force  transducers,  for  redundancy,  a  load  cell 
( Entran  elf-tclOOO)  and  a  Kistler  quartz  force  transducer. 

2.2  Calibration  and  operation 

After  the  sensors  were  calibrated,  we  conducted  an  exten¬ 
sive  set  of  experiments  to  verify  the  accuracy  of  energy  and  power 
measurements  and  to  assess  the  internal  losses  in  the  mechanism. 
Weights  were  hung  through  wires  from  the  tail  of  the  RoboTuna  and 
motions  of  the  robot  were  commanded,  while  measuring  the  forces 
and  motions  of  the  actuating  strings.  In  addition  the  motions  and 
forces  acting  on  the  strings  supporting  the  hanging  weights  were  di¬ 
rectly  measured  (calibration  apparatus).  We  conducted  tests  both 
with  slow  motions  (static  tests)  and  fast  oscillating  motions  (dy¬ 
namic  tests). 

All  verification  tests  were  conducted  by  commanding  each  link 
separately  to  move  through  a  certain  rotation.  The  motion  resulted 
in  a  motion  of  the  tail  and  hence  of  the  hanging  weight,  which 
was  directly  measured.  The  motion  of  the  tail  as  estimated  from 
the  motor  motion  agrees  to  within  5%  with  the  directly  measured 
motion;  the  difference  is  attributed  to  the  partial  flexibility  of  the 
robot.  The  error  in  the  force  measurements  was  below  10%,  the 
error  reducing  for  links  near  the  tail  where  the  weights  were  hung. 
We  conclude  that  for  swimming  experiments  the  expected  discrep¬ 
ancy  is  below  5%,  since  the  force  is  distributed  along  the  length  and 
not  concentrated  in  a  single  point. 

Next,  the  energy  required  to  produce  a  commanded  motion 
by  each  link  was  compared  to  the  energy  expended  by  the  motors. 


Each  link  was  commanded  to  move  through  a  certain  distance  at  a 
slow  speed,  while  known  weights  were  hung  from  the  calibration  ap¬ 
paratus.  The  potential  energy  change  associated  with  this  motion 
was  compared  to  the  power  expended  by  the  motors  over  a  known 
time  interval.  Deviations  were  generally  within  12%,  with  the  high¬ 
est  recorded  discrepancies  again  for  links  furthest  away  from  the 
tail.  Internal  losses  in  the  mechanism  result  consistently  in  measur¬ 
ing  higher  motor  energy  than  the  actual  potential  energy.  Finally, 
known  weights  were  hung  from  the  calibration  apparatus,  and  each 
individual  link  was  commanded  to  oscillate  at  a  constant  amplitude 
and  at  a  frequency  1  Hz.  The  power  utilized  by  the  motors  was 
averaged  over  10  cycles  and  compared  to  the  power  recorded  by  the 
force  and  motion  transducers  of  the  calibration  apparatus.  Results 
agreed  generally  to  within  15%,  with  higher  discrepancies  further 
away  from  the  tail.  Hence,  the  dynamic  error  estimates  represent 
an  upper  bound,  particularly  for  the  links  further  away  from  the 
tail,  since  in  the  swimming  experiments  fluid  forces  are  distributed 
along  the  entire  body.  We  estimate  that  the  actual  power  losses  are 
on  the  order  of  5%,  similar  to  errors  found  for  links  close  to  the  tail. 

2.3  Swimming  kinematics 

We  selected  the  motions  of  the  robot  to  be  close  to  the  actual 
motions  observed  in  live  tuna  [20] .  The  backbone  motion  consists  of 
a  smooth,  purely  sinusoidal,  amplitude-modulated  traveling  wave, 
and  the  wave  travels  along  the  body  length  with  a  phase  speed 
Cp  =uj/k,  which  in  general  may  differ  from  the  swimming  speed  U. 
The  transverse  backbone  wave  motion  y(x,t),  where  x  is  measured 
along  the  backbone  of  the  fish,  is  given  the  form: 

y(x,  t)  =  a(x)  sin  (kx  —  ut)  (1) 

where  k  =  27r/A  is  the  wavenumber,  corresponding  to  wavelength  A, 
uj  is  the  circular  frequency  of  oscillation,  and  a(x)  is  the  amplitude 


464 


envelope,  given  as: 


(8) 

(9) 


a(x)  =  cix  +  C2X2  (2) 

where  c\  and  C2  are  adjustable  parameters,  ci  is  independently 
varied,  while  C2  is  chosen  to  achieve  a  specific  value  of  the  double¬ 
amplitude  of  motion,  denoted  by  A ,  at  the  tail.  The  distance  x 
is  measured  from  the  edge  of  the  second  link,  which  is  rigidly  at¬ 
tached  to  the  towing  strut,  and  is  non-dimensionalized  by  the  body 
length.  Typically,  the  phase  speed  cp  =  u/k  is  larger  than  the  for¬ 
ward  speed  U,  while  the  wavelength  A  is  close  in  value  to  the  body 
length.  The  frequency  scaling  of  data  observed  in  fish  is  based 
on  the  wake  Strouhal  law  [21,22],  i.e.  keeping  constant  the  non- 
dimensional  parameter  St: 

St  =  fA/U  (3) 

where  /  is  the  frequency  of  oscillation  in  Hertz  and  A  is  the  average 
lateral  excursion  of  the  tail  fin. 

3  Unsteady  Swimming  Experiments 

3.1  Definitions 

In  conventional  marine  propulsion  studies,  where  the  main 
body  is  rigid  and  the  propulsor  is  a  relatively  small  device,  the 
thrust  of  the  propulsor  can  be  measured  directly  at  the  interface 
between  the  body  and  the  propulsor.  Hence  the  drag  of  the  body 
can  be  also  found:  in  self-propulsion  tests  it  is  equal  to  the  propul¬ 
sor  thrust.  This  is  impossible  to  do  with  a  flexible  hull  swimming 
body,  where  the  body  and  the  propulsor  are  nearly  indistinguish¬ 
able.  Hence,  we  must  estimate  the  drag  of  an  actively  swimming 
body  as  follows. 

Let  U  denote  the  speed  at  which  the  body  is  moving  and  Ta 
the  average  thrust  provided  by  the  propulsor;  Da  denotes  the  av¬ 
erage  drag.  By  conservation  of  energy,  the  average  power  provided 
by  the  motors,  Pp,  can  be  written  as  the  sum  of  the  useful  power 
PE  —  Ta  U  (used  to  propel  the  body)and  power  losses  Pi  and  Pw: 

Pp  =  PB  +  Pl+  pw  (4) 

where  all  quantities  are  time-averaged;  Pi  denotes  the  transmission 
losses  from  the  motors  to  the  propulsor;  Pw  denotes  the  energy 
wasted  in  the  wake  (such  as,  for  example,  the  rotational  energy 
imparted  to  the  fluid  by  a  screw-propeller). 

For  a  self-propelled  body  Ta  =  Da>.  Hence: 

Pp  =  DAU  +  Pi+Pw  (5) 

Both  Pi  and  Pw  are  positive,  hence  concluding: 

Da  <  Pp/U  (6) 

We  define  the  ratio  Pp/U  as  the  upper  estimate  of  body  drag ,  Du : 

Du  =  Pp/U  (7) 

If  D0  denotes  the  drag  of  the  towed  rigid  body,  drag  reduction  is 
defined  to  occur  when  Du  <  D0 . 

If  the  mechanism  is  not  self-propelled,  then  it  is  produc¬ 
ing  a  net  axial  force,  the  mast  force  Fn.  Then,  one  substitutes 
Ta  —  Fa  +  Da,  where  Fa  is  the  time  average  of  the  mast  force,  to 
find  for  a  net-force-producing  mechanism,  forced  to  move  at  con¬ 
stant  speed  U : 


Da  ^  Du 

Du  =  Pp/U  -  Fa 

The  criterion  for  drag  reduction  is  conservative,  hence  the  utility  of 
Du  as  a.  gauge  of  drag  reduction  depends  on  having  small  transmis¬ 
sion  losses  and  high  hydrodynamic  efficiency. 

3.2  Experimental  flapping  body  drag  and  power 

The  calculation  of  an  upper-bound  of  the  flapping  body  drag, 
Du,  is  based  on  (9),  involving  two  quantities:  the  measured  mast 
force  Fa;  and  the  motor  power  Pp,  which  is  found  using  the  force 
and  motion  data  of  the  string  actuators  as  described  in  the  follow¬ 
ing. 

Two  strings  are  connected  to  each  motor,  resulting  in  a  total  of 
twelve  strings.  For  the  jth  motor  the  first  string  is  pulled  in  (paid 
out)  with  velocity  Vj  while  registering  force  Fij,  and  the  second 
string  is  paid  out  (pulled  in)  with  equal  velocity  Vj  while  register¬ 
ing  force  Fjy.  The  forces  represent  the  tensions  measured  on  the 
string  and  are  always  positive;  hence  the  net  input  power  from  the 
jth  motor  is  Pj  =  F\j  Vj  —  F^j  Vj  =  ( F\j  —  F2j)  Vj.  We  define 
the  jth  joint  force  as  Fj  —  F\j  -  F2j  and  then  the  instantaneous 
input  power  is  found  as  Pj  =  Fj  Vj.  The  overall  instantaneous 
power  is  calculated  as  the  sum  of  the  input  power  in  all  six  joints 
and  then  integrated  to  find  the  average  power  absorbed.  An  average 
over  several  cycles  was  calculated  after  steady  state  was  achieved. 

The  mast  force,  as  measured  in  the  present  set  of  experiments, 
i.e.  at  the  top  of  the  mast,  contains:  the  drag  of  the  strut,  the  inter¬ 
action  drag  between  the  flexible  mechanism  and  the  mast,  and  the 
drag  of  the  mechanism  including  the  attached  fins  and  the  tail.  In 
order  to  obtain  estimates  of  the  drag  coefficient  on  the  body  alone, 
the  drag  of  these  components  (correction  drag)  must  be  measured 
and  then  used  to  correct  the  measured  axial  force.  For  this  reason, 
we  measured  experimentally,  as  function  of  speed,  the  drag  of  all 
appendages. 

We  provide  detailed  measurement  data  for  a  typical  case,  with 
a  Reynolds  number  based  on  the  body  length  Re  =  UL/v  = 
800,000  and  with  a  Strouhal  number  of  St  —  0.273.  The  flow 
was  stimulated  to  be  turbulent,  tripped  by  a  ring  at  the  interface 
between  the  rigid  nose  cone  and  the  flexing  body,  as  well  as  the 
rough  Lycra  cloth  of  the  skin  structure.  Figure  2  provides  the  mea¬ 
sured  forces  and  velocities  of  the  six  joints  as  functions  of  time  after 
steady-state  conditions  have  been  established.  Run  parameters  for 
this  case,  with  length  scales  nondimensionalized  by  body  length 
(BL):  St  =  0.273,  U  —  0.656  BL/s,  wavelength  A  =  1.08  BL, 
tail  circular  frequency  u)  =  8.095  rad/s ,  tail  tip  double  amplitude 
A  =  0.139  BL,  tail  angle  of  attack  a  =  21.0°,  and  the  phase  angle 
between  angular  pitch  and  lateral  heave  of  the  tail  at  the  attach¬ 
ment  point  <j>  =  97.7°.  The  phase  speed  for  this  backbone  waveform 
is  cp  =  1.39  BL/s. 

Figure  3  provides  the  mast  force  and  total  power  measure¬ 
ments.  The  measured  total  average  power  in  this  case  was  Pf  = 
2.04  W  and  the  net  average  thrust  Ta  =  1-98  N.  The  drag  of  the 
rigid  system  at  the  same  speed  was  measured  to  be  D0  —  1.66  AT, 
including  the  drag  of  the  appendages,  which  include:  the  submerged 
part  of  the  mast,  the  tail  fin  and  two  smaller  fins  attached  on  the 
body,  as  well  as  interaction  drag.  First  we  use  a  propulsive  index, 
which  does  not  require  subtraction  of  a  correction  drag:  we  find 
that  (Ta-\-D0)U=  2.55  W;  hence  (TA  +  D0)U  /  Pp  =  1.25  >  1, 
and  we  can  confirm  drag  reduction.  In  this  case,  the  tail  requires 
small  but  positive  power.  The  upper  bound  estimate  of  the  moving 
body  drag  is  obtained  using  (9),  after  correcting  for  the  drag  of  the 
appendages.  Separate  experiments  established  the  drag  of  the  mast, 
after  streamlining  the  lower  edge  to  avoid  edge  drag.  The  drag  of 
the  support  mast  is  then  subtracted  from  both  the  flexing  body  and 
rigid  body  values  of  drag  in  determining  the  drag  reduction,  and 
although  other  interference  effects  are  not  easily  measurable,  the 
drag  reduction  realized  is  47.94%. 


465 


Force  (N) 


0.05 

0 


Velocity  (m/s) 


-0.05  1 - 

19.5 
0.1 1 - 


200 

100 

0 


t ime  ( s ) 


20.5  21 

time  (s) 


Figure  2:  Force  and  velocity  time  history  records  for  the  individual  joints.  St  =  0.273. 


Figure  3:  Total  mast  force  and  total  input  power  time  history 
records.  Mean  total  input  power  2.04  W.  St  =  0.273. 

We  have  investigated  speeds  ranging  from  0.5  to  1.0  m/ s,  which 
are  the  speeds  allowed  by  the  limits  of  our  current  equipment: 
length  of  tank,  time  to  settle  down  transients,  capability  of  the 
skin  structure  to  support  lateral  pressure.  The  results  were  repeat- 
able  within  4%  and  consistent.  Transition  to  turbulence  through 
stimulation  was  complete  in  terms  of  its  effects  on  the  drag  coeffi¬ 
cient  of  the  rigid  body  at  speeds  higher  than  0.6  m/s ,  so  a  speed 
of  U  =  0.7  m/s  was  chosen  to  investigate  the  sensitivity  of  drag 
reduction  to  parametric  change,  since  it  provided  sufficiently  long 
time  records  for  accurate  power  and  drag  estimation. 

3.4  Sensitivity  to  parametric  variation 

Through  comprehensive  testing,  we  have  been  able  to  show 
that  there  is  strong  parametric  dependence  on  the  qualitative  and 
quantitative  form  of  the  data.  Six  principal  parameters  were  varied 
to  investigate  their  dependence  on  performance:  (a)  Strouhal  num¬ 
ber,  St;  (b)  tail  nominal  angle  of  attack,  a;  (c)  phase  angle  at  the 


tail  between  lateral  and  angular  motions,  ip;  (d)  amplitude  of  mo¬ 
tion  at  the  tail,  A ;  and  (e)  body  wavelength,  A;  and  (f)  amplitude 
coefficient  kinematic  parameter  c\  (2). 

Over  six  hundred  experiments  were  conducted,  concentrating 
in  parametric  combinations  where  drag  reduction  was  found  to  be 
the  largest.  After  several  genetic  iterations,  about  three  hundred 
experiments  resulted  in  conditions  of  self-propulsion,  i.e.  zero  aver¬ 
age  mast  force.  The  dependence  of  drag  reduction  on  the  principal 
parameters  for  self-propulsion,  because  of  its  direct  relevance  on  fish 
propulsion,  is  found  as  follows: 

•  Strouhal  number,  St:  There  are  two  peaks  of  maximum  drag 
reduction,  one  at  about  St  =  0.19  and  a  second  at  about 
St  =  0.31. 

•  Tail  nominal  angle  of  attack,  or.  A  high  angle  of  attack  was 
found  to  provide  highest  drag  reduction  in  most  cases,  be¬ 
tween  20  and  28  degrees. 

•  Tail  phase  angle,  ip:  Values  in  the  range  of  80  to  100  degrees 
provide  maximum  drag  reduction. 

•  Tail  tip  double  amplitude  A:  Drag  reduction  is  relatively 
insensitive  to  this  parameter. 

•  Body  wavelength,  A:  A  wavelength  comparable  to  the  body 
length  is  found  to  provide  maximum  drag  reduction. 

•  Kinematic  parameter  c\:  Drag  reduction  is  relatively  insen¬ 
sitive  to  this  parameter. 

These  results  are  generally  in  agreement  with  the  flapping  foil 
experiments  of  Anderson  et  al.  [3].  Vorticity  control  is  a  principal 
mechanism  through  which  flapping  foils  achieve  high  efficiency  [3], 
and  also  recover  energy  from  oncoming  vortical  flow  [5];  this  is  also 
the  reason  why  the  Strouhal  number,  which  governs  the  dynamics 
of  the  shed  vorticity,  is  a  principal  parameter  in  the  present  exper¬ 
iments. 

All  experiments  which  exhibit  drag  reduction  share  one  com¬ 
mon  characteristic:  the  phase  speed  of  the  traveling  wave  imposed 
on  the  body  cp  was  larger  than  the  forward  speed  t/,  identical  with 
the  conclusions  of  Taneda  [9]  that  turbulence  suppression  and  drag 


466 


reduction  are  seen  in  the  flow  around  a  two-dimensional  flexible 
sheet  in  a  uniform  flow  undergoing  periodic  traveling  wave  trans¬ 
verse  oscillation.  This  is  the  single  parametric  condition  that  seems 
to  be  unrelated  to  wake  management  and  indicative  drag  reduction 
on  the  body  itself. 

We  can  see  from  Figure  4  that  drag  reductions  of  up  to  70% 
within  the  range  considered  are  observed. 


Drag 

Reduction  % 


Figure  4:  Apparent  drag  reduction  as  function  of  Strouhal  number 
for  a  range  of  Reynolds  numbers. 

4  Drag  Reduction  Mechanisms 

4.1  Discussion 

The  drag  reduction  realized  must  be  caused  exclusively  by  the 
actively-controlled  transverse  motion.  From  the  parametric  studies 
and  the  aggregate  of  force  and  power  data,  we  can  conclude  the 
most  plausible  mechanisms  contributing  to  this  drag  reduction  in¬ 
clude  a  laminarization  of  the  boundary  layer  and  vorticity  control 
by  the  tail  fin. 

Taneda  [9]  realized  laminarization  of  the  boundary  layer  in  his 
experiments  with  a  flexible  rectangular  sheet  undergoing  periodic 
traveling  wave  oscillations  within  an  oncoming  stream,  at  Reynolds 
numbers  up  to  3  X  106.  He  observed  that  when  the  phase  speed 
of  the  traveling  wave  cp  exceeded  that  of  the  free  stream  speed  Z7, 
separation  was  delayed  or  absent  and  turbulence  was  suppressed. 
By  estimating  the  wall  stress,  he  concluded  that  wall  stress,  and 
hence  drag,  diminished  as  cp/U  increased. 

In  all  cases  where  substantial  drag  reduction  was  observed 
in  our  experiments,  the  phase  velocity  of  the  traveling  wave  cp 
exceeded  the  swimming  velocity  17,  in  complete  agreement  with 
the  experiments  of  Taneda.  The  similarity  between  our  three- 
dimensional  and  Taneda’s  quasi-two-dimensional  results  is  not  coin¬ 
cidental.  DPIV  visualization  tests  around  live  fish  by  Anderson  [23] 
and  around  the  robotic  mechanism  described  herein,  have  shown 
that  the  flow  patterns  around  the  body  of  the  fish  at  mid-depth, 
within  a  plane  parallel  to  the  direction  of  lateral  motion,  are  quali¬ 
tatively  similar  to  the  two-dimensional  patterns  predicted  theoret¬ 
ically  for  an  undulating  plate  by  Wu  [13,14].  Substantial  spanwise, 
body-bound  traveling  vorticity  develops,  which  is  shed  by  the  time 
it  reaches  the  caudal  peduncle,  forming  large  vortices,  which  are 
then  manipulated  by  the  tail  to  form  a  propulsive  reverse  Kdrm&n 
street.  Similarly,  these  results  are  upheld  by  the  numerical  simula¬ 
tions  of  Cheng,  et  al  [24],  for  a  three-dimensional  flapping  plate. 

Additionally,  flapping  tail  parameters  such  as  the  Strouhal 
number  must  be  within  optimal,  narrow,  parameter  ranges  to 
achieve  substantial  overall  drag  reduction,  due  to  the  tail’s  role  as 
an  efficient  unsteady  lifting  surface  [3]  and  in  manipulating  vorticity 


generated  by  the  unsteady  flapping  of  the  body.  Vorticity  control 
[5]  mechanisms  are  basic  to  the  manipulation  of  body-generated 
vorticity  by  the  tail  in  live  fish  [23],  and  explains  the  sensitivity  of 
the  drag  reduction  to  variations  in  Strouhal  number. 

The  present  results  seem  also  to  confirm  the  basic  premise  in 
Gray’s  paradox  [15],  i.e.  that  fish-like  propulsion  must  be  associated 
with  drag  reduction,  albeit  at  a  lower  Reynolds  number  than  for  the 
dolphins  considered  by  Gray. 

4.2  Further  experiments 

To  further  elucidate  the  mechanisms  discussed  above,  further 
experimental  methods  have  been  developed  to  visualize  both  the 
wake  and  near-body  flows  of  the  experimental  mechanism.  To  study 
the  flow  around  the  tail  fin  and  the  subsequent  wake  dynamics,  and 
dye  injection  system  has  been  fitted  into  the  robotic  hull.  Fluores¬ 
cent  dye  is  injected  at  a  point  close  to  the  caudal  peduncle  at  the 
tail’s  mid-span,  and  a  blacklight  is  used  to  illuminate  the  dye  as  it 
is  manipulated  by  the  motions  of  the  robotic  tail.  A  dye-injection 
system  similar  to  this  is  shown  in  Triantafyllou  &  Triantafyllou  [17]. 

Our  other  goal  is  to  illuminate  and  characterize  the  near-hull 
flow  structure  within  the  boundary  layer.  Flow  visualizations  and 
quantitative  measurements  with  digital  particle  image  velocimetry 
(DPIV)  are  the  first  measurements  of  this  type  that  may  quantify 
the  details  of  boundary  layer  laminarization.  To  achieve  these  re¬ 
sults,  a  laser  particle  imaging  system  has  been  set  up  in  the  MIT 
Testing  Tank  Facility  (Figure  5).  A  plane  of  the  flow,  near  the 
centerline  of  the  fish,  is  illuminated  using  a  laser  beam  fanned  to 
form  a  plane  sheet.  The  surrounding  fluid  is  uniformly  seeded  with 
neutrally  buoyant  fluorescent  particles  (diameter  «  40  to  70  fim) 
which  reflect  wavelengths  in  the  range  of  560-580  nm.  Ten  to  twenty 
particles  per  interrogation  window  were  sufficient  to  ensure  good 
correlations  [19]. 


Figure  5:  Schematic  view  of  digital  particle  image  velocimetry 
(DPIV)  setup  for  boundary  layer  investigation.  The  pulsed  laser 
beam  is  directed  through  a  set  of  optics  external  to  the  tank  and 
fanned  into  a  sheet.  The  laser  sheet  illuminates  a  plane  of  fluid 
perpendicular  to  the  fish  body  at  mid-depth.  An  underwater  CCD 
camera  and  mirror  samples  the  particle  images. 


467 


The  laser  used  to  illuminate  the  flow  field  is  a  dual  cavity 
pulsed  NdrYAG  laser  from  Spectra  Physics,  Inc.,  designed  specifi¬ 
cally  for  PIV  applications.  The  laser  is  capable  of  delivering  400 
mJ /pulse  of  green  (532  nm)  light  at  15  Hz.  The  beam  is  passed 
through  a  series  of  optics  which  fan  the  light  into  a  larger  sheet  on 
the  order  of  1  mm  thick.  The  laser  timing  is  controlled  through  a 
four-channel  timing  box  and  is  synched  with  the  vertical  drive  on  a 
high  resolution,  black  and  white  CCD  video  camera,  Texas  Instru¬ 
ments  MULTICAM  MC1134P,  which  is  used  to  capture  the  particle 
motion.  The  camera  records  the  flow  with  a  maximum  pixel  reso¬ 
lution  of  1134  x  480  pixels  at  a  standard  frame  rate  of  30  Hz.  Dual 
field  exposure  renders  full  vertical  resolution  with  no  interlace.  The 
video  from  the  CCD  camera  is  stored  real-time  by  a  MuTech  Frame 
grabber  into  128  Mb  Ram  on  a  133  MHz  Pentium  Processor  PC. 
The  camera  placement  is  fixed  with  respect  to  the  testing  tank,  and 
focused  on  the  illuminated  plane.  Experiments  were  conducted  us¬ 
ing  both  the  stationary  YAG  pulse  laser  with  a  camera  fixed  to  the 
floor  of  the  tank,  and  a  carriage  mounted  laser  diode  with  a  camera 
that  moved  with  the  robot. 

5  Computational  Results 

The  experimental  results  suggest  that  significant  reduction  in 
body  drag  is  achievable  through  fish-like  propulsion.  Because  the 
power  measured  by  the  motors,  is  principally  influenced  by  inviscid 
hydrodynamic  mechanisms  in  the  absence  of  large  form-drag,  invis¬ 
cid  numerical  methods  may  provide  accurate  estimates  of  the  neces¬ 
sary  propulsive  power,  provided  the  vorticity  shed  from  sharp  trail¬ 
ing  edges  (such  as  the  tail  fin)  is  properly  modeled  and  accounted 
for.  In  this  manner,  we  may  further  investigate  the  mechanisms  of 
large-scale  vorticity  control  by  simulation  of  the  flow  kinematics  and 
forces  around  a  three-dimensional  body  under  the  same  conditions 
used  in  the  experiments. 

We  consider  a  flexible,  streamlined  body  equipped  with  a  sharp 
trailing-edge,  rigid  caudal  fin.  We  study  through  simulation  the 
problem  of  this  body  starting  from  rest  to  reach  a  constant  hori¬ 
zontal  velocity  U  while  undergoing  periodic  undulations  about  its 
mean  line  within  an  inviscid,  incompressible  fluid.  A  thin  shear 
layer  wake  is  continuously  shed  from  the  trailing  edge  of  the  caudal 
fin  as  time  proceeds.  The  flow,  with  the  exception  of  the  thin  wake, 
is  assumed  to  be  irrotational,  allowing  for  the  existence  of  a  velocity 
potential  <p(x,t).  All  time  and  length  scales  are  chosen  to  be  nondi- 
mensional  with  respect  to  the  body  length  t  =  1  and  swimming 


speed  U  =  1.  A  three-dimensional  numerical  panel  method  based 
on  Green’s  theorem  is  employed  to  find  the  velocity  potential  on 
the  body  and  in  the  wake. 

The  surface  of  a  body  similar  to  the  robotic  mechanism  de¬ 
scribed  above  is  numerically  represented  by  quadrilateral  panels. 
The  body,  excluding  the  caudal  fin,  employs  0(2,000)  panels,  and 
the  caudal  fin  is  gridded  with  0(1,000)  panels.  The  motion  of  the 
body  is  described  by  (1)  and  (2),  identical  to  that  of  the  flexible, 
fish-like  robot.  The  tail  follows  the  path  of  the  caudal  peduncle  but 
pivots  with  oscillatory  angular  motion  of  amplitude  a  and  arbitrary 
phase  angle  with  respect  to  the  lateral  motion  0.  The  simulation 
starts  with  the  body  in  a  flexed  position,  and  the  caudal  fin  wake 
is  shed  continuously  in  time  as  the  fish  begins  to  move.  After  sev¬ 
eral  periods  of  the  motion,  transients  associated  with  initial  condi¬ 
tions  are  eliminated,  and  steady-state  wake  structure,  motions  and 
forces  are  achieved.  The  time  step  depends  on  the  Strouhal  number 
and  the  frequency  of  the  backbone  wave,  but  is  typically  chosen 
around  dt  —  0.05.  The  wake  and  body  panels  are  desingularized 
as  described  by  Krasny  [25]  with  radius  5  =  0.025  to  eliminate  the 
short-wavelength  instability,  and  the  wake  generally  contains  up  to 
0(10,000)  panels  at  the  conclusion  of  the  simulation.  The  evolving 
wake  structure  behind  the  fish  compares  well  qualitatively  with  dye 
visualization  experiments  performed  in  the  wake  of  the  Robotuna , 
such  as  those  illustrated  in  Triantafyllou  &  Triantafyllou  [17]. 

Power  time  histories  for  both  the  experimental  runs  and  the 
numerical  simulations  can  be  found  in  Figure  6.  The  case  is  iden¬ 
tical  to  the  one  detailed  previously  in  Section  3.2,  with  a  Strouhal 
number  St  =  0.273,  which  achieved  an  experimental  drag  reduction 
of  47.94%.  The  time  records  compare  well  qualitatively,  revealing  a 
second  harmonic  in  the  time  history  of  the  power  expended.  In  ad¬ 
dition,  quantitative  agreement  is  good  under  the  assumptions  made. 
Flexibility  of  the  experimental  apparatus  was  shown  to  have  affected 
the  exact  timing  among  the  robotic  links  and  may  have  caused  devi¬ 
ations  in  the  overall  power  time  record.  Also,  natural  resonances  in 
the  mechanical  system  and  mechanical  losses  are  expected  to  cause 
some  deviations  between  theory  and  experiment.  However,  despite 
the  simplifying  assumptions  inherent  in  the  numerical  method  and 
the  unmodeled  mechanical  behavior  and  losses,  the  difference  in  the 
mean  power  between  theory  and  experiment  is  only  17.6%,  with  an 
88.4%  numerically  computed  propulsive  efficiency. 


(a)  Experimental  (b)  Numerical 


Figure  6:  Total  power  into  the  fluid  for  straight-line  swimming.  The  mean  power  deviation  between  the  (a)  experimental  (2.04  W)  and 
the  (b)  numerical  (1.68  W)  time  history  power  records  is  17.6%.  Run  parameters  are  identical  to  those  of  the  case  shown  in  Section  3.2. 


468 


6  Conclusions 

Drag  on  a  swimming  flexible  body  is  found  to  be  smaller  than 
the  drag  on  the  same  body  towed  rigid.  The  maximum  drag  re¬ 
duction  recorded  was  in  excess  of  70%,  at  Reynolds  number  106 
with  turbulence  stimulation.  Drag  reduction  is  particularly  sensi¬ 
tive  to  the  speed  of  the  traveling  wave  over  the  body,  which  must 
exceed  the  speed  of  travel,  and  the  Strouhal  number  which  must  be 
within  a  range  which  varies  with  the  specific  thrust  developed  and 
lies  between  St  —  0.12  and  0.35. 

Numerical  simulations  were  performed  with  an  inviscid  bound¬ 
ary  integral  scheme  for  arbitrary  body  geometry  and  motions,  em¬ 
ploying  a  desingularized  infinitesimal  wake  sheet  to  model  the  non¬ 
linear  dynamics  of  the  wake  vorticity.  Numerical  predictions  for  the 
power  expended  by  a  body  similar  to  the  robotic  apparatus  under¬ 
going  identical  movements  were  in  good  qualitative  and  quantitative 
agreement  with  experimental  measurements. 

We  propose  that  the  combination  of  two  flow  control  mech¬ 
anisms  are  plausible  contributors  to  the  drag  reduction  realized: 
(a)  laminarization  of  the  boundary  layer  as  a  result  of  body  flexing 
in  the  form  of  a  traveling  wave;  (b)  vorticity  control  by  the  tail, 
which  manipulates  body-shed  vorticity  to  create  a  propulsive  re¬ 
verse  Karman  street.  Using  experimental  techniques  such  as  dye 
visualization  in  the  wake  and  near-body  DPIV,  we  can  further  elu¬ 
cidate  the  principals  leading  to  boundary  layer  laminarization  and 
wake  vorticity  control. 

ACKNOWLEDGMENTS 

Financial  support  of  the  Office  of  Naval  Research  under  con¬ 
tract  N00014-96-1-1141  monitored  by  P.  Purtell,  T.  McMullen  &  J. 
Fein;  the  Office  of  Naval  Research  under  grants  N000 1 4-89- J-3 186 
and  N00014-93-1-0774;  the  Advanced  Research  Project  Agency  un¬ 
der  contract  N00014-94-1-0735;  and  the  Sea  Grant  Program  under 
Grant  Number  NA46RG0434  is  gratefully  acknowledged. 

REFERENCES 

1.  I.  Gursul  &  C.M.  Ho  “High  aerodynamic  loads  on  an  airfoil 
submerged  in  an  unsteady  stream”,  AJAA  Journal ,  30:1117- 
1119,  1992. 

2.  K.  Streitlien,  G.S.  Triantafyllou,  &  M.S.  Triantafyllou  “Effi¬ 
cient  foil  propulsion  through  vortex  control”,  AIAA  Journal , 
34(11):2315-2319,  1996. 

3.  J.M.  Anderson,  K.  Streitlien,  D.S.  Barrett  h  M.S.  Tri¬ 
antafyllou  “Oscillating  foils  of  high  propulsive  efficiency”, 
J.  Fluid  Mech .,  360:41-72,  1938. 

4.  M.M.  Koochesfahani  &;  P.  Dimotakis  “A  cancellation  exper¬ 
iment  in  a  forced  turbulent  shear  layer”,  AJAA  88-3713-CP , 
1988. 

5.  R.  Gopalkrishnan,  M.S.  Triantafyllou,  G.S.  Triantafyllou  & 
D.S.  Barrett  “Active  vorticity  control  in  a  shear  flow  using  a 
flapping  foil”,  Journal  of  Fluid  Mechanics ,  274:1-21,  1994. 

6.  J.E.  Ffowcs- Williams  &.  B.C.  Zhao  “The  active  control  of 
vortex  shedding”,  J.  Fluids  Struct .,  3:115-122,  1989. 


7.  P.T.  Tokomaru  &  P.E.  Dimotakis  “Rotary  oscillation  control 
of  a  cylinder  wake”,  Journal  of  Fluid  Mechanics ,  224:77-90, 
1991. 

8.  S.  Taneda  “Visual  observations  of  the  flow  past 
a  circular  cylinder  performing  a  rotary,  oscillation” , 
J.  Phys.  Soc.  Japan ,  45:1038-1043,  1978. 

9.  S.  Taneda  “An  experiment  on  the  flow  around  a  waving 
plate”,  J.  Phys .  Soc.  Japan ,  36:1683-1689,  1974. 

10.  Y.  Aleyev,  Nekton ,  W.  Junk:  The  Netherlands,  1977. 

11.  D.G.  Harper  &  R.W.  Blake  “Fast-start  performance  of  rain¬ 
bow  trout  ( Salmo  gairdneri)  and  Northern  Pike  ( Esox  Lu¬ 
cius) i”,  J.  Exp .  Biol,  150:321-342,  1990. 

12.  J.  Lighthill,  Mathematical  Biofluiddynamics,  SIAM: 
Philadelphia,  1975. 

13.  T.Y.  Wu  “Swimming  of  a  waving  plate” ,  Journal  of  Fluid 
Mechanics ,  10:321-344,  1961. 

14.  T.Y.  Wu  “Hydromechanics  of  swimming  propulsion.  Part 
1.  Swimming  of  a  two  dimensional  flexible  plate  at  variable 
forward  speeds  in  an  inviscid  fluid”,  Journal  of  Fluid  Me¬ 
chanics,  46:337-355,  1971. 

15.  J.  Gray  “Studies  in  animal  locomotion  VI:  The  propulsive 
powers  of  the  dolphin”,  J.  Exp.  Biol,  13:192-199,  1936. 

16.  D.S.  Barrett  &  M.S.  Triantafyllou  “The  design  of  a  flexi¬ 
ble  hull  undersea  vehicle  propelled  by  an  oscillating  foil”, 
9th  International  Symposium  on  Unmanned  Untethered  Sub¬ 
mersible  Technology,  September  1995. 

17.  M.S.  Triantafyllou  &:  G.S.  Triantafyllou  “An  efficient  swim¬ 
ming  machine”,  Scientific  American ,  272(3):64-70,  1995. 

18.  J.R.  Adrian  “Particle  imaging  techniques  for  experimental 
fluid  mechanics”,  Ann.  Rev.  Fluid  Mech.  23:261-304,  1991. 

19.  C.E.  Willert  &  M.  Gharib  “Digital  particle  image  velocime- 
try”,  Exp.  Fluids  10:181-193,  1991. 

20.  H.L.  Fierstine  and  V.  Walters  “Studies  in  lo¬ 
comotion  and  anatomy  of  scombroid  fishes”, 
Mem.  Soc.  South.  Calif.  Acad.  Sci .,  6:1-31,  1968. 

21.  M.S.  Triantafyllou,  G.S.  Triantafyllou  &  R.  Gopalkrishnan 
“Wake  mechanics  for  thrust  generation  in  oscillating  foils”, 
Phys.  Fluids  A,  3:2835-2837,  1991. 

22.  G.S.  Triantafyllou,  M.S.  Triantafyllou  &  M.A.  Grosenbaugh 
“Optimal  thrust  development  in  oscillating  foils  with  appli¬ 
cation  to  fish  propulsion”,  J.  Fluids  Struct.,  7:205-224,  1993. 

23.  J.M.  Anderson  “Vortex  control  for  efficient  propulsion”,  PhD 
Thesis,  Joint  Program,  Massachusetts  Institute  of  Technol¬ 
ogy  &:  Woods  Hole  Oceanographic  Institution,  1996. 

24.  J.Y.  Cheng,  L.X.  Zhuang  &  B.G.  Tong  “Analysis  of  swim¬ 
ming  three-dimensional  waving  plates”,  Journal  of  Fluid  Me¬ 
chanics,  232:341-355,  1991. 

25.  R.  Krasny  “Desingularization  of  periodic  vortex  sheet  roll¬ 
up”,  Journal  of  Computational  Physics,  65:292-313,  1986b. 


469 


FLOW  SEPARATION  CONTROL  BY  MEANS  OF  FLAPPING  FOILS 


M.F.  Platzer 

Naval  Postgraduate  School,  Monterey,  CA,  USA 
J.C.S.  Lai 

Australian  Defence  Force  Academy,  Canberra’  Australia 
CM  Dohring 

German  Armed  Forces  University,  Munich,  Germany 

Abstract  -  A  sinusoidally  flapping  foil  adds  energy  to  the  flow  which  manifests  itself  in  the  form  of  a  jet  flow  downstream  of  the  flapping  foil. 
This  effect  is  greatly  enhanced  if  the  foil  is  flapping  close  to  a  solid  surface.  Therefore,  flapping  foils  can  be  used  for  boundary  layer  control 
if  positioned  close  to  a  surface  or  in  the  near  wake  of  a  body.  In  this  paper,  the  authors’  recent  flow  visualization  and  laser-doppler 
experiments  are  described.  They  comprise  the  flow  past  single  flapping  foils,  the  flow  past  a  foil  which  is  flapping  in  close  proximity  to  a  flat 
plate,  the  flow  over  a  backward-facing  step  with  a  flapping  foil  in  the  recirculatory  flow  region,  and  the  effect  of  a  flapping  foil  flow  on 
trailing  edge  flow  separation. 


I.  INTRODUCTION 

Our  interest  in  the  flow  physics  of  flapping  airfoils  derives 
from  several  fundamental  and  applied  aspects.  As  first  recognized  by 
Knoller  (1909)  and  Betz  (1912),  a  flapping  airfoil  generates  thrust. 
This  Knoller-Betz  effect  was  first  confirmed  experimentally  by 
Katzmayr  (1922).  The  first  theoretical  investigations  of  the 
aerodynamics  of  flapping  airfoils  were  based  on  flat-plate  airfoil 
theory,  notably  those  of  Bimbaum  (1924),  von  Karman  and  Burgers 
(1935)  and  Garrick  (1936),  who  showed  that  the  propulsive  efficiency 
of  flapping  airfoils  is  rather  poor  (not  exceeding  50  percent)  unless  the 
airfoil  is  flapping  rather  slowly.  Schmidt  (1965)  proposed  the  tandem 
airfoil  arrangement  and  demonstrated  experimentally  that  a  stationary 
airfoil  positioned  in  the  wake  of  a  flapping  airfoil  nearly  doubles  the 
propulsive  efficiency  of  the  single  flapping  airfoil  because  the 
stationary  airfoil  converts  the  vortical  energy  generated  by  the  flapping 
airfoil  into  additional  thrust.  This  experimental  finding  was  confirmed 
by  Bosch  (1978)  who  showed  by  means  of  an  oscillatory  flat-plate 
analysis  that  a  sinusoidally  flapping  airfoil  upstream  of  a  stationary 
airfoil  increases  the  propulsive  efficiency  of  such  an  arrangement  to 
almost  100  percent.  However,  little  information  was  available  in  the 
literature  about  the  precise  flow  characteristics  generated  by  flapping 
airfoils. 

Therefore,  we  first  endeavoured  to  identify  the  nature  of 
the  vortical  wakes  generated  by  flapping  airfoils.  We  then  attempted  to 
investigate  the  effect  of  a  flapping  airfoil  on  the  flat-plate  boundary 
layer  flow,  on  the  flow  over  a  backward-facing  step,  and  on  the  flow 
separation  downstream  of  an  airfoil  with  a  cusped  or  semi-circular 
trailing  edge. 

It  is  the  objective  of  this  paper  to  summarize  the  major 
results  obtained  in  these  experiments  and  to  draw  some  conclusions 
concerning  the  potential  of  flapping  foils  for  flow  control.  For  the 
analysis  of  the  experimental  results  we  used  both  potential  and  viscous 
flow  methods.  Therefore,  we  first  give  a  description  of  these  analysis 
tools  and  then  describe  the  experimental  approach. 

n.  COMPUTATIONAL  APPROACHES 
Unsteady  Panel  Code 

The  unsteady  panel  code  models  the  wake  by  releasing  a 
discrete  vortex  at  each  time  step  equal  in  magnitude  and  opposite  in 
direction  to  the  change  in  circulation  about  the  airfoil  from  the  previous 
time  step.  After  release  the  vortex  is  convected  downstream, 
influencing  and  being  influenced  by  the  airfoil  and  the  other  discrete 
wake  vortices.  In  order  to  enable  visualization  of  the  unsteady  wake 
formation  and  evolution  an  interactive  graphics  animation  interface 
was  developed  which  greatly  facilitates  the  understanding  of  the  vortex 
shedding  phenomena.  Further  details  are  given  by  Platzer  et  al  (1993), 
Jones  et  al  (1996),  Jones  &  Center  (1996),  Teng  and  Pang  (1988). 

Navier-Stokes  Code 

The  Navier-Stokes  code  is  based  on  the  strong 
conservation-law  form  of  the  compressible  two-dimensional,  thin-layer 
Navier-Stokes  equations  in  a  curvilinear  coordinate  system.  Additional 
details  are  described  by  Tuncer  &  Platzer  (1996). 


HI.  EXPERIMENTAL  APPROACH 
Water  Tunnel  Tests 

The  experiments  were  carried  out  in  the  Naval  Postgraduate 
School  water  tunnel  facility.  This  tunnel  is  a  closed  circuit,  continuous 
flow  facility  with  a  contraction  ratio  of  6:1.  The  test  section  is  38  cm 
wide,  51  cm  high,  and  150  cm  long.  The  flow  velocity  can  be  set  in  a 
range  from  O  to  0.5  m/s.  The  flapping  excitation  of  the  airfoil  was 
induced  by  a  vertical  shaker  which  was  mounted  on  the  top  of  the  test 
section.  The  frequency  could  be  adjusted  continuously  from  5  Hz  to  30 
Hz.  The  amplitude  could  be  varied  from  zero  to  a  maximum  value 
which  depended  on  the  chosen  frequency.  The  LDV  measurements 
were  performed  with  a  dual  beam  frequency  shifted  300  mW  Argon 
Ion  laser  with  a  beam  separation  of  50  mm,  a  focal  length  of  350  mm 
and  back  scatter  receiving  optics. 

IV.  RESULTS 

Wakes  Shed  from  Single  Flapping  Airfoils 

Qualitative  and  quantitative  comparisons  of  the  wake 
structures  shed  from  a  flapping  (plunging)  NACA  0012  airfoil  of  10  cm 
chord  length  are  shown  in  Figure  1 .  The  reduced  flapping  frequency  is 
defined  as 

k  =  2nfc/U 

where  f  is  the  frequency  of  oscillation,  c  is  the  airfoil  chord,  and  U  is 
the  flow  velocity.  If  this  reduced  frequency  is  multiplied  with  the  non- 
dimensional  flapping  amplitude  h/c  a  non-dimensional  maximum  plunge 
velocity  can  be  defined  as  vp  =  k(h/c). 

Figure  1  shows  the  vortical  wake  produced  by  an  airfoil 
which  is  flapping  sinusoidally  with  a  non-dimensional  amplitude  of  h/c 
=  0.2  at  a  reduced  frequency  of  3.0.  The  flow  velocity  is  10.5  cm/s 
yielding  a  Reynolds  number  of  1040.  It  is  seen  that  the  wake  is 
symmetric  about  the  center  line,  and  the  wake  vortices  are  evenly 
spaced.  Note  that  the  upper  vortices  are  counter-clockwise  and  the 
lower  ones  are  clockwise.  Such  a  vortex  pattern  is  indicative  of  a  thrust 
producing  pattern.  This  symmetric  wake  behavior  is  also  observed  for 
lower  frequencies'  the  only  difference  being  the  vortical  wave  length. 
However,  as  the  non-dimensional  plunge  velocity  is  reduced  below 
values  of  0.2,  the  measured  time-averaged  wake  velocity  profiles  show 
the  velocity  defects  indicative  of  drag.  At  non-dimensional  plunge 
velocities  of  approximately  0.2  the  vortices  are  aligned  along  a  straight 
line  as  shown  in  Figure  2.  At  values  in  excess  of  0.2  one  observes 
counterclockwise  upper  vortices  and  clockwise  lower  vortices  and  the 
wave  length  becomes  shorter.  However,  there  is  an  upper  non- 
dimensional  plunge  velocity  limit  beyond  which  the  vortical  wake 
pattern  changes  from  a  symmetric  pattern  to  an  asymmetric  one 
because  the  large  eddies  begin  to  pair  up  and  travel  away  from  the 
centerline.  Tests  with  three  different  airfoil  chords  showed  that  this 
pairing  and  switching  to  an  asymmetric  wake  occurs  at  a  non- 
dimensional  plunge  velocity  greater  than  approximately  0.75. 
Additional  details  on  the  jet  characteristics  of  plunging  airfoils  have 
recently  been  given  by  Lai  and  Platzer  (1998a). 

Before  discussing  the  asymmetric  wake  behavior  it  is 
instructive  to  examine  the  symmetric  case.  In  Figure  3  the  results  of 
computations  of  the  time-averaged  velocity  profiles  upstream  and 
downstream  of  a  flapping  airfoil  are  shown  using  the  unsteady  panel 
code.  The  non-dimensional  flapping  amplitude  is  0.1.  The  profiles  are 


471 


depicted  at  three  different  locations,  0.5  chord  lengths  upstream  and 
1.5  and  3  chord  lengths  downstream  of  the  airfoil  leading  edge.  The 
reduced  frequency  is  10.  It  can  be  seen  that  the  airfoil  produces  a  jet 
profile  downstream  of  the  trailing  edge  and  that  the  maximum  jet 
velocity  exceeds  the  free-stream  value  by  a  factor  of  2.4.  The  flapping 
airfoil  therefore  imparts  a  momentum  increase  to  the  fluid  which 
manifests  itself  as  airfoil  thrust.  It  is  also  interesting  to  observe  the 
amount  of  flow  which  is  captured  by  the  flapping  foil,  as  manifested 
by  the  velocity  distribution  upstream  of  the  leading  edge.  It  is  seen  that 
the  capturing  area  extends  to  roughly  three  chord  lengths  above  and 
below  the  airfoil.  In  Figure  4  a  comparison  is  given  between  the 
computed  and  measured  time-averaged  velocity  profile  at  0.75c 
downstream  of  an  airfoil,  flapping  at  a  reduced  frequency  of  S.4  with  a 
non-dimensional  flapping  amplitude  of  0.088.  It  is  seen  that  there  is 
good  agreement  between  the  measurement  and  the  computation. 

If  the  product  of  reduced  frequency  and  non-dimensional 
flapping  amplitude  is  increased  beyond  a  critical  value,  such  that  the 
non-dimensional  maximum  plunge  velocity  becomes  approximately 
0.75,  the  vortical  wake  pattern  becomes  asymmetric,  as  shown  in 
Figure  5.  The  vortical  wake  is  deflected  either  upward  or  downward 
and  therefore  generates  not  only  thrust  but  also  a  finite  average  lift. 
This  experimentally  observed  asymmetric  vortex  pattern  is  also  found 
in  the  numerical  computations  using  the  unsteady  pane]  code.  The 
inclination  of  the  vortex  pattern  (up  or  down)  is  determined  by  the 
starting  conditions  used  in  the  panel  code.  The  qualitative  agreement 
between  the  numerical  and  experimental  wake  structures  is  excellent. 
Even  the  small  remnants  of  vorticity,  visible  at  the  bottom  of  Figure  5, 
that  break  off  from  the  vortex  pairs  at  higher  frequencies  are 
consistent  in  both  approaches. 

Wall  Effect 

Dohring  et  al  (1996)  and  Dohring  (1998)  showed  that 
another  interesting  effect  occurs  if  the  airfoil  executes  a  pure  flapping 
oscillation  in  close  proximity  to  a  flat  plate.  Figure  6  presents  a 
comparison  of  the  measured  time-averaged  velocity  distribution  0.75 
chord  length  downstream  of  the  trailing  edge  of  a  20  mm  chord  airfoil 
which  executes  a  flapping  oscillation  with  a  nondimensional  flapping 
amplitude  of  0.088  at  a  reduced  frequency  of  57  (based  on  free-stream 
velocity).  It  is  seen  that  there  is  a  significant  velocity  increase  as  the 
airfoil  is  positioned  closer  to  the  wall  (4  mm  rather  than  8.5  mm).  Also 
shown,  for  comparison,  is  the  velocity  distribution  without  the  flat  plate. 
The  leading  edge  of  the  airfoil  was  located  100  mm  downstream  of  the 
leading  edge  of  the  flat  plate.  Therefore  the  airfoil  was  embedded  in 
the  laminar  boundary  layer  of  the  flat  plate. 

This  flow  behavior  could  be  confirmed  with  Navier-Stokes 
calculations.  Dohring  et  al  (1996)  and  Dohring  (1998)  provided 
detailed  flowfield  calculations  and  showed  that  the  thrust  increases  as 
the  non-dimensional  airfoil  distance  from  the  wall  is  decreased  to 
values  less  than  1.5. 

This  wall  effect  can  also  be  simulated  to  some  extent  by  the 
inviscid  unsteady  panel  code.  It  is  well  known  that  the  aerodynamic 
characteristics  of  an  airfoil  flying  close  to  the  ground  can  be  calculated 
by  placing  an  image  airfoil  and  computing  the  inviscid  flow  over  the 
two-airfoil  combination.  Similarly,  the  ground  effect  on  a  flapping 
airfoil  can  be  computed  with  the  two-airfoil  code  described  by  Pang 
(1988)  if  the  two  airfoils  are  flapping  in  counter-phase.  The  application 
of  this  code  again  showed  that  there  is  a  significant  thrust  increase 
generated  by  each  airfoil  if  they  are  flapping  in  close  proximity  to  each 
other.  Furthermore,  the  thrust  increases  nonlinearly  with  reduced 
frequency.  These  results  are  quite  consistent  with  the  measurements 
and  the  Navier-Stokes  calculations. 


Flow  Separation  Control 

Another  series  of  experiments  was  performed  to  investigate 
the  effectiveness  of  flapping  airfoils  to  suppress  the  flow  separation 
caused  by  the  flow  over  a  stationary  airfoil  with  either  a  cusped  or 
rounded  trailing  edge  as  shown  in  Figure  7.  The  stationary  airfoil  had  a 
chord  length  of  28  cm  and  a  maximum  thickness  of  4.5  cm.  The 
flapping  airfoils  had  chord  lengths  of  either  2  cm  or  10  cm.  The  gap 
between  the  trailing  edge  of  the  stationary  airfoil  and  the  leading  edge 
of  the  flapping  airfoil  was  varied  between  0.5  to  2  cm.  Dye  injection 
was  used  to  observe  the  wake  flow  characteristics.  The  flapping 


amplitude  and  frequency  were  increased  until  complete  flow 
reattachment  was  achieved.  It  was  found  that  the  important  controlling 
parameter  is  the  non-dimensional  plunge  velocity.  This  is  seen  in  Figure 
8  where  for  the  stationary  airfoil  with  cusped  trailing  edge  and  a  gap  of 
2  cm  between  the  stationary  and  the  flapping  airfoil  of  10  cm  chord 
reattachment  occurred  as  soon  as  the  plunge  velocity  exceeded  a  value 
of  4.35.  Other  more  detailed  results  are  documented  by  Dohring 
(1998).  Figure  9  shows  the  effectiveness  of  the  2  cm  flapping  airfoil, 
oscillating  with  a  reduced  frequency  of  k  =  100  and  a  non-dimensional 
amplitude  of  h/c  =  0.038  to  suppress  the  flow  separation  behind  the 
rounded  trailing-edge  airfoil. 

Control  of  Backward  Facing  Step  Flow 

Figure  10  depicts  the  experimental  set-up  which  was  used 
for  the  experiment  to  demonstrate  the  effectiveness  of  a  flapping 
airfoil  to  control  the  extent  of  the  recirculatory  flow  region  caused  by 
the  flow  over  a  backward-facing  step.  The  step  height  was  3  cm  and 
the  step  width  38  cm.  The  plate  upstream  of  the  step  was  91  cm.  The 
free  water  surface  was  42  cm  above  the  upper  plate.  The  free-stream 
velocity  was  0.32  m/s,  giving  a  Reynolds  number  (based  on  step  height) 
of  12,700.  The  flapping  airfoil  was  a  NACA  0012  foil  with  a  chord 
length  of  1  cm.  Laser-doppler  measurements  were  carried  out  to 
measure  the  mean  streamwise  velocity  and  streamwise  turbulence 
intensity  distributions  which  are  documented  by  Lai  et  al  (1997).  Figure 
11a  shows  the  streamlines  for  backward-facing  step  flow  without 
flapping  foil  control.  Reattachment  occurs  between  5  and  6  non- 
dimensional  step  heights,  a  value  in  agreement  with  other  experiments. 
Figure  lib  shows  the  effect  of  the  flapping  airfoil  on  the  size  of  the 
recirculation  flow  region.  The  airfoil  was  located  at  1.83  non- 
dimensioanl  step  heights  downstream  from  the  comer  and  0.2  step 
heights  above  the  downstream  plate.  It  is  seen  that  the  recirculation 
region  is  reduced  to  about  one  third  its  original  size. 

Additional  Results 

For  additional  detailed  results  about  the  jet  characteristics 
generated  by  airfoils  which  are  flapping  in  a  free-stream  or  in  still  air 
we  refer  to  the  papers  by  Lai  and  Platzer  (1998a,  1998b).  Furthermore, 
the  performance  limits  of  flapping  airfoils  were  determined  with  a 
Navier-Stokes  code.  The  objective  of  this  study  was  to  identify  the 
dynamic  stall  boundary  of  flapping  airfoils.  It  was  found  that  the  main 
controlling  parameter  is  again  the  nondimensional  plunge  velocity.  For 
details  we  refer  to  Tuncer  et  al  (1998). 

V.  SUMMARY  &  OUTLOOK 

Bimbaum  was  the  first  one  to  refer  to  the  sinusoidally 
flapping  (plunging)  airfoil  as  a  flapping-foil  propeller  and  to  point  out 
that  it  can  be  regarded  as  the  two-dimensional  equivalent  of  the 
conventional  propeller.  In  our  recent  experimental  and  computational 
investigations  we  have  endeavoured  to  provide  specific  information 
about  the  performance  characteristics  of  flapping-foil  propellers.  It 
was  found  that  the  main  control  ling  parameter  is  the  non-dimensional 
plunge  velocity.  The  flapping  foil  starts  to  produce  thrust  as  soon  as  the 
plunge  velocity  exceeds  values  of  approximately  0.2.  It  could  also  be 
shown  that  there  exists  a  favorable  wall  or  ground  effect  which  can  be 
used  for  purposes  of  boundaiy  layer  propulsion.  Also,  it  could  be 
shown  that  flow  separation  could  be  suppressed  completely  or,  as  in  the 
case  of  flow  over  a  backward-facing  step,  the  recirculatory  flow 
region  could  be  reduced  significantly.  Because  of  the  necessity  to 
exceed  a  critical  value  of  non-dimensional  plunge  velocity,  the 
effectiveness  of  the  flapping-foil  propeller  is  limited  to  relatively  small 
free-stream  velocities  unless  high  flapping  frequencies  and/or  large 
chord  lengths  are  used.  Further  studies  are  needed  to  explore  the 
potential  of  flapping-foil  propellers  for  drag  reduction  by  means  of 
flow  separation  control. 

VI.  ACKNOWLEDGMENT 

The  authors  gratefully  acknowledge  the  support  of  the 
Office  of  Naval  Research  (Dr.  Peter  Majumdar  and  Dr.  Edwin  Rood), 
of  the  Naval  Research  Laboratory  (Mr.  Kevin  Ailinger),  and  of  the 
Naval  Postgraduate  School  Internal  Research  Program. 

VII.  REFERENCES 

Betz,  A.,  MEin  Beitrag  zur  Erklaerung  des  Segelfluges",  Z.  f. 
Flugtechnik  und Motorluftschiffahrt,  Vol.  3,  1912,  pp.  269-272,  1912 


472 


Bimbaum,  W.,  "Der  Schlagfluegelpropeller  und  die  kleinen 
Schwingungen  elastisch  befestigter  Tragfluegel",  Zeitschrift  fuer 
Fiugtechnik  und  Motorlufitschiffahrt,  Vol.  15,  pp.  128-134,  1925 

Bosch,  H.,  "Interfering  Airfoils  in  Two-Dimensional  Unsteady 
Incompressible  Flow,"  AGARD  CP-227, 1978 

Dohring,  CM,  Platzer,  M.F.,  Jones,  K.D.,  Tuncer,  I.H.,  Computational 
and  Experimental  Investigation  of  the  Wakes  Shed  from  Flapping 
Airfoils  and  their  Wake  Interference/Impingement  Characteristics", 
AG ARD-CP-5 84,  Paper  No.  33,  November  1996 

Dohring,  C.M.,  "Der  Schub  des  schlagenden  Fluegels  und  seine 
Anwendung  zur  GrenzechichUbeeinflussung-eine  experimentelle  und 
numerische  Untersuchung",  Doctoral  Dissertation,  German  Armed 
Forces  University,  Munich,  Germany,  May  1998 

Garrick,  I.E.,  "Propulsion  of  a  Flapping  and  Oscillating  Airfoil,"  NACA 
Report  567,  1936 

Jones,  K.D.  and  Center,  K.B.  1996,  "Numerical  Wake  Visualization  for 
Airfoils  Undergoing  Forced  and  Aeroelastic  Motions,"  AIAA  Paper 
96-0055,  January  1996 

Jones,  K.D.,  CM.  Dohring,  Platzer,  M.F.,  "Wake  Structures  behind 
Plunging  Airfoils:  A  Comparison  of  Numerical  and  Experimental 
Results,"  AIAA  Paper  96-0078,  January  1996 

Katzmayr,  R.,  "Effect  of  Periodic  Changes  of  Angle  of  Attack  on 
Behaviour  of  Airfoils,"  NACA  TM  147, 1922 

Knoller,  R.,  "Die  Gesetze  des  Luftwiderstandes,"  Flug-  und 
Motortechnik  (Wien),  Vol.  3,  No.  21,  pp.  1-7, 1909 

Lai,  J.C.S.,  Yue,  J.W.,  Platzer,  M.F.,  "Control  of  Backward  Facing  Step 
Flow  Using  a  Flapping  Airfoil",  ASME  Fluids  Engineering  Division 
Summer  Meeting,  FEDSM97-3307,  Vancouver,  Canada,  22-26  June 
1997 

Lai,  J.C.S.  and  Platzer,  M.F.,  (199Sa)  "The  Jet  Characteristics  of  a 
Plunging  Airfoil",  AIAA  Paper  98-0101,  January  12-15, 1998 

Lai,  J.C.S.  and  Platzer,  M.F.,  (199Bb)  "The  Jet  Characteristics  of  a 
Plunging  Airfoil  in  Still  Air,  ASME  Fluids  Engineering  Division 
Summer  Meeting,  Washington,  D.C.,  20-25  June  1998 

Pang,  C.K.,  "A  Computer  Code  for  Unsteady  Incompressible  Flow  past 
Two  Airfoils,"  Aeronautical  Engineer's  Thesis,  Naval  Postgraduate 
School,  Monterey,  CA,  September  1988 

Platzer,  M.F.,  Neace,  K.S.,  Pang,  C.K.,  "Aerodynamic  Analysis  of 
Flapping  Wing  Propulsion,"  AIAA  Paper  93-0484,  1993 

Schmidt,  W.,  "Der  Wellpropeller,  ein  neuer  Antrieb  fur  Wasser-, 
Land-,  und  Luftfahrzeuge,"  Zeitschrift  fur  Flugwissen-schaften,  Vol. 
13,  pp.  472-479, 1965 

Teng,  N.H.,  "The  Development  of  a  Computer  Code  for  the  Numerical 
Solution  of  Unsteady,  Inviscid,  and  Incompressible  Flow  over  an 
Airfoil,"  Master’s  Thesis,  Naval  Postgraduate  School,  Monterey,  CA, 
June  1987 

Tuncer,  I.H.  and  Platzer,  M.F.,  "Thrust  Generation  due  to  Airfoil 
Flapping,"  AIAA  Journal,  Vol.  34,  No.  2,  pp.  324-331, 1996 

Tuncer,  I.H.,  Ekaterinaris,  J.A.,  Platzer,  M.F.,  "A  Novel  Viscous 
Inviscid  Interaction  Method  for  Unsteady  Low-Speed  Airfoil  Flows, 
AIAA  Journal,  Vol.  33,  No.  l,pp.  151-154,  January  1995 

Tuncer,  I.H.,  Walz,  R.,  Platzer,  M.F.,  "A  Computational  Study  on  the 
Dynamic  Stall  of  a  Flapping  Airfoil",  AIAA  Paper  98-2519,  June  1998 

von  Karman,  T.  and  Burgers,  J.M.,  "Aerodynamic  Theory,  "  Vol.  2, 
Springer  Berlin,  pp.  280-310, 1935 


473 


Fig.  1  Wake  Comparison 

The  upper  figure  shows  the  panel  code  computed  wake 
The  lower  figure  shows  the  wake  flow  visualization 


Fig.  5  Asymmetric  Wake  Comparison 
(upper  figure:  panel  code,  lower  figure:  visualization) 


475 


Fig . 


Visualization  of  Flow  Control 


477 


Fig.  10  Experimental  Set-up 


x/h 

(a)  stationary  airfoil  (b)  airfoil  flapping  at  20  Hz  with  amplitude  0.123c 


Fig.  11  Flow  over  Backward-Facing  Step 
(without  and  with  flapping  foil  control) 


THE  VORTICITY  CONTROL  UNMANNED  UNDERSEA  VEHICLE— 
A  BIOLOGICALLY  INSPIRED  AUTONOMOUS  VEHICLE 


Jamie  M.  Anderson 
Charles  Stark  Draper  Laboratory 
555  Technology  Square,  MS  23 
Cambridge,  MA  02139 
jamie@draper.com 


Abstract  -  Recent  interest  in  improving  the  operating  performance  of  unmanned  undersea  vehicles  (UUVs)  has  led  to  the  notion  of  mimicking 
the  form  and  function  of  fish  and  marine  mammals.  Often,  capabilities  of  the  biological  systems  far  exceed  those  of  modem  engineered 
vehicles  with  conventional  power  supplies  and  propulsors.  Of  particular  interest  are  the  possible  energetic  benefits  and  the  improved 
maneuvering  characteristics  of  fish-like  propulsion.  In  this  paper  we  describe  the  first  autonomous  mission-scale  fish-like  vehicle  in 
development  at  Draper  Laboratory,  the  Vorticity  Control  UUV  (VCUUV).  Named  after  the  flow  control  mechanisms  inherent  in  fish 
swimming,  the  VCUUV  mimics  the  form  and  movement  of  a  large  yellowfin  tuna.  Designed  and  built  as  a  proof  of  concept  test  platform,  the 
VCUUV  will  provide  unambiguous  measurements  of  the  power  required  to  swim  and  maneuver  like  a  tuna.  Drag  reduction  will  be 
investigated  by  comparing  the  power  consumed  during  swimming  and  that  required  for  straight  coasting  at  the  same  speed. 


I.  INTRODUCTION 

Fish  swimming  propulsion  has  recently  gained  wide  attention  in  the 
underwater  vehicle  community  as  a  viable  alternative  to  traditional 
marine  propulsors.  Fish  possess  many,  abilities  which  are  desirable  for 
unmanned  undersea  vehicles  (UUVs):  they  are  able  to  cruise  great 
distances,  maneuver  well  in  cluttered  environments  and  accelerate  and 
decelerate  quickly.  Although  the  form  and  movement  of  fish  and 
cetaceans  vary  widely  across  species,  the  fundamental  swimming 
movements  of  many  “swimmers”  such  as  tunas,  sharks,  dolphins,  etc.,  are 
notably  similar  [1]  which  suggests  that  nature  has  evolved  optimal 
propulsive  interaction  with  water. 

Many  use  the  phrase  “swim  like  a  fish”  to  describe  superior 
interaction  with  the  aquatic  environment,  that  is,  high  propulsion  and 
maneuvering  proficiency.  The  secret  to  fish  swimming  performance 
appears  to  lie  in  the  use  of  unsteady  flow  mechanisms  (such  as  a  highly 
vortical  wake)  to  achieve  both  steady  swimming  and  unsteady 
maneuvers.  Propulsion  and  steering  are  integrated  into  one  system  which 
performs  well  over  a  wide  range  of  speed. 

The  utility  of  bio-propulsion  and  maneuvering  is  apparent  when  one 
considers  the  current  UUV  missions  of  interest  as  illustrated  in  Figure  1. 
Today’s  missions  are  challenging  in  that  they  often  require  long  transit, 
long  duration  on  site,  loitering  without  loss  of  power,  movement  in  close 
proximity  to  objects  for  docking,  tagging,  etc.,  and  operation  in  dynamic 
environments  such  as  shallow  waters  near  the  beach  zone.  Vorticity 
control  propulsion  and  maneuvering  may  prove  to  be  essential  in 
realizing  these  missions  in  that  fish-like  maneuverability  may  not  be  as 
energetically  taxing  as  conventional  means  of  generating  large  side 
forces  (such  as  thrusters)  in  varying  conditions.  For  example,  fish  can 
loiter  at  zero  speed  and  rapidly  accelerate  in  nearly  any  direction.  Blake 
et  al  [2]  report  turning  radii  of  tunas  of  less  than  half  a  body  length, 
which  outperforms  conventional  vehicle  systems  by  an  order  of 
magnitude. 

A  common  misconception  of  the  bio-propulsion  concept  is  that 
possible  improved  efficiency  and  maneuvering  capability  is  not 
worthwhile  when  compared  to  the  required  displacement  for  the 
propulsion  system.  However,  experience  has  shown  that  attempts  to 
achieve  both  long  range  and  highly  maneuverable  rigid  body  UUV’s 
have  met  with  disappointment,  largely  due  to  the  need  for  both  propulsion 
and  maneuvering  systems  that  rarely  operate  together  effectively.  Cross¬ 
axis  thrusters,  for  instance,  are  both  heavy  and  detract  from  useful 
vehicle  displacement,  and  can  only  be  used  at  zero  speed  without 
concern  of  control  nonlinearities  (that  can  even  include  control  reversal). 
For  high  speed  maneuvers,  for  which  thrusters  are  useless,  a  rigid  body 
UUV  must  also  have  a  conventional  propulsor  and  control  surfaces 
which  cannot  produce  turning  diameters  less  than  several  vehicle  lengths. 

By  comparison,  bio-propulsion  can  provide  both  efficient  propulsion 
and  maneuvering  at  any  speed  with  modest  investment  in  vehicle 


displacement.  For  example,  the  Vorticity  Control  UUV  (VCUUV) 
propulsion  system  occupies  only  23%  of  the  total  displacement  (32%  of 
the  envelope  displacement  due  to  some  free-flood  volume).  Thurmiform 
(tuna)  morphology  and  kinematics  allow  this  modest  propulsion  system 
displacement  with  excellent  steady  swimming  and  maneuvering 
performance. 

The  Thurmiform  model  possesses  several  advantages  for  use  on  an 
underwater  vehicle  system.  As  with  other  carangiform  fishes,  the 
propulsion  and  maneuvering  movements  are  localized  to  the  last  30-40% 
of  die  body  length  and  are  moderate  in  amplitude.  Tuna  caudal  fin  peak- 
to-peak  excursions  rarely  exceed  15  to  20%  of  the  body  length  [3].  The 
localized  tail  motion  allows  the  forward  body  be  used  as  a  rigid  housing 
for  energy,  intelligence,  payload,  etc.,  without  the  complexity  of  flexible 
pressure  hulls  or  the  power  required  to  move  them.  The  tuna’s  fusiform 
forward  body  has  nearly  elliptical  sections  within  which  internal 
arrangements  are  more  easily  made  than  with  cylindrical  sections.  The 
body  is  low  drag  but  contains  significant  packaging  space. 

For  the  underwater  surveillance  mission,  biologically  inspired 
vehicles  may  be  able  to  inspect  an  object  of  interest  more  closely,  rapidly 
avoid  if  necessary  and  precisely  place  objects  if  desired,  without  loss  of 
efficient  survey  speed  and  range.  Vorticity  control  propulsion  and 
maneuvering  provides  the  range  and  speed  of  conventional  low  drag 
hulls  driven  by  propellers,  with  the  added  capability  of  ship-deployed 
remotely  operated  vehicles  which  can  precisely  maneuver  in  a  location 
of  interest. 

II.  BACKGROUND 

In  recent  years,  researchers  at  the  Massachusetts  Institute  of 
Technology  have  investigated  rigid  flapping  foils  (combined  translation 
with  simultaneous  heave  and  pitch)  as  a  means  of  generating  large 
propulsion  forces  at  very  high  efficiencies.  Anderson  et  al.  [4]  have 
demonstrated  propulsive  efficiencies  in  excess  of  85%  with  proper 
selection  of  the  Strouhal  number,  angle  of  attack,  heave  amplitude  ratio 
and  the  phasing  of  the  combined  motions.  Flow  visualization  studies  with 
live  fish  have  shown  that  the  propulsion  and  maneuvering  performance 
of  fishes  is  related  to  their  ability  to  control  their  wake  vorticity.  Contrary 
to  drag  producing  bodies,  fish  generate  an  oscillatory  wake  consisting  of 
alternating  vortices  arranged  in  a  jet  pattern.  Manipulation  of  wake 
vorticity  appears  to  be  a  dominant  factor  affecting  the  propulsive 
performance  of  fish  [5]. 

The  MIT  research  has  culminated  in  the  development  of  Robotuna , 
a  1.2  m  biologically  inspired  tow  tank  model  built  to  study  propulsive 
efficiency  and  how  it  relates  to  body  movement  [6].  Robotuna  was 
exercised  in  the  MIT  Ocean  Engineering  Testing  Tank  by  prescribing  a 
set  of  kinematic  parameters  (angular  deflections  of  each  joint,  tow  speed, 
phase  relationships)  and  measuring  the  net  power  transmitted  to  the 
linkages  and  the  reaction  force  between  the  tuna  and  carriage.  Optimal 


479 


motion  was  defined  as  that  set  of  motion  parameters  that  produced  no  net 
force  on  the  carriage  (self  propelled  status)  with  minimum  input  energy. 

The  Robotuna  project  has  demonstrated  that  significant  “apparent” 
drag  reduction  can  be  achieved  even  without  careful  tuning  of  the  drive 
mechanism.  The  observed  drag  reduction  is  referred  to  as  “apparent” 
because  in  a  towed  experiment,  it  is  not  possible  to  discriminate  between 
thrust  and  drag  in  a  single  measurement.  The  input  power  of  the 
swimming  Robotuna  was  compared  to  the  “dead  fish”  (straightened  body 
and  towed)  power.  An  estimated  thrust  power  ratio  (mean  drag  power  of 
“dead  fish”  over  the  mean  input  power  of  the  swimming  fish)  of  1.27  and 
an  apparent  drag  reduction  of  49%  were  achieved  [6].  This 
demonstrates  that  vorticity  control  for  the  most  part,  is  a  macro  effect  that 
can  be  readily  applied  to  an  engineered  vehicle  without  fine  tuning  the 
body  shape,  skin  surface  smoothness  and  compliance  and  fin  shape. 

III.  VCUUV  SYSTEM  DESCRIPTION 

At  the  Charles  Stark  Draper  Laboratory,  the  next  generation  of 
flexible  hull  robots  is  in  development.  The  Vorticity  Control  Unmanned 
Undersea  Vehicle  (VCUUV)  is  a  freely  swimming,  tuna-shaped  vehicle 
built  to  demonstrate  tuna-like  swimming  and  maneuvering.  Constructed 
as  a  proof-of-concept  demonstration  of  vorticity  control  propulsion,  the 
VCUUV  serves  as  a  mission-scale  exercise  in  design  and  packaging  as 
well  as  a  research  platform  with  which  we  can  quantify  the  energetics  of 
swimming. 

Although  the  first  VCUUV  prototype  is  not  intended  as  an  ocean 
going  vehicle,  the  vehicle  does  contain  all  of  the  necessary  components 
of  autonomy:  onboard  energy,  actuation  and  control.  The  vehicle  will  be 
operated  in  shallow,  controlled  environments  where  the  propulsion 
system  performance  can  be  quantified.  Critical  vehicle  issues  addressed 
in  the  VCUUV  project  including  sizing  of  actuators,  design  of  articulated 
body,  pressure  hull  design,  and  On-board  intelligence,  sensors  and  power 
are  described  in  detail  by  Anderson  and  Kerrebrock  [7,  8]. 

The  VCUUV  will  operate  in  swimming  pool  depths  (<  10  m),  at 
speeds  up  to  one  body  length  per  second  (3.9  knots)  which  approaches 
the  typical  cruising  speed  of  yellowfin  tunas  (1-2  body  lengths  per 


second)  [9].  Preliminary  tests  will  be  done  at  the  lower  speed  of  2.6 
knots  for  direct  comparisons  with  the  MIT  Robotuna  studies. 


System  Characteristics 

The  need  to  demonstrate  a  fieldable  vehicle  which  can  serve  as  a 
research  tool  has  driven  both  the  mechanical  and  electrical  system 
designs.  The  following  requirements  were  imposed  on  the  prototype 
vehicle  design: 

Mechanical  systems 

•  Independent  control  of  profile  (phase  and  amplitude  of  each  link)  at 
variable  frequencies  and  vehicle  speeds 

•  Near  neutral  buoyancy  in  articulated  tail 

•  Minimum  speed  of  2.5  knots 

•  2  body  length  turning  diameter 

•  Minimum  mission  duration  of  3  hours 

•  Swimming  pool  missions  in  depths  less  than  10  m 

SSMML 

•  Measurement  of  vehicle  location  and  orientation  as  a  function  of  input 
kinematics 

•  Measurement  of  propulsive  power  (i.e.,  tail  linkage  velocity  and 
force) 

•  Measurement  of  tail  linkage  position 

QqMlqL 

•  Closed  loop  control  of  tail  linkage  position 

•  Stable  depth  and  heading 

The  key  parameters  in  Thunniform  steady  swimming  are  the  vehicle 
speed,  oscillation  frequency  and  amplitude,  propulsive  wavelength,  shape 
parameters  which  describe  the  envelope  of  transverse  motion,  tail 
phasing  and  angle  of  attack  [6]. 


480 


Figure  2:  Draper  Laboratory  Vorticity  Control  UUV 


For  steady  straight  swimming,  a  traveling  propulsive  wave  is 
required  which  moves  from  head  to  tail  with  increasing  amplitude  near 
the  tail.  The  kinematics  are  described  in  detail  by  Barrett  [6],  Dewar  and 
Graham  [3]  and  Anderson  and  Kerrebrock  [7,  8].  Turning  kinematics 
are  less  understood  and  consequently,  the  VCUUV  design  has  most  of  its 
design  margin  in  the  turning  requirements  (amplitudes  and  loading 
conditions). 

Table  1  summarizes  the  VCUUV  prototype  characteristics.  The 
vehicle  is  8  feet  (2.4  m)  long  and  displaces  approximately  300  lb  (1334 
N).  The  forward  half  of  the  vehicle  is  comprised  of  rigid  pressure  hull 
while  the  aft  portion  is  articulated  and  freely  flooded.  The  pressure  hull 
houses  all  of  the  dry  components  including  batteries,  electronics 
(computer,  sensors,  etc.),  hydraulic  power  plant  and  payload  (Figures  2 
and  3). 

The  articulated  tail  structure  consists  of  a  planar,  four  degree  of 
freedom  robot  arm  that  acts  upon  a  tuna-shaped  flexible  exostructure. 
The  entire  tail  area  is  freely  flooded  with  an  impermeable  skin  which 
prevents  exchange  of  water  across  the  envelope  boundary.  Three  equal 
length  links  and  the  caudal  fin  are  independently  actuated  with  hydraulic 
cylinders  integrated  into  the  links  themselves. 

The  tail  exostructure  converts  the  discrete  movements  of  the 
underlying  robot  linkage  to  the  smooth,  fluid  movements  of  a  fish  tail. 
The  key  elements  of  the  exostructure  are  rigid  buoyant  foam  “ribs” 
which  are  shaped  like  hollowed  out  tuna  “steaks”  and  are  connected  to 
one  another  by  flexible  splines.  The  splines  produce  smooth  curvature 
along  the  tail  envelope  which  simulates  a  linkage  of  much  higher 
resolution  (as  though  there  are  a  greater  number  of  links).  At  three 
locations  along  the  tail,  a  follower  rod  mechanism  transmits  the 
hydrodynamic  loads  on  the  exostructure  to  the  actuation  linkage. 

The  structure-fluid  interface  is  a  dermal  layer  of  overlapping  scales 
which  prevent  transverse  folds  between  the  ribs  similar  to  their  function 
in  real  fish.  The  outermost  layer  consists  of  neoprene  rubber  that  is 
bonded  to  lycra  on  both  sides.  This  “skin”  prevents  water  movement 


Table  1:  VCUUV  System  Summary 


Component  _  Description 


Pressure  hull 

Carbon  graphite/epoxy  with  aluminum 
mating  surface 

Computer  and 
actuator  control 

PC  104  486,  DSP,  hard  drive 

Sensors 

3  accelerometers,  3  rate  gyros,  compass, 
pressure  (depth),  cylinder  displacement  and 
force,  leak  detectors,  internal  temperature 

Actuators 

Recirculating  hydraulic  system  for  tail 
linkage,  motors  for  pectoral  fins 

Energy 

Sealed  lead  acid  batteries, 

60  VDC,  800  W-hr 

Communications 

Ethernet  through  umbilical  when  attached 
status  indicator  lights 

across  the  boundary  while  maintaining  an  extremely  smooth  flexible 
surface  which  is  nearly  impermeable  to  water. 

The  largest  and  most  heavily  loaded  fin  on  the  vehicle  is  the  rigid 
caudal  fin  which  is  the  primary  propulsive  actuator.  The  fin  shape  was 
determined  by  averaging  direct  measurement  of  our  cast  yellowfin  tuna 
and  measurements  made  from  photographs  of  freshly  caught  fish.  The 
cross  section  was  determined  by  sectioning  the  cast  caudal  fin  in  multiple 
locations.. 

As  in  actual  tunas,  dive  plane  control  (and  buoyancy  adjustment) 
will  be  provided  by  means  of  two  pectoral  fins  located  near  the  midbody. 
Real  tunas  (which  are  negatively  buoyant)  use  the  pectoral  fins  for  speed 
dependent  buoyancy  adjustment.  At  low  speeds,  the  fins  are  fully 
splayed  for  maximum  lift;  as  the  speed  increases,  the  fin  sweepback 
angle  is  increased  until  the  fins  are  fully  adducted,  effectively  reducing 
the  lifting  area  [3], 

The  VCUUV  pectoral  fins  are  positioned  in  the  same  place  as  real 
tuna  pectoral  fins,  slightly  forward  of  the  center  of  gravity.  Thus,  the 
pectoral  fins  act  as  canards.  Unlike  actual  tunas  which  can  articulate 
their  pectoral  fins  in  pitch  and  sweep  angle,  the  VCUUV  pectoral  fins 
will  only  pitch,  controlled  by  torquemotors  located  inside  the  pressure 
hull.  For  simplicity,  the  pectoral  fin  shapes  are  swept  and  tapered  NACA 
0015  sections  roughly  matching  the  chord  and  span  of  actual  tuna  fins. 
Because  of  the  large  metacentric  height  of  the  vehicle,  pectoral  fin  lift 
will  cause  little  change  in  the  vehicle  attitude  which  allows  us  to  control 
both  depth  and  buoyancy  with  the  same  actuation  system. 

Two  rigid  keel  like  fins  (dorsal  and  anal)  attached  just  aft  of  the 
hull/tail  interface  are  included  for  stability  and  are  constructed  in  the 
same  manner  as  the  caudal  fin.  The  remaining  fins  are  not  included  in 
the  VCUUV  as  they  are  not  critical  in  straight  swimming  and 
maneuvering:  two  forward  ventral  fins,  the  first  dorsal  fin  (may  be 
added  later  for  maneuvering  stability),  and  the  finlets  along  the  tail. 

Electronics  and  control 

At  this  time  the  VCUUV  is  not  intended  to  demonstrate  advanced 
autonomy;  thus,  it  will  initially  operate  in  an  open  loop,  pre-programmed 
capacity  to  demonstrate  simple  swimming  and  turning,  not  sophisticated 
intelligence  such  as  in-flight  trajectory  planning  or  obstacle  avoidance. 
However,  our  system  components  (processor,  guidance  sensors,  etc.) 
have  been  selected  with  an  eye  towards  future  capabilities  in  complex 
missions  and  control. 

The  center  of  the  electronics  system  is  a  PC 104  486  computer 
which  monitors  sensor  input,  vehicle  status,  logs  data,  etc..  The  tail 
actuators  are  controlled  with  a  dedicated  digital  signal  processor  (DSP). 
The  sensor  suite  includes  conventional  underwater  vehicle  sensors 
required  for  autonomous  operation:  inertial  measurements  of  all 
accelerations  and  rates,  depth  (pressure),  heading  (compass),  and 
auxiliary  sensors  for  vehicle  status  (temperature  in  the  hull  and  leak 
detection).  High  bandwidth  sensing  for  linkage  control  (hydraulic 
cylinder  position,  hydraulic  pressure,  motor  speed)  are  directly  input  to 
the  DSP  which  controls  tail  articulation.  In  addition,  hydraulic  force  is 
measured  at  the  point  of  application  so  that  propulsive  efficiency  can  be 
directly  measured. 

Initially,  only  the  tail  linkage  will  be  operated  under  closed  loop 
control.  In  this  configuration,  the  vehicle  will  be  tested  with  a  variety  of 
open  loop  commands  to  characterize  the  propulsor  in  straight  swimming 
and  maneuvering.  System  identification  techniques  will  be  used  to  detail 
the  input-output  relationships  necessary  to  attain  closed  loop  trajectory 
control. 


481 


Electronics  assembly 


Hydraulic  power  unit 


IV.  TECHNICAL  PROGRESS 

At  this  writing,  the  VCUUV  has  completed  system  integration  and 
preliminary  testing.  The  first  swimming  test  in  April,  1998,  was  very 
successful  (Figure  4);  the  vehicle  propelled  itself  forward  in  a  very 
stable  manner  without  yaw,  pitch  or  roll  oscillations. 

Extended  experiments  are  planned  for  Spring  and  Summer,  1998, 
during  which  the  following  specific  studies  will  be  performed: 

•  Straight  swimming  with  the  MIT  Robotuna  self  propelled  optimal 
motion  parameters.  Loads,  power  and  efficiency  of  straight,  steady 
swimming  will  be  quantified.  Results  will  be  compared  to  steady  drag 
power  estimated  by  deceleration  studies  around  the  steady  swimming 
speed. 

•  Sensitivity  study  of  optimal  motion.  Performance  sensitivity  to 
frequency,  angle  of  attack,  propulsive  wave  speed  and  amplitude  of 
motion  will  be  assessed. 

•  Speed  trials  in  straight  swimming.  Stability,  controllability  and 


energetics  will  be  quantified  while  varying  tail  oscillation  frequency 
only. 

•  Maneuvering  studies.  Turn  rate  as  a  function  of  vehicle  speed  will 
be  measured  by  applying  bias  curvatures  to  the  body  during  steady 
swimming.  The  energetic  cost  of  maneuvering  will  be  quantified. 

V.  SUMMARY 

The  Draper  Laboratory  VCUUV  is  the  first  autonomously  operated 
fish-like  UUV  that  is  realistically  sized  for  real  world  missions  and 
payload  and  able  to  move  with  arbitrary  Thunniform  kinematics.  The  fish 
propulsion  paradigm  offers  order  of  magnitude  improvement  in 
maneuvering  capability  which  is  required  for  today’s  challenging  UUV 
missions  in  dynamic,  cluttered  environments.  The  VCUUV  prototype  will 
prove  the  concept  while  serving  as  a  research  testbed.  Lessons  learned 
from  the  VCUUV  can  be  applied  to  new  vehicles  mechanically 
optimized  to  achieve  fish-like  capabilities  in  engineered  vehicles. 

VI.  ACKNOWLEDGMENTS 

This  project  is  funded  internally  by  the  Charles  Stark  Draper 
Laboratory. 

VII.  REFERENCES 

1.  Triantafyllou,  MS  and  Triantafyllou,  GS  (1995),  “An  Efficient 
Swimming  Machine”,  Scientific  American,  March,  1995. 

2.  Blake,  RW,  Chatters,  LM  and  P  Domenici  (1995),  “Turning  radius  of 
yellowfin  tuna  ( Thunnus  albacares)  in  unsteady  swimming  manoeuvres”, 
J.  Fish  Biology ,  v.  46,  pp  536-538. 

3.  Dewar,  H  and  Graham,  JB  (1994),  “Studies  of  tropical  tuna  swimming 
performance  in  a  large  water  tunnel,  Part  III:  Kinematics”,  Journal  of 
Experimental  Biology,  Vol  192,  pp  45-59. 

4.  Anderson,  JM,  Streitlien,  K,  Barrett,  DS  and  MS  Triantafyllou  (1998), 
“Oscillating  Foils  of  High  Propulsive  Efficiency”,  Journal  of  Fluid 
Mechanics ,  Vol  360,  1998. 

5.  Anderson,  JM  (1996),  “Vorticity  Control  for  Efficient  Propulsion”, 

Ph  D.  Thesis,  Massachusetts  Institute  of  Technology/Woods  Hole 
Oceanographic  Institution  Joint  Program. 


Figure  4:  VCUUV  Testing 


482 


6.  Barrett,  DS  (1996),  “Propulsive  efficiency  of  a  flexible  hull 
underwater  vehicle”,  PhD.  Thesis ,  Massachusetts  Institute  of 
Technology . 

7.  Anderson,  JM  and  PA  Kerrebrock,  (1997a),  “The  Vorticity  Control 
Unmanned  Undersea  Vehicle — An  Autonomous  Vehicle  Employing  Fish 
Swimming  Propulsion  and  Maneuvering”,  Proc  l(f  lnt.  Symp  on 
Unmanned  Untethered  Submersible  Technology ,  Durham,  NH,  7-10  Sept, 
1997,  pp  189-195. 

8.  Anderson,  JM,  Kerrebrock,  PA  and  MS  Triantafyllou  (1997b), 
“Concept  Design  of  a  Flexible-Hull  Unmanned  Undersea  Vehicle”, 

Proc.  of  the  7th  lnt.  Offshore  and  Polar  Engineering  Conference , 
Honolulu,  USA,  May  25-30, 1997  (Vol.  II),  pp  82-88. 

9.  Magnuson,  JJ  (1978),  “Locomotion  by  Scombrid  Fishes: 
Hydromechanics,  Morphology  and  Behavior”,  in  Fish  Physiology ,  Vol. 
VII,  Academic  Press,  Inc. 


483 


484 


A  Fast-Starting  and  Maneuvering  Vehicle,  the  ROBOPIKE 


John  Muir  Kumph 

Massachusetts  Institute  of  Technology 
77  Massachusetts  Ave.  Room  48-015 
Cambridge,  MA  02139 
ninjo@mit.edu 

March  20,  1998 


M.S.  Triantafyllou 

Massachusetts  Institute  of  Technology 
77  Massachusetts  Ave.  Room  5-323 
Cambridge,  MA  02139 
mistetri@mit.edu 


ABSTRACT 


We  describe  the  biomimetic  development  of  an  autonomous  flexible-hull  vehicle,  81  cm  in  length,  capable  of  emulating  the 
fast-start  and  rapid  maneuvering  performance  of  live  fish.  The  design  was  based  on:  the  geometrical  body  characteristics  and 
swimming  kinematics  of  a  chain  pickerel  ( Esox  Niger);  principles  of  vorticity  control;  and  experience  and  data  obtained  in  the 
development  and  testing  of  the  RoboTuna.  The  development  of  the  vehicle  required  experimenting  with  novel  actuation  and 
skin  structure  support  devices,  which  resulted  in  a  functional  prototype  capable  of  fish-like  agility. 


1  Introduction 

An  81  cm  long  robotic  fish-like  vehicle  was  developed  to  test  de¬ 
sign  ideas  about  fast-starting  and  rapidly  turning  vehicles  employ¬ 
ing  vorticity  control.  The  design  used  the  process  of  biomimesis 
to  arrive  at  its  hull  shape  and  kinematic  requirements.  The  goal 
of  biomimesis  is  to  use  biological  inspiration  to  engineer  machines 
capable  of  emulating  outstanding  animal  performance.  By  building 
this  vehicle  we  have  identified  the  principal  design  characteristics 
that  give  fish  their  superior  performance  capabilities.  We  will  use 
this  information  to  develop  novel  and  simple  technology  to  equip 
vehicles  with  outstanding  maneuvering  capabilities.  The  design  was 
modelled  after  the  chain  pickerel  ( Esox  Niger),  a  small  pike  closely 
related  to  the  northern  pike  ( Esox  Lucius  ),  which  have  superb 
fast-starting  capabilities  (Harper  &:  Blake  1990).  The  vehicle  (see 
Figure  1)  was  built  and  tested  at  MIT  in  the  Ocean  Engineering 
Testing  Tank  Facility  (Towing  Tank). 

There  has  been  an  increasing  interest  in  the  development  of 
fish-like  vehicles  for  two  reasons.  First,  it  has  now  become  possible 
for  advanced  electromechanical  and  control  technology  to  be  pur¬ 
chased  off-the-shelf,  so  that  the  building  of  a  small,  experimental 
underwater  craft  can  be  undertaken  at  reasonable  cost.  Second, 
there  has  been  a  growing  interest  in  alternative  propulsion  schemes 
for  small  craft  because  conventional  propulsion  and,  especially,  ma¬ 
neuvering  technology  has  reached  a  level  of  maturity  that  does  not 
allow  rapid  progress. 

Observation  of  live  fish  and  cetaceans  reveals  that  they  have 
achieved  high  swimming  performance  by  employing  a  completely 
different  paradigm,  substantially  flexing  their  hull  and  using  rapidly 
moving  fins.  It  is  our  aim  at  the  MIT  Towing  Tank  to  discover  the 
physical  mechanisms  of  fish  swimming,  and  develop  simple  technol¬ 
ogy  to  implement  these  mechanisms  to  improve  vehicle  agility. 

Previous  work  in  the  field  of  fish  hydrodynamics  has  centered  in 
two  areas.  Some  researchers  have  developed  theoretical  models  of 
fish  propulsion  which  offer  insight  into  the  physics  of  fish  swimming 
(Lighthill  1975;  Wu  1961,  1971).  Others  have  studied  the  mechanics 
and  fluid  mechanics  of  live  fish,  to  discover  models  of  fish  locomotion 
(Gray  1968,  Rosen  1963,  Harper  &  Blake  1991). 

Our  research  takes  a  different  approach,  by  constructing  bio- 
mimetically  a  fish-like  robot,  which  allows  a  detailed  study  of  the 
flow  around  a  body  swimming  exactly  like  a  fish;  but  also  allows 
arbitrary  variation  of  the  principal  parameters  to  reverse-engineer 
nature’s  solutions  and  assess  the  sensitivity  and  impact  of  the  pa¬ 
rameters  involved.  Finally,  testing  technological  devices  of  various 
degrees  of  complexity  allows  the  eventual  development  of  simple 
technological  solutions  properly  suited  to  engineering  vehicles,  but 
closely  emulating  the  performance  of  live  organisms. 


Figure  1:  The  robotic  pike  swims  in  the  MIT  towing  tank. 


1.1  Vorticity  Control 

A  maneuvering  streamlined  rigid  hull  vehicle  generates  a  substantial 
drag  wake.  This  occurs  because  the  flow  separates  as  the  angle 
of  attack  between  its  longitudinal  axis  and  the  incoming  velocity 
exceeds  a  certain  value,  first  generating  symmetric  helical  vortices 
and  ultimately  alternatively  shedding  vortices. 

Fast-starting  and  maneuvering  fish  bend  their  body  to  form 
a  curvature  that  travels  along  the  body  length,  thus  generating 
body-bound  vorticity.  This  vorticity  is  shed  just  anterior  to  the 
caudal  peduncle  generating  pairs  of  large-scale  free  vortices,  which 
cause  maneuvering  forces.  To  avoid  generating  drag  wakes,  the 
body  vorticity  must  be  manipulated  by  the  tail  which  switches  each 
shed  vortex  from  one  side  of  the  fish  to  the  other;  hence  shed  vortices 
become  propulsive.  This  is  the  essence  of  vorticity  control  as  applied 
to  maneuvering  (Anderson  1996,  Triantafyllou  et  al.  1996). 

The  body  bending  must  be  asymmetrical  with  respect  to  the 
plane  of  symmetry  of  the  fish  in  order  to  generate  side  forces:  A  C- 
shape  and  an  S-shape  curving  of  the  body  classifies  often- observed 
fish  fast  starts  (Harper  &;  Blake  1990);  the  former  corresponds  to 
mild  fast-starts  and  the  latter  to  rapid  starts,  reaching  peak  accel¬ 
erations  in  excess  of  200  m/s2. 

As  a  first  step  we  decided  to  perform  mild  maneuvers.  Hence, 


485 


the  vehicle  was  designed  to  bend  in  a  C-shape,  travel  the  curvature 
down  the  body  and  then  use  the  tail  to  control  the  forming  eddies. 

2  Design 

When  building  a  biomimetic  robot,  the  intent  is  to  emulate  the  per¬ 
formance  of  live  fish  and  not  to  copy  the  detailed  structures  of  living 
organisms,  which  are  very  complex,  and  not  necessarily  suitable  for 
existing  technology.  One  of  the  basic  principles  that  has  emerged 
from  our  work  so  far,  however,  is  that  embedded  in  the  complexity 
of  living  organisms  are  basic  principles,  the  identification  of  which 
leads  to  emulating  their  performance.  Significant  simplification  of 
the  developed  technology  is  possible  once  these  principles  are  un¬ 
derstood. 

Still,  one  realizes  that  animals  have  evolved  over  millions  of 
years  and  have  developed  materials,  structures  and  control  systems 
that  are  best-suited  for  their  mode  of  operation,  and  which  are  hard 
to  replicate  with  our  present  technology.  Hence  the  simplification 
process  that  will  allow  biomimetic  development  of  fish-like  vehicles 
requires  extensive  work  and  continuous  introduction  of  the  newest 
materials  and  methodologies.  Biotechnology  seems  to  offer  entic¬ 
ing  solutions  in  the  near  future  for  actuation  and  for  building  skin 
structures. 

For  example,  simply  trying  to  copy  the  articulated  wings  of  a 
bird  to  achieve  agile  flight  leaves  out  a  host  of  other  technologies 
of  birds  such  as  adaptive  flight  control,  vision,  and  extremely  high 
power-to- weight  ratio  muscles.  A  successful  biomimesis  of  agile  bird 
flight  may  require  leaps  of  our  technology.  A  more  positive  example 
is  the  successful  biomimesis  of  walking  creatures  (G.  Pratt  1995). 
These  machines  use  biological  inspiration  to  uncover  successful  de¬ 
sign  ideas  grounded  in  classical  physics.  Once  these  design  ideas 
have  become  understood,  they  become  another  possibility  for  the 
design  engineer  to  use  in  his  or  her  quest  to  optimize  any  design. 

By  studying  live  fish,  theoretical  fluid  dynamics,  and  testing  the 
RoboTuna  (D.  Barrett  &  M.  Triantafyllou  1995,  D.  Barrett  1996, 
J.  Anderson  1996)  we  concluded  that  the  outstanding  performance 
of  fish  is  obtained  through  vorticity  control,  achievable  through  their 
body  morphology  and,  especially,  close  control  of  their  kinemat¬ 
ics.  Other  contributing  factors,  such  as  small-scale  skin  control  and 
polymer  injection,  appear  to  be  secondary  compared  to  vorticity 
control. 

^From  the  outset  it  was  our  aim  to  build  a  mechanical  fish  which 
would  have  the  same  shape  and  movements  of  live  fish.  Thus  we 
could  test  various  hypotheses  about  fish  locomotion  repeatably  and 
with  close  attention  to  details  in  the  flow.  In  order  for  the  system 
to  achieve  the  kinematics  of  maneuvering  live  fish  it  is  preferable 
to  implement  a  free-swimming  design,  because  an  external  support 
would  interfere  with  the  dynamics  of  the  robot.  This  posed  novel 
problems  compared  to  the  RoboTuna ,  which  this  paper  addresses. 
All  the  power  actuation  and  control  needed  to  be  placed  on  the 
mechanism.  And  it  was  necessary  to  control  the  depth  and  attitude 
of  the  robot  during  swimming.  The  first  part  of  the  design  revolved 
around  two  central  goals:  to  have  reliable  actuation  and  to  create  a 
flexible  hull  which  could  undulate  in  the  way  fish  do.  Once  the  hull 
and  actuators  were  selected,  performance  was  maximized  with  the 
constraints  that  the  robot  needed  to  be  self-powered  and  neutrally 
buoyant. 

2.1  Hull  Shape  and  Materials 

The  external  shape  of  the  mechanism  is  modelled  after  a  chain  pick¬ 
erel  that  is  56  cm  long.  We  digitized  a  taxidermist’s  model  of  the 
fish  and  corrected  the  computer  model  to  make  it  symmetric  about 
the  vertical  plane  and  geometrically  fair.  This  was  to  correct  for 
errors  in  the  casting  of  the  physical  model.  Inspection  of  live  pike 
shows  that  the  fish  is  indeed  symmetric  and  has  a  faired  body,  ex¬ 
cept  at  the  mouth  where  there  is  a  slight  saddle  shape. 


Figure  2:  First  section  of  the  spiral  wound  spring  be¬ 
fore  assembly  with  the  rest  of  the  mechanism.  There  are 
two  splines  attached  at  the  top  and  bottom  of  the  spring 
which  constrain  this  to  act  like  a  flexure  bearing. 


Figure  3:  Tail  assembly  of  the  robotic  fish  shows  the  spiral 
wound  fiberglass  spring. 

The  vehicle  hull  is  fabricated  from  two  sections  of  fiberglass 
spiral  wound  spring  which  supports  a  skin  of  latex,  lycra,  and  steel 
mesh.  See  Figures  2  and  3  for  the  first  and  second  spiral  spring 
sections.  This  spirally  wound  spring  is  attached  to  splines  made 
of  fiberglass  (first  body  section)  or  delrin  (second  body  section). 
These  splines  act  as  constraints  so  that  the  spirally  wound  springs 
essentially  become  two  in-line  flexure  bearings.  The  machine  inside 
the  hull  pushes  and  pulls  at  the  hull  to  make  it  bend. 

It  was  decided  to  use  a  flooded  hull  design  for  this  robot  be¬ 
cause  of  the  difficulty  in  making  a  reliable  and  accessible  flexible 
sealed  hull.  This  design  decision  created  the  requirement  that  any 
components  in  the  flooded  hull  would  need  to  be  waterproof  or  wa¬ 
ter  compatible.  Because  the  head  of  the  fish  did  not  need  to  flex 
(we  eliminated  the  mouth  capability  in  our  robot),  that  part  of  the 
fish  could  be  made  dry  so  that  electronics  could  easily  be  housed 
there. 

After  the  hull  was  digitized,  the  hull  was  filled  with  mechanisms 
that  make  the  hull  undulate  like  a  fish.  Because  of  the  limitations 
in  motor  technology,  it  was  decided  in  this  first  implementation  to 
try  to  make  the  fish  undulate  in  the  same  shapes  as  live  fish,  but 
at  a  slower  rate,  using  vorticity  control  principles  to  scale  timing 
in  actuation  of  the  kinematics.  This  effectively  relaxes  the  con¬ 
trol  problems  for  implementing  the  fish  kinematics.  Off-the-shelf 


486 


Figure  4:  Assembled  servo  box  doesn’t  show  the  actual 
servo  or  servo  faceplate  but  does  show  the  output  shaft 
and  transmission  for  the  first  body  segment. 

motors,  which  have  the  power  to  achieve  the  extremely  powerful 
movements  of  fish  would  be  too  heavy  for  this  size  vehicle.  Assum¬ 
ing  that  strict  hydrodynamic  scaling  is  achieved,  so  that  drag  forces 
are  prevented  from  building  up,  the  recorded  motions  of  the  present 
vehicle  can  be  scaled  up  to  be  used  in  new  vehicles  equipped  with 
more  powerful  motors. 

2.1.1  Actuation 

We  selected  model  airplane  servo  motors  because  of  their  ease  of 
control,  i.e.  a  pulse  width  modulated  signal  sets  their  command 
position,  and  the  fact  that  they  are  small  in  size  and  light  -weight. 

To  seal  the  servo  motors,  a  face  plate  was  epoxied  to  the  model 
airplane  servo,  and  the  lower  half  of  the  servo  was  sealed  with  epoxy. 
A  box  with  mechanical  feedthroughs,  and  a  sealing  surface  was 
bolted  to  the  faceplate  on  the  servo.  This  arrangement  also  allowed 
for  a  transmission  to  be  housed  in  the  servo  box  (see  Figure  4). 

Three  servos  were  selected  as  the  minimum  number  to  create- 
the  shapes  used  by  fish  in  C-shaped  starts  and  turns.  The  minimum 
size  hull  that  would  fit  the  three  servos  and  associated  equipment 
was  estimated  at  81  cm;  hence  the  computer-generated  hull  shape 
was  scaled  up  from  56  cm  to  81  cm. 

Two  small  servos  were  installed  to  control  pectoral  fins  on  the 
robot  to  actively  control  depth  and  attitude  of  the  vehicle.  We  did 
not  implement  ventral  fins  because  it  appeared  that  they  were  not 
used  in  forward  swimming,  turning,  and  starting  (our  main  areas 
of  study). 

The  articulation  of  the  hull  is  performed  by  two  servos,  while 
the  third  servo  controls  the  pitch  angle  of  the  caudal  fin.  Each  servo 
is  individually  controlled  and  the  transmission  was  selected  so  that 
there  is  no  kinematic  coupling  between  the  servos.  The  transmission 
between  the  servos  and  the  hull  is  specialized  for  each  section  of  the 
fish. 

2.1.2  Transmission 

Our  goal  for  the  articulation  of  the  fish  is  to  bend  the  first  two 
body  segments  and  to  control  the  pitch  on  the  caudal  fin.  The  first 
body  segment  does  not  need  to  flex  more  than  30°,  while  the  second 
body  segment  needed  to  flex  as  much  as  180°  of  arc  length.  These 
requirements  led  to  drastically  different  transmission  and  linkage 
designs. 

For  the  pitch  on  the  caudal  fin  a  simple  revolute  joint  was  used. 
However,  the  hull  near  the  tail  of  the  fish  has  small  available  volume 


Figure  5:  Bulkhead  behind  head  shows  tile  layout  of  the 
pectoral  fin  servos  and  how  they  are  packaged  into  this 
area.  The  servos  are  epoxied  to  their  faceplates  and  the 
faceplates  are  bolted  and  sealed  to  the  servo  housings 
which  also  house  a  mitre  gear  to  redirect  the  servo  shaft’s 
movement  out  of  the  hull  to  the  pectoral  fin  shaft. 


Figure  6:  Servo  assembly  of  robot  before  placement  of 
the  spiral  wound  spring  shows  the  location  of  the  three 
servos  which  drive  the  body. 


487 


Figure  7:  This  construction  picture  of  the  tail  linkage 
shows  the  individual  links  which  are  driven  from  a  single 
servo. 


fiberglass  model  of  the  chain  pickerel  and  drawings  of  the  fish.  The 
cross  section  of  the  fins  was  not  accurately  reproduced  (due  the  the 
section  being  very  thin).  By  inspecting  natural  fish,  it  was  seen  that 
reproducing  the  extremely  thin  fins  of  fish  would  be  very  difficult. 
A  NACA  12  section  was  chosen  because  it  has  been  reported  to  be 
employed  by  many  fish  for  their  fins  and  tails.  The  caudal  fin  is 
rigid  unlike  the  other  fins.  This  is  because  the  caudal  fin,  being  the 
main  propulsor,  was  designed  using  the  experience  from  oscillating 
foils  (Triantafyllou  et.  al.  1996). 

2.3  Power  and  Electronics 

The  head  of  the  fish  is  the  only  large  dry  space  and  contains  elec¬ 
tronics  of  control  and  communication.  A  68332  based  computer  is 
mounted  along  with  a  radio  modem  which  allows  communication 
over  short  distances  through  the  water.  This  allows  one  to  control 
the  robot,  monitor  the  status  of  the  machine,  or  send  new  programs 
to  the  computer  while  it  is  in  the  water  without  a  tether. 

Batteries  are  rubber  encapsulated  NiCd  rechargeables.  There  is 
12V  at  1.5  Ah  of  energy  when  fully  charged.  This  should  be  enough 
for  at  least  1  hour  worth  of  continuous  testing. 


and  it  is  not  possible  to  put  a  motor  near  the  tail.  Also,  because  of 
the  bending  of  the  body  it  was  not  possible  to  use  a  simple  linkage 
running  between  the  tail  and  the  tail  servo.  A  pulley  and  sheave 
mechanism  running  down  the  centerline  of  the  body  was  deemed 
too  complex,  while  hydraulics  at  this  small  scale  are  very  difficult 
to  implement.  Fortunately,  data  from  the  RoboTuna  project  showed 
that  the  amount  of  power  used  by  the  caudal  fin  joint  is  very  low  in 
contrast  to  the  other  joints.  This  meant  that  a  relatively  inefficient 
transimission  for  this  joint  would  not  adversely  affect  the  overall 
system  efficiency.  A  simple  pull-pull  cable  mechanism  utilizing  cable 
housing  (such  as  employed  in  bicycle  brakes)  was  selected  for  this 
axis.  This  let  us  put  the  servo  for  the  caudal  fin  far  from  the  tail 
area.  A  waterproofed  servo  with  a  dual  rotary  to  linear  conversion 
supplies  the  motion  for  this  pull-pull  cable  motion. 

For  the  second  body  segment,  the  one  requiring  up  to  180°  of 
flexing,  a  more  complex  system  was  required.  It  was  important  to 
control  the  shape  of  the  tail,  so  a  simple  haptic  mechanism,  mod¬ 
elled  after  a  human  finger,  could  not  be  used.  Instead  a  mechanism 
which  bent  into  a  tight  arc  was  needed.  A  series  of  joints  was  chosen 
to  approximate  the  arc,  and  one  motor  was  needed  to  control  all 
the  joints.  If  one  ran  separate  linkages  or  cables  to  each  joint,  the 
mechanism  would  be  very  complex.  In  order  to  simplify  this  section 
of  the  fish,  each  joint  was  coupled  to  the  previous  joint’s  motion. 
One  difficulty  of  this  mechanism  is  that  since  one  is  superimposing 
joint  on  top  of  joint,  the  cumulative  error  (backlash  and/or  com¬ 
pliance)  can  become  large.  The  other  difficulty  of  this  mechanism 
is  that  one  motor  is  controlling  a  long  segment  of  the  fish,  so  there 
is  a  lot  of  amplification  of  the  motion,  resulting  in  a  small  amount 
of  available  force  at  the  end  of  the  linkage.  A  waterproofed  rotary 
servo  supplies  the  motion  for  this  series  of  joints.  A  series  of  cables 
is  used  to  transmit  the  motion  from  joint  to  joint. 

The  first  body  segment  requires  only  30°  of  flexing.  This  can  be 
done  by  bending  a  spline  with  an  applied  moment  at  the  end  of  the 
spline.  This  is  achieved  with  a  linear  contraction  and  expansion  of 
a  linkage  running  between  the  end  of  the  segment.  A  waterproofed 
servo  with  a  rotary  to  linear  conversion  is  used  for  this  segment. 

To  control  the  pectoral  fins  two  small  model  airplane  servos 
were  used.  For  packaging  reasons,  it  was  necessary  to  use  a  mitre 
gear  box  to  control  the  shafts  of  the  pectoral  fins. 

2.2  Fins 

The  pectoral  fins,  dorsal,  and  anal  fins  are  all  made  from  RTV 
silicone  rubber.  The  rubber  used  is  rated  at  shore  A  40,  making 
these  fins  flexible.  The  profile  of  these  fins  was  obtained  from  the 


2.4  Stability 

When  observing  live  fish,  it  is  not  obvious  whether  the  system  is 
open-loop  stable,  or  whether  the  fish  is  using  some  form  of  control 
to  keep  its  body  to  swimming  straight.  The  lack  of  horizontal  sta¬ 
bilizing  fins  in  the  rear  of  the  fish’s  body  suggests  that  the  depth 
control  of  the  fish  is  open-loop  unstable.  Our  robot  will  have  the 
same  hydrodynamic  stability  characteristics  of  the  chain  pickerel 
because  it  has  the  same  morphology  and  kinematics. 

Because  of  the  articulation  of  the  hull,  certain  unusual  weight 
distribution  requirements  exist.  The  hull  of  the  robot  changes  shape 
as  it  oscillates,  hence  it  is  important  to  distribute  the  weight  inside 
so  that  the  articulation  of  the  vehicle  does  not  create  an  adverse 
separation  of  the  center  of  mass  (C.O.M.)  and  center  of  buoyancy 
(C.O.B.)  This  requires  that  any  component  with  a  different  density 
than  water  have  enough  space  near  it  to  allow  it  to  be  trimmed  and 
become  neutrally  buoyant. 

The  pectoral  fins  of  a  fish  act  like  the  hydroplanes  on  a  subma¬ 
rine  controlling  dive  rate,  but  without  the  rear  stabilizing  fins  of  a 
submarine  there  is  little  counter  moment  to  stop  the  rate  of  pitch¬ 
ing.  If  the  C.O.M.  and  C.O.B.  are  separated,  then  there  is  a  small 
moment  against  the  pectoral  fins.  However,  testing  showed  that 
separating  the  C.O.M.  and  C.O.B.,  such  as  is  done  in  traditional 
marine  vehicles,  has  undesirable  consequences. 

The  symmetric  caudal  fin  has  a  center  of  lift  in  the  middle  of  the 
fin.  If  the  C.O.M.  is  not  horizontal  with  the  center  of  lift  of  the  foil, 
then  a  rolling  moment  is  placed  on  the  robot.  Pectoral,  dorsal,  and 
anal  fins  will  act  as  roll  stabilizers  in  this  configuration,  but  this  roll 
moment  is  a  side  effect  of  making  the  vehicle  passively  stable.  We 
want  to  minimize  the  roll  moment  while  keeping  the  robot  passively 
stable.  However,  with  the  robot  barely  stable  (statically),  the  pec¬ 
toral  fins  will  make  the  fish  dynamically  unstable  in  pitch  because 
of  the  lack  of  stabilizing  rear  fins.  The  simplest  solution  for  initial 
testing  is  to  eliminate  depth  control  by  making  the  robot  slightly 
positively  buoyant.  This  constrains  the  mechanism  to  operate  near 
the  free  surface. 

3  Control 

The  control  of  the  mechanical  fish  implemented  for  the  series  of 
tests  presented  here  consists  of  an  open-loop  series  of  waveforms. 
To  avoid  having  to  control  depth,  the  tests  presented  here  were  all 
performed  with  the  fish  made  slightly  buoyant. 

The  model  airplane  servos  have  an  on-board  proportional  con¬ 
troller  which  allows  us  to  send  command  positions  to  the  actuators. 


488 


The  onboard  computer  sends  position  commands  to  the  servos  and 
the  servos  respond  by  flexing  the  body.  By  sending  a  traveling  wave 
profile  down  the  body,  the  robotic  body  undulates  and  swims  for¬ 
ward.  For  fast-starting,  one  can  simply  send  a  traveling  wave  down 
the  body,  just  as  in  regular  swimming.  Vorticity  control  princi¬ 
ples,  however,  supported  by  literature  on  fish  kinematics  (Harper  & 
Blake  1990)  suggests  a  far  more  effective  way:  By  bending  the  body 
into  a  C-shape  and  then  traveling  this  shape  downstream  along  the 
body  while  springing  back  out  into  a  normal  swimming  motion,  a 
rapid  start  can  be  achieved.  This  C-shape  start  is  depicted  in  Fig¬ 
ure  8.  For  turning,  the  normal  forward  swimming  undulation  is 
interrupted  by  a  similar  large  flexing  of  the  body. 

The  ”C”  shaped  start  utilizes  vorticity  control  to  obtain  a  high 
starting  thrust.  Looking  at  Figure  8  one  sees  the  body  and  hydro¬ 
kinematics  of  this  start.  In  frames  1-4  the  fish  winds  up  its  body 
and  creates  a  vortex  ultimately  controlled  by  its  tail.  In  frame  5  the 
fish  sheds  this  vortex  as  its  tail  reverses  direction.  And  in  frames 
6-8  creates  a  vortex  of  opposite  sign,  thus  finishing  the  creation  of 
a  large  thrust  dipole. 

4  Testing 


Testing  was  performed  initially  at  the  Towing  Tank  and  then  later 
at  IS  Robotics,  Somerville  MA.  The  first  tests  revolved  around  get¬ 
ting  the  robot  to  swim  in  a  straight  line.  These  first  tests  were 
performed  without  the  pectoral  fins  installed.  The  robot  was  made 
slightly  buoyant  so  that  it  was  constrained  near  the  free  surface. 
And  example  of  such  testing  is  shown  in  Figure  9.  Swimming  for¬ 
ward  was  shown  to  be  stable  in  yaw. 

The  next  series  of  tests  was  performed  to  investigate  the  starting 
and  turning  performance  of  the  machine.  Testing  revealed  that  the 
“C”  shaped  start  used  by  the  northern  pike  and  trout  (see  Harper 
&  Blake  1990)  was  much  more  effective  at  accelerating  the  machine 
to  full  speed  than  simply  starting  the  forward  swimming  motion. 
Acceleration  was  increased  by  an  order  of  magnitude  over  starting 
motion  with  the  steady  state  traveling  wave  profile. 

While  this  series  of  tests  did  not  measure  performance  precisely 
it  did  prove  the  concept  of  flapping  foil  propulsion.  The  maximum 
forward  speed  of  this  system  was  1  m/s  or  slightly  more  than  a  body 
length  per  second.  The  testing  also  showed  that  articulation  of  the 
main  propulsor  has  serious  benefits  for  fast  start  performance. 

For  turning,  our  tests  showed  that  the  turning  was  much  higher 
performance  than  if  we  just  used  the  caudal  fin  as  a  rudder.  How¬ 
ever,  testing  continued  to  show  that  the  skin  was  too  stiff  for  turn¬ 
ing  maneuvers  as  tight  as  a  pike.  We  are  currently  implementing  a 
much  more  flexible  skin  which  will  not  constrain  the  body’s  flexing 
as  much. 

5  Future  Work 

We  have  planned  extensive  testing  of  the  vehicle  involving  quanti¬ 
tative  measures  of  the  performance  of  the  vehicle,  as  well  as  flow 
visualization.  Since  the  essence  of  success  is  the  formation  of  body- 
bound  vortices  and  their  ultimate  control  by  the  tail,  flow  visual¬ 
ization  using  digital  particle  image  velocimetry  (DPIV)  is  the  tool 
of  choice  to  optimize  vehicle  performance. 

Next,  stronger  motors  and  a  more  compliant  skin  will  be  in¬ 
stalled  to  allow  for  faster  maneuvers.  A  second  set  of  actuators, 
designed  for  rapid  delivery  of  power  will  also  be  implemented  to 
allow  for  very  rapid  maneuvering.  This  will  parallel  the  use  in  live 
fish  of  red  muscle  for  long  periods  of  slow  swimming,  versus  using 
white  muscle  for  short  periods  of  burst  activity. 

More  important  to  the  performance  of  the  vehicle  than  better 
motors  and  more  compliant  skin,  is  the  optimization  of  swimming, 
turning,  and  starting.  Since  we  have  built  a  system  with  many 
parameters, optimizing  the  performance  of  this  machine  will  require 
a  strategic  search  of  the  possibilities.  This  kind  of  strategic  search 


Figure  8:  Sequence  of  pictures  of  major  vorticity  as  fish 
executes  C  shaped  start. 


Figure  9:  Testing  swimming  performance  at  the  MIT 
Towing  Tank. 


489 


was  also  used  on  RoboTuna  to  determine  the  best  forward  swimming 
parameters. 

Additionally,  this  vehicle  will  be  a  testbed  for  miniature  un¬ 
manned  underwater  vehicle  technology.  One  of  the  driving  thrusts 
for  this  research  is  the  desire  to  make  small  highly  capable  UUV’s 
and  so  a  natural  progression  of  this  research  is  to  make  it  more 
autonomous. 

ACKNOWLEDGMENTS 

Financial  support  of  the  Office  of  Naval  Research  under  con¬ 
tracts  N00014-96-C-0328  (subcontract  to  IS  Robotics)  monitored 
by  T.  McMullen,  and  N00014-96-1-1141  monitored  by  P.  Purteil, 
T.  McMullen  &:  J.  Fein;  the  Sea  Grant  Program  under  Grant  Num¬ 
ber  NA46RG0434;  and  Draper  Laboratory  IR&D  funding,  is  grate¬ 
fully  acknowledged. 

6  References 

1.  Aleev  Y.,  1977,  “Nekton”,  Publisher:  Junk,  The  Hague. 

2.  Anderson  J.M.,  1996,  “Vortex  Control  for  Efficient  Propul¬ 
sion”,  PhD  Thesis ,  Joint  Program,  Massachusetts  Institute 
of  Technology  &;  Woods  Hole  Oceanographic  Institution. 

3.  D.S.  Barrett  &  M.S.  Triantafyllou,  “The  design  of  a  flex¬ 
ible  hull  undersea  vehicle  propelled  by  an  oscillating  foil”, 
9th  International  Symposium  on  Unmanned  Untethered  Sub¬ 
mersible  Technology ,  September  1995. 

4.  D.S.  Barrett,  1996,  “Forces  and  efficiency  of  a  flexible  hull 
vehicle”,  PhD  Thesis ,  Massachusetts  Institute  of  Technology. 

5.  Bennett  M.B.,  Ker  R.F.,  Alexander  R.M.,  1987,  "Elastic 
properties  of  structures  in  the  tails  of  cetaceans  (phocaena 
and  lagenorhynchus)  and  their  effect  on  the  energy  cost  of 
swimming”,  J.  Zoology,  211,  pp.  177-192. 

6.  Domenici  P.  &:  Blake  R.W.,  1997,  ”The  kinematics  and  per¬ 
formance  of  fish  fast-start  swimming”,  J.  exp.  Bio.,  200, 
1165-1178. 

7.  Gray  J.,  1968,  “Animal  Locomotion”,  Weidenfeld  Sz  Nicol- 
son,  London. 

8.  Harper  D.G.  and  Blake  R.W.,  1990,  ” Fast-start  Performance 
of  Rainbow  Trout  (Salmo  gairdneri)  and  Northern  Pike  (Esox 
Lucius)”,  Journal  of  Experimental  Biology,  Vol.  150,  pp. 
321-342. 

9.  Harper  D.G.  and  Blake  R.W.,  1991,  "Prey  capture  and  the 
fast-start  performance  of  northern  pike  ( Esox  Lucius)”,  J. 
exp.  Biol.,  155,  175-192. 

10.  Lighthill  J.,  1975,  Mathematical  Biofluiddynamics,  SIAM, 
Philadelphia. 

11.  Rosen  M.  W.,  1963,  "Flow  Visualization  Experiments  with 
a  Dolphin”,  U.S.  Naval  Ordnance  Test  Station,  NAVWEPS 
Report  8062,  NOTS  TP  3065,  China  Lake,  California. 

12.  M.S.  Triantafyllou,  D.S.  Barrett,  D.K.P.  Yue,  J.M.  Ander¬ 
son,  M.A.  Grosenbaugh,  K.  Streitlien  &  G.S.  Triantafyllou, 
1996,  “A  New  Paradigm  of  Propulsion  and  Maneuvering  for 
Marine  Vehicles”  Transactions  of  the  Society  of  Naval  Ar¬ 
chitects  and  Marine  Engineers ,  104,  81-100. 

13.  Wu  T.Y.,  1961,  “Swimming  of  a  waving  plate”,  Journal  of 
Fluid  Mechanics ,  10,  321-344. 


14.  Wu  T.Y.,  1971,  “Hydromechanics  of  swimming  propulsion. 
Part  1.  Swimming  of  a  two  dimensional  flexible  plate  at 
variable  forward  speeds  in  an  inviscid  fluid”,  Journal  of  Fluid 
Mechanics ,  46,  337-355. 


490 


INDEX  BY  AUTHOR 


Adrian,  R.  -  University  of  Illinois  at  Urbana-Champaign . . .  33 

Amfilokhiev,  W.  -  Saint  Petersburg  State  Marine  Technical  University. . 305 

Amonlirdviman,  K.  -  Massachusetts  Institute  of  Technology .  135 

Anderson,  J.  -  Charles  Stark  Draper  Laboratory . 479 

Babenko,  V.  -  National  Academy  of  Sciences,  Kiev .  113,  319, 

451,453 

Balachandar,  S.  -  University  of  Illinois  at  Urbana-Champaign . 33 

Bandopadhyay,  P.  -  Naval  Undersea  Warfare  Center  Division  Newport .  373,  457 

Bannasch,  R.  -  Technische  Universitdt  Berlin . 435 

Barrett,  D.  -  Massachusetts  Institute  of  Technology .  463 

Benilov,  A.  -  Stevens  Institute  of  Technology. . 205 

Biringen,  S.  -  University  of  Colorado  at  Boulder .  413 

Bogdevich,  V.  -  Siberian  Branch  of  the  Russian  Academy  of  Sciences .  327 

Botton,  V.  -  PAMIR  Team  LEG  I .  389 

Branover,  H.  -  Ben-Gurion  University  of  the  Negev .  109,  379 

Breidenthal,  R.  -  University  of  Washington .  127 

Breuer,  K.  -  Massachusetts  Institute  of  Technology .  135 

Brown,  G.  -  Princeton  University .  369 

Bushnell,  D.  -  NASA  -  Langley  Research  Center .  7 

Cantwell,  B.  -  Stanford  University . . . 29 

Carpenter,  P.  -  University  of  Warwick .  185 

Casper,  J.  -  Newport  News  Shipbuilding. ; .  53 

Castano,  J.  -  Naval  Undersea  Warfare  Center  Division  Newport .  335,  373,  457 

Chkhetiana,  0.  -  Ben-Gurion  University  of  the  Negev. .  109 

Choi,  K.S.  -  University  of  Nottingham .  13,  229 

Clayton,  B.  -  University  of  Nottingham .  229 

Cotel,  A.  -  University  of  Manitoba. .  127 

Crawford,  C.  -  Brown  University .  99,  407 

Dahlburg,  R.  -  Naval  Research  Laboratory .  131 

Dhanak,  M.  -  Florida  Atlantic  University . , .  237 

Dohring,  C.  -  German  Armed  Forces  University . . 471 

Du,  Y.  -  Brown  University .  407 

Eidelman,  A.  -  Ben-Gurion  University  of  the  Negev .  109,  379 

Fan,  X.  -  Princeton  University .  369 


491 


Fein,  J.  -  Office  of  Naval  Research . 

Fey,  U.  -MHD  Dept.,  Forschungszentrum  Rossendorf. .  395 

Fish,  F.  -  West  Chester  University .  443 

Fitzgerald,  E.  -  The  Johns  Hopkins  University .  211 

Fitzgerald,  J.  -  Kildare  Corporation .  211,215 

Forestier,  B.  -  I.RP.H.E.,  France .  83 

Gad-el -Hak,  M.  -  University  of  Notre  Dame .  197 

Gasljevic,  K.  -  University  of  California  at  Santa  Barbara .  281 

Gerbeth,  G.  -  MHD  Dept.,  Forschungszentrum  Rossendorf . .  395 

Giovannelli,  G.  -  I.RP.H.E.,  France .  83 

Golbraikh,  E.  -  Ben-Gurion  University  of  the  Negev .  109,  379 

Grosenbaugh,  M.  -  Woods  Hole  Oceanographic  Institution .  463 

Guin,  M.  -  The  Johns  Hopkins  University .  313 

Handler,  R.  -  Naval  Research  Laboratory. .  131 

Hanson,  J.  -  The  Johns  Hopkins  University .  163 

Holliday,  D.  -  Tracor  Aerospace .  149 

Hover,  F.  -  Massachusetts  Institute  of  Technology .  463 

Hoyer,  K.  -  University  of  California  at  Santa  Barbara .  281 

Hoyt,  J.W.  -  San  Diego  State  University .  1 

Ivanyuta,  Y .  -  A. N.  Krylov  Central  Research  Institute .  295 

Kamiadakis,  G.  -  Brown  University .  99,  407 

Kato,  H.  -  The  University  of  Tokyo .  313 

Kodama,  Y.  -  Ship  Research  Institute,  Tokyo .  331 

Koryenna,  L.  -  Institute  of  Hydromechanics  of  Ukrainian  National  Academy  of  Sciences .  257 

Kovach,  B.  -  Florida  Institute  of  Technology .  169 

Kowalski,  T.  -  University  of  Rhode  Island .  289 

Kulik,  V.  -  Russian  Academy  of  Sciences,  Novosibirsk. .  299 

Kumph,  J.  -  Massachusetts  Institute  of  Technology .  485 

Kwa,  T.  -  Tao  Systems,  Inc .  53 

Lai,  J.  -  Australian  Defence  Force  Academy . .  471 

LaTorre,  R.  -  University  of  New  Orleans .  319 

Lielausis,  O.  -  Institute  of  Physics  Riga .  395 

Lin,  Z.  -  The  Ohio  State  University .  277 

Madigosky,  W.  -  A&T,  Inc .  219 

Maltzev,  L.  -  Siberian  Branch  of  the  Russian  Academy  of  Sciences .  327 

Maluga,  A.  -  Siberian  Branch  of  the  Russian  Academy  of  Sciences .  327 

Mangalam,  S.  -  Tao  Systems,  Inc .  53 

Marmanis,  H.  -  Brown  University .  99 

Martin,  J.  -  Kildare  Corporation .  215 

Matthys,  E.  -  University  of  California  at  Santa  Barbara .  281 


492 


Mazaev,  K.  -  Saint  Petersburg  State  Marine  Technical  University . 305 

McGillis,  W.  -  Woods  Hole  Oceanographic  Institution . 463 

Meir,  A.  -  Auburn  University. . 401 

Meng,  J.  -  Naval  Undersea  Warfare  Center  Division  Newport. .  341,  359 

Merkulov,  V.  -  Siberian  Branch  of  the  Russian  Academy  of  Sciences .  263,  385 

Mochizuki,  S.  -  Yamaguchi  University. .  121 

Modert,  E.  -  Kildare  Corporation . 215 

Moghadam,  H.  -  Newport  News  Shipbuilding. . 53 

Moiseev,  S.,  -  Space  Research  Institute,  Moscow .  109,  379 

Mutschke,  G.  -  MHD  Dept.,  Forschungszentrum  Rossendorf. . . . 395 

Myska,  J.  -  Czech  Academy  of  Sciences . 277 

Nedderman,  W.  -  Naval  Undersea  Warfare  Center  Division  Newport .  373,457 

Nigon,  R.  -  Naval  Surface  Warfare  Center,  Car  derock  Division . .  53 

O’Sullivan,  P.  -  University  of  Colorado  at  Boulder . 413 

Osaka,  H.  -  Yamaguchi  University .  121 

Pfouts,  R.  -  Tao  Systems,  Inc .  53 

Philips,  R.  -  Naval  Undersea  Warfare  Center  Division  Newport . 335 

Platacis,  E.  -  Institute  of  Physics  Riga .  395 

Platzer,  M.  -  U.S.  Naval  Postgraduate  School . 471 

Pognant,  M.  -  MS  L.A.I.A.T.  -  Universite  de  Toulon . .  83 

Posdziech,  O.  -  Inst.  Aerospace  Eng.,  TU Dresden . 395 

Progrebnyak,  V.  -  Ecological  Center  of  Scientific  and  Applied  Researches . 295 

Rathnasingham,  R.  -  Massachusetts  Institute  of  Technology . . .  135 

Riahi,  D.  -  University  of  Illinois  at  Urbana-Champaign. . 225 

Rivir,  R.  -  Wright-Patterson  Airforce  Base .  143 

Rossi,  L.  -  PAMIR  Team  LEGI. . 389 

Russell,  S.  -  Naval  Surface  Warfare  Center,  Carderock  Division .  63 

Sandberg,  W.  -  Naval  Research  Laboratory .  131 

Sarma,  G.  -  Tao  Systems,  Inc .  53 

Savchenko,  Y.  -  Institute  of  Hydromechanics  of  Ukrainian  National  Academy  of  Sciences . 249 

Schmidt,  P.  -  Auburn  University. . 401 

Schultz,  M.  -  Florida  Institute  of  Technology .  175 

Semonov,  B.  -  Siberian  Branch,  Russian  Academy  of  Sciences . . .  189,  269 

Semonova,  A.  -  Siberian  Branch,  Russian  Academy  of  Sciences . .  189 

Si,  C.  -  Florida  Atlantic  University . . 237 

Sirovich,  L.  -  Brown  University . . .  131 

Smith,  C,  -  Lehigh  University . 39 

Smits,  A.  -  Princeton  University . .  89 

Snarski,  S.  -  Kohler,  WI . . 419 

Stace,  J.  -  Naval  Undersea  Warfare  Center  Division  Newport.. . .  335 


493 


Swain,  G.  -  Florida  Institute  of  Technology .  155,  169,  175 

Takahashi,  Y.  -  IHI,  Ltd. .  313 

Tardu,  S.  -  Laboratoire  des  Ecoulements  Geophysiques  et  Industriels . 241 

Techet,  A.  -  Massachusetts  Institute  of  Technology . 463 

Thibault,  J.P.  -  PAMIR  Team  LEG I. . 389 

Thivierge,  D.  -  Naval  Undersea  Warfare  Center  Division  Newport .  373,457 

Tolkoff,  S.  -  Massachusetts  Institute  of  Technology .  463 

Triantafyllou,  M.  -Massachusetts  Institute  of  Technology .  463,  485 

Uberall,  H.  -  Catholic  University  of  America. .  219 

Uhlman,  J.  -  Naval  Undersea  Warfare  Center  Division  Newport . 341 

Waleffe,  F.  -  University  of  Wisconsin-Madison .  47 

Wallace,  M.  -  Newport  News  Shipbuilding .  53 

Watanabe,  K.  -  Tokyo  Metropolitan  University. .  19 

Weier,  T.  -  MHD  Dept.,  Forschungszentrum  Rossendorf. . 395 

Wolfgang,  M.  -  Massachusetts  Institute  of  Technology . 463 

Yaremchuk,  A.  -  National  Academy  of  Sciences,  Kiev . 451 

Yue,  D.  -  Massachusetts  Institute  of  Technology . 463 

Yurchenko,  N.  -  National  Academy  of  Sciences,  Kiev. .  143 

Zagarola,  M.  -  Creare,  Inc. . .  89 

Zakharenkov,  M.  -  Central  Aero-Hydrodynamic  Institute .  73 

Zakin,  J.  -  The  Ohio  State  University. .  277 


494